WITH MOLYBDENUM AND TUNGSTEN by
THOMAS CARSON FEARNEY, Jr.
B.S., Michigan Technological University 1973
Submitted in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY at the
Massachusetts Institute of Technology
September 1978
O
Massachusetts Institute of Technology 1978Signature redacted
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Department of Materit s Science and Engineering August 11, 1978
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MASSACHUSETTS INSTITUTEOF TECHNOLOGY
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6
UK3
ABSTRACT
CREEP BEHAVIOR OF BINARY SOLID SOLUTIONS OF NICKEL
WITH MOLYBDENUM AND TUNGSTEN
by
THOMAS CARSON TIEARNEY, Jr.
Submitted to the Department of Materials Science and Engineering on August 11, 1978 in partial fulfillment of the requirements for the
degree of Doctor of Philosophy.
Development of high temperature.alloys for the ever increasing temperatures in gas turbine applications requires new approaches to the problem. This study took the approach of the development of
alternative alloy systems for use in the matrix phase of advanced high temperature alloys. Nickel-molybdenum and nickel-tungsten alloys, as
opposed to nickel-chromium alloys, were examined with respect to their
creep properties as a function of several structural and material parameters. Elastic moduli, stacking fault energies and short range order.parameters were measured as a function of solute content (and temperature for all but the stacking fault energy). These were p combined with literature values of the chemical interdiffusivity, D, and weighted diffusivity, D, to correlate to the measured steady-state creep rates. Semi-empirical formulations for dislocation glide and dislocation climb mechanisms were calculated to give series summation creep rates as a function of temperature and composition. These creep rates were then compared with the measured creep rates at constant stress/modulus
levels.
The results show calculated creep rates in nearly all cases lower than the observed creep rates. In addition, the stress dependence of steady-state creep rate, n, and the activation energy of creep,
Qc,
displayed some very high values for solid solution alloys. Both systems displayed a trend from climb to glide controlled creep with increasing solute content, with the degree of short range order an important
contributor in nickel-molybdenum alloys and solute-solvent size differ-ence the overwhelming contributor in nickel-tungsten alloys.
The differences between measured and calculated creep rates and the high n and Qc values were attributed to oxidation effects in the air tests. Nickel-tungsten alloys displayed n values generally between 5.8 and 7.0 and Qc values greater than 100 kcal/mole for the two most
concentrated alloys. The gap between measured and calculated creep rates was larger than that for the nickel-molybdenum alloys. The latter
overly high n and
Qc
values. These results were explained by dividing
the log a versus log Cs curves into regions of low, intermediate and
high stress. At low stresses, low pressure oxygen permeates the extensive
intercrystalline cracking and causes strengthening of the matrix by
forming a subscale M002 or WO2 dispersion ahead of the crack front. At
intermediate stresses, oxidation reduces the surface energy and
cross-sectional area and thus slightly increases the steady-state creep rate
in air relative to vacuum testing. At high stresses, approaching the
equicohesive break, no effect of oxidation should be evident due to
the very short test times. Thus, at stresses below this approach to an
equivalent curve for air and inert tests, the inert testing should
give steeper slopes and lower stress
dependence of steady-state creep
rate than air testing, with the junction point of the two curves
occurring at a higher creep rate as temperature increases.
The alloys recommended for further investigation were Ni-17.8 a/o Mo
and Ni-12.2 a/o W, with the former preferable for high temperature
strength-to-weight ratio, because of the peaks in modulus and short
range order at this composition.
Thesis Supervisor: Nicholas J. Grant
TABLE OF CONTENTS Chapter Page ABSTRACT 2 LIST OF FIGURES 6 LIST OF TABLES 12 ACKNOWLEDGEMENTS 13 I INTRODUCTION 14 II LITERATURE SURVEY 17
11.1. General Creep Overview 17
11.2. Climb Controlled Creep 21
11.3. Glide Controlled Creep 24
11.3.1. Cottrell Atmospheres 25
11.3.2. Suzuki Stacking Fault Segregation 28
11.3.3. Fisher SRO interaction 29
II.4. Criterion for Crossover 33
11.5. Series Summation of Creep Rates 34 11.6. Grain Size and Environmental Effects 37 11.7. Creep Studies on Ni-W and Ni-Mo 42
11.8. Order Studies 50
11.9. Stacking Fault Studies 52
III PLAN OF WORK 54
IV MATERIALS AND PROCEDURE 58
IV.l. Materials 58
IV.2. Processing 63
IV.3. Creep Rupture Testing 67
TABLE OF CONTENTS (Cont'd.)
Chapter Page
IV.5. Dynamic Modulus Testing 72
IV.6. Transmission Electron Microscopy 75
IV.7. X-ray Diffuse Scattering 78
IV.8. Optical Microscopy 81
IV.9. Miscellaneous 82
V RESULTS 84
V.1. Elastic Modulus Results 84
V.2. Stacking Fault Energy Determination 88
V.3. Short Range Order Coefficients 101
V.4. Tensile Results 116
V.5. Creep Rupture Results 123
V.6. Diffusion Coefficients 155
V.7. . Miscellaneous Literature Values 158
VI DISCUSSION 161
VI.l. Creep Mechanisms in the Absence of Oxidation 161 VI.2. Oxidation and Other Surface Effects 172
VII SUMMARY AND CONCLUSIONS 184
VIII SUGGESTIONS FOR FURTHER WORK 187
IX BIBLIOGRAPHY 189
APPENDIX A 196
APPENDIX B 201
APPENDIX C 203
LIST OF FIGURES
Figure Page
1 ormalized creep rate vs. stress, from reference (3) 19 2 Short range order effect on stress-strain behavior 32 3 Graphical display of climb to glide transition as 35
per reference (29)
4 Deformation mechanism map for a solid solution alloy 39 5 Creep strength vs. atomic percent solute, from (1) 43 6 Contributions of Eqn. 2.01 parameters to iS, Ref. (42) 47
7 Nickel-molybdenum phase diagram 61
8 Nickel-tungsten phase diagram 62
9a Standard one half size round tensile specimen 68 9b Flat addition to the above for grain boundary 68
sliding measurements
lOa Pulse-echo modulus set-up 74
lOb Oscilloscope representation of sample echoes 74 11 Young's and shear moduli as a function of solute 85
content
12 Thermal expansion coefficient vs. percent solute 87
13 Lattice parameter at room temperature 89
14 a. Alloy M-178 bright field TEM micrograph @ 190,OOOX 91 b. Alloy M-178 weak beam TEM micrograph @ 190,OOOX 91
LIST OF FIGURES (Cont'd.)
a. Alloy W-134 bright field TEM micrograph @ 240,OOOX
b. Alloy W-134 weak beam TEM micrograph @ 240,OOOX c. Alloy W-134 diffraction pattern
Stacking fault energy vs. atomic percent solute Preliminary determination of y/Gb for alloys not
tested, by correlation of known y/Gb to stacking fault density, a.
Plot of In y/y against c 2/(1+c)2 where c -X B/(XB)
max
Alloy M-78 rolled 15% CW, at 45,750X, TEN photo Alloy M-178 rolled 15% CW, at 45,750X, TEM photo Alloy W-122 rolled 15% CW, at 64,500X, TEM photo Alloy M-156, as homogenized, at
Alloy M-78 quenched from 982*C Alloy M-78 quenched from 815*C Alloy M-125 quenched from 982*C Alloy M-125 Alloy M-125 Alloy M-156 Alloy M-156 Alloy M-156 Alloy M-178 Alloy M-178 Alloy M-212 Alloy M-212 quenched quenched quenched quenched quenched quenched quenched quenched quenched from 899*C from 8150C from 9820C from 899*C from 815*C from 982*C from 8990C 54,00OX, (1255*K), (10880K), (1255*K), (11720K), (1088*K), (1255*K), (11720K), (1088*K), (1255*K), (1172*K), TEM photo 10 X-ray results 10; X-ray results 102 X-ray results 103 X-ray results 103 X-ray results 104 X-ray results 104 X-ray results 105 X-ray results 105 X-ray results 106 X-ray results 106 )
from 1038*C (1311*K), X-ray resultsl07
from 982*C (1255*K), X-ray results 107
7 Figure 15 16 17 18 19a 19b 20a Page 92 92 92 94 95 97 99 99 100 20b 21a 21b 22a 22b 22c 23a 23b 23c 24a 24b 25a 25b
LIST OF FIGURES (Cont'd.) Figure 26a 26b 27a 27b 27c 28a 28b 28c 29a 29b 29c Page from 1093*C (1366*K), X-ray results 108 from 1038*C (1311*K), X-ray results 108 from 8150C (1088*K), X-ray results Alloy M-234 quenched Alloy M-234 quenched Alloy W-134 quenched Alloy W-134 quenched Alloy W-134 quenched Alloy W-122 quenched Alloy W-122 quenched Alloy W-122 quenched Alloy'W-100 quenched Alloy W-100 quenched
Alloy W-100 quenched from 982*C Short range order parameter vs. including the curve for (o )
Tensile strength values at room
solution treated (11720K), (1255*K), (1088*K), (1172*K), (1255*K), (1088*K), (1172*K), (12550K), X-ray results X-ray results X-ray results X-ray results X-ray results X-ray results X-ray results X-ray results
solute content,
temperature, as
109 109 110 110 111 111 112 112 113 117 118 124 125 Alloy W-100 at 899*C (1172*K) and 6,000 psi(41.37 MPa). Decreasing primary creep rate Alloy W-134 at 899*C (1172*K) and 15,000 psi
(103.4 MPa). Double creep curve.
Alloy M-234 at 1038*C (13110K) and 13,000 psi (89.64 MPa). Inverse transient creep.
Alloy M-156 at 8150C (1088*K) and 16,000 psi (110.32 MPa). Negative creep
Ni-Mo and Ni-W at 8150
C (1088*K), log a vs. log &s
126 127 129 from 8990C from 982*C from 8150C from 899*C from 982*C from 8150C from 8990C
30
31 32 33 3435
36LIST OF FIGURES (Cont'd.)
Figure Page
37 Ni-Mo alloys, log a vs. log 1 at 899*C (1172*K) 130 38 Ni-W alloys, log a vs. log &s at 899*C (1172*K) 131
39 Ni-Mo alloys, log a vs. log ta at 982*C (1255*K) 132
40 Ni-W alloys, log a vs. log ts at 982*C (1255*K) 133
41 Alloys M-212 and M-234 at 1038*C (13110K) and 134
1093*C (1366*K), log a vs. log tS
42 Stress exponent, n, as a function of solute 136 content and temperature
43 Log a vs. log tr curves for Ni-W alloys at 899*C 138
(1172*K)
44 Ni-Mo alloys - log a vs log tr at 9820C (12550K) 139
45 Alloy W-100 tested at 982*C (1255*K) and 7,000 psi 142
(tr-0.8 hrs.). Unetched. (a) Magnification 100X,
(b) Magnification 500X
46 Alloy W-134 tested at 899*C (1172*K) and 10,000 psi 143 (tr-ll.8 hrs.). Magnification 50OX. (a) Unetched,
(b) Etched.
47 Alloy M-156 tested at 982*C (12550K), (a) Magnification 145 50aK for 4,100 psi (tr=26 .3 hrs.); (b) and (c)
Mag-nification 160X for stress of 3,300 psi. Etched. Stress axis in (b) is horizontal.
48 Stress for one hour life vs. atomic percent solute, '148 including the solubility limits at the respective
LIST OF FIGURES (Cont'd.)
Figure Page
49 Stress for one hundred hour life vs. atomic 149
percent solute, including the solubility limits at the respective temperatures.
50 Steady-state creep rate vs. atomic percent Nb, 151 measured.
51 Steady-state creep rate vs. atomic7ZW,measured. 152 52 Alloy W-134 grain boundary sliding marker at 100 X 154
magnification. Etched. Stress axis vertical.
53 Chemical interdiffusivity vs. atomic percent solute. 156
54 Thermodynamic factor, 1 + 3knyB/atnXB, vs. atomic 157 percent solute.
55 Weighted diffusivity vs. atomic percent solute 159 56 Theoretical and experimental creep rates of 167
the Ni-Mo system, showing the poorer fit at low solute content levels and generally low theoretical values at higher stress/modulus ratios.
57 Theoretical and experimental creep rates of Ni-W 168 alloys, showing the wide gap between the two, which
increases with a/G ratio
58 Calculated creep rates for climb and glide mechanisms 170 in Ni-Mo alloys, assuming A-9xlO. Note the
significant difference in the variations with solute content
LIST OF FIGURES (Cont'd.)
Figure Page
59 Experimental normalized creep rate versus the 173 magnitude of 't, with least squares lines of slopes:
Ni-W--2.76. Ni-Mo--2.27.
60 (a) Alloy M-78 tested at 982*C (1255*K) and 181
2,400 psi (16.6 HPa), magnified 80X; (b) Alloy M-234 tested at 1038*C (1311*K) and 4,100 psi (28.3 MPa) magnified 500X.
61 The effect of environment on the slope of the log a 183 vs. log i8 curve, showing the position of the junction
point relative to the chosen values of a/G for three
LIST OF TABLES
Table Page
1 Stress for One Hundred Hour Life for Several Nickel 45 Solid Solutions.
2 Composition of Alloys 59
3 Impurity Concentrations, w /o 60
4 Solidus, Liquidus Temperatures and T/TM Ranges 64
5 Homogenization Times and Resultant Grain Sizes 66 6 Quench Temperatures for X-ray Scattering 79 7 Measured Density as a Function of Solute Content 86 8 Calculation of Stacking Fault Energies from Aobserved 90
9 X-ray Order and Size Effect Parameters 115
10 Elevated Temperature Short Time Mechanical Properties 121 11 Stress Exponent, n, and Activation Energy,
Qc
135for Creep Tests
12 Steady State Creep Rates as a Function of Atomic 150 Percent Solute
ACKNOWLEDGEMENTS
The author wishes to acknowledge: the expert guidance and timely encouragement of his thesis advisor, Dr. N. J. Grant, over the course of
this study. His patience has been greatly appreciated.
The faculty members on the thesis review board, Dr. K. C. Russell and Dr. R. E. Ogilvie , for their critical assessment of the manuscript.
The Center for Materials Science and Engineering, for its excellent
testing and microscopy facilities.
The Army Materials and Mechanics Research Center, for assistance in performing the elastic modulus tests.
Climax Molybdenum Co. of Ann Arbor, Michigan, for financial support
for this program.
Thomas Diller, for the figure inking and Robert Allen, for doing the weak beam electron microscopy work.
Linda Sayegh, for typing the preliminary and final manuscript.
The members of the high temperature research group and other friends and roomates, for their encouragement and their assistance in plotting graphs and rough draft typing.
I. INTRODUCTION
In today's energy conscious world, much effort is being channeled into tapping every possible energy source available, including improve-ment of the efficiency of present-day energy conversion systems. Such
systems as the gas turbine and steam turbine have undergone continual modification to upgrade the maximum possible usable energy output for a
given input. One of the ways to facilitate this increased efficiency in gas turbines is to increase the inlet temperature of the gases. This exposes most of the structure of the turbine to higher operating tem-peratures in the already hostile environment of these gases. As a
result, materials used in the construction of turbine or other conversion systems operating on the same thermodynamic principles have had to
keep pace with these increasingly stringent environmental requirements. The traditional candidates for these applications, the superalloys, have nearly reached their temperature limit in present designs. Any further temperature increases will require a shift to new and more exotic materials. New concepts include directionally solidified high melting point eutectics, oxide dispersed superalloys, ceramics, and several new processing sequences designed to rapidly quench superalloy melts with much higher hardener content because of the greater homo-geneity possible at these high cooling rates.
Another approach for improving high temperature properties of superalloys involves the use of alternative alloy systems for the matrix phase. The Ni-Cr system, which is the primary choice for the matrix phase in nickel-base superalloys, provides excellent oxidation
and hot corrosion resistance, but lacks the solid solution strengthening
afforded by other nickel solid solutions. The Ni-Mo and Ni-W systems
are of particular interest here because of the work done by Pelloux1 and Rubin2 on the high temperature strength of these and other potential-ly attractive nickel solid solutions. Their results showed conclusively that molybdenum and tungsten displayed superior creep resistance to chromium and other refractory solutes in solid solution in nickel at 8150C (1088*K). In addition, since chromium imports to the United States depend highly on the political climates of the producing countries, the trend today is to use as little chromium as possible. Thus, although the Ni-Mo and Ni-W systems sacrifice oxidation and hot corrosion
resistance, their strength advantage over the Ni-Cr system coupled.with the market instability for chromium at present make these systems
attractive for further study. This thesis, then, is a study of these two nickel-rich solid solution systems of potential importance for superalloy matrix applications.
Although ultimately developmental, through optimization of com-position and processing sequence, this program is primarily involved with understanding why these systems display this high strength at elevated temperatures. Pelloux1 found that at greater then ten atomic
percent solute and at temperatures of 650*C (923*K ) and 8150C (10880K), molybdenum was a superior strengthener in stress rupture tests as
compared with tungsten and chromium in the solid solution region. This superiority vanishes at 982*C (12 550K) with respect to tungsten as shown by Rubin2 in tests run on the same alloys. A satisfactory
explanation for this phenomenon has still not been formulated. The
study by Pelloux evaluated the relative strengthening effects with
reference to solute atom size, valency and melting points. This study
expands the evaluation to include the stacking fault energy, shear
modulus, diffusion coefficients and the degree of short range order.
This research has attempted to quantify all these possible contributors
to solid solution strengthening in creep and to correlate these results
with the observed creep behavior. It is significant that these binary
solid solution alloys have a constant grain size, are tested at greater
than 0.5 Tm (diffusion-controlled creep), and are tested at stresses
3
within the power law creep regime, as described by Sherby and Burke
The significance is found in the simplicity of this approach to the
complex problem of understanding creep mechanisms and structure-proper.ty
relationships. The problem would otherwise be too broad and complicated
to solve. However, the inclusion of all the physical and structural
parameters is essential to an understanding of the power law creep
behavior of these materials.
II. LITERATURE SURVEY II.l. General -.reep Overview
Of first importance in any study of creep processes at high tem-perature, where extremely heterogeneous deformation takes place, is the definition of the salient materials and environmental parameters. Once these have been defined, the dependence of the creep properties on each parameter should then be categorized into specific bounded regimes over which mechanisms and relationships do not change significantly. The excellent review of Sherby and Burke3 uses this approach in describing
the creep behavior of pure metals, compounds, solid solutions, and two-phase alloys for the entire creep curve, but with specific emphasis on
the secondary creep stage. The two important environmental parameters which are foremost in this review, temperature and stress, will be briefly
described here in relation to important transition points separating regimes defined by different steady-state deformation mechanisms in single phase materials.
The temperature dependence of creep rate is primarily an exponential dependence of the form of the Arrhenius equation, c, - Kexp -Qc (T)/RT. The activation energy is also a function of temperature and reflects changes in the rate-determining mechanisms taking place as the temper-ature varies. At lower tempertemper-atures, dislocation intersection processes and cross slip are rate controlling and hence the activation energy for creep is the activation energy for these processes. Above approximately 0.5 Tm, most pure metals and solid solutions are controlled by a
glide in the presence of viscous drag obstacles or non-conservative motion of jogged screw dislocations. Thus, the activation energy for creep in the region should equal the activation energy for the appropriate diffusion coefficient . It is in this region, which entails the most commercially useful homologous temperature range for materials applica-tions in creep, that this study will focus.
Stress affects the steady-state creep rate in widely varied ways, depending upon its magnitude. The low stress regime, as shown in Fig. 1 for a pure polycrystalline metal at T>O.5Tm, displays a linear relation-ship between steady-state creep rate and stress. This region is one of diffusional creep which involves little or no dislocation movement, but primarily is a result of stress-directed atom migration. The high stress region involves the dislocation climb process in the presence of a stress
created excess vacancy concentration which leads to an exponential dependence of the steady-state creep rate on stress. Other mechanisms not included in this figure are superplasticity with is KO2, and Coble
5
creep, with diffusion along grain boundaries more important than matrix
4
diffusion and a linear dependence of steady-state creep rate on stress The area of interest in this study is the power law or Andrade creep region, where the steady-state creep rate is proportional to the stress
raised to the nth power. Diffusion controlled dislocation mechanisms control the creep rate, and several material and structural variables significantly affect the position and slope of the curve. Ashby5 has proposed a method for delineating the boundaries between these various deformation regimes in stress and temperature space. After plotting normalized stress, a/G, against homologous temperature, T/TM#
IU
-II
10' -13 101 10-I0
-10
-10
-10
-10
=K cr
5=K o-"
K e w
10-10'
10 2
10 310
4
T' (arbitrary units)
he equates pairs of constitutive equations and solves for stress as a function of temperature to form the boundaries of the fields. In
addition, contours of constant strain-rate can be plotted from the constitutive equations in a particular field. These maps are all done for a particular grain size on pure metals or compounds. For most FCC metals plotted, the power law creep region extended over a range of
a/G from approximately 10 to 10-2 for a grain size of 32 microns.
This region expands slightly for larger grain sizes, such as those in this study.
Sherby and Burke developed a phenomenological relationship for Andrade steady-state creep rate of pure metals of the form:
-AD ySF. (o/E) (2.01)
where D is the self-diffusion coefficient, yS.F. is the stacking fault energy, E is Young's modulus and A is a constant in units of cm5
/ergs3.5 As can be readily seen, this equation contains the power law stress dependence, with n-5, and the exponential temperature dependence in the self-diffusion coefficient D-D exp .D/RT. Two additional parameters, YS.F. and E, appear to have a marked influence on the creep rate as well. But it is obvious that this is an empirical correlation not based on theory, because of the rather unusual units on what should be a
universal, dimensionless constant. A reformulation of this equation by Bird and co-workers6 yields the dimensionally correct relation
E kT = Y n
DGb F.)(b ) (2.02)
which can be used, less the stacking fault energy function, for all diffusion controlled creep mechanisms. The parameters G and b
correspond to the shear modulus and Burgers vector respectively. The ratio of the creep rate to the diffusion coefficient is normalized by the factor kT/Gb (in units of cm2) and the stacking fault energy is normalized in order to avoid the implication that at infinite y S.F. the
e would also be infinite. This formulation, then, will be the starting point for a discussion of the dislocation climb mechanism in pure metals and, later, in solid solutions.
11.2. Climb Controlled Creep
Values of n and
Qc
for a large number of pure metals deformed in this region tend to corroborate the values put forth by Sherby andBurke 3 of n5 and
Qc
SD, whereQSD
is the activation energy for self-diffusion. To attempt to account for these observations, the theoretical derivation of the equation for creep rate when dislocation climb is rate7
controlling was performed by Weertman . He hypothesized a series or sequential process during creep, which involves dislocations alternately gliding and climbing. The rate determining step, as with any sequential processes, is the slower of the two. When this slow step is the
dislocation climbing to a new plane, the creep rate is defined by:
- 4.5 E (cl) 2.27 0.5M0.5 3.5kT (2.03) or e kT 4.5 DGb 2.27(t) b-.M
where M is the density of Frank-Read dislocation sources per slip system and the rest have their usual meanings. The latter form is of particular interest since it is of the same form as the Dorn equation, Eq. (2.02),
mentioned above,with A-2.27b-l.5M-0.5; however, the stacking fault energy does not appear in this equation, though it would be expected that a
change of stacking fault energy (and thus, the fault width) would markedly affect the ability of the partial dislocations to cross-slip and climb. Another interesting feature of this equation concerns the predicted inverse square root dependence of the creep rate on dislocation source density. This would seem to follow from reason. The most
important features of this theory, though, are the creep model of sequential dislocation mechanisms, the predicted value of n, and the use of the activation energy of self diffusion as the primary temperature
dependence.
Pure metals, then, creep at a rate determined by the rate of dislocation climb. This creep rate is markedly decreased with a
moderate increase in elastic modulus, all other variables held constant. Weertman explained this by describing the ease of climb of a dislocation over an obstacle in terms of the stress field of the barrier, which
increases in magnitude with the elastic modulus. With stronger stress fields at the barriers, the climbing dislocation must climb higher before
7
surmounting its barrier and proceeding on by glide . It has also been reported that the temperature variation of the elastic modulus should be included in calculations of the creep activation energy . At any
rate, its presence in the creep rate equation, equation (2.02), is primarily as a normalizing factor for stress and stacking fault energy.
Lowering the stacking fault energy lowers the subgrain size formed in a material deformed at constant stress by dislocation climb. It is
thought that this effect may be the reason for the resultant lowered creep rates, since it has been shown that decreasing the subgrain size, to a certain minimum value, improves creep resistance . In any case, decreasing the stacking fault energy does impede the climb of the partials at either end of the fault and thus lowers the climb rate.
Dislocation climb is controlled by the rate of diffusion of vacancies to the locked dislocations (or partial dislocations). This mechanism is equally valid for some solid solutions, hereafter referred -to as Class II alloys. When solute is present, the diffusion coefficient of climb is a weighted diffusion coefficient,
* *
-
AB
D- (2.04)
AD B D A
where the starred values are tracer diffusion coefficients 8. As can be readily seen, this equation approaches D-D ADA, the solvent self-diffusion coefficient, as XB approaches zero.
Solid solutions which deform by dislocation climb controlled creep generally tend to exhibit the following characteristics: (1) high elastic modulus, (2) small size misfit of solute atoms, (3) low stacking fault
9,10
energy, and (4) low solute concentration . The creep curves of climb controlled materials exhibit a significant primary creep range and initial creep strain . Dislocations, after creep into the steady-state region, are largely contained in the walls of subgrains formed during primary creep. Those that are not have generally no directionality, form coarse networks, avoid pile-ups, and sometimes form incomplete subboundaries9
11.3. Glide Controlled Creep
When solute concentration is large, solid solution alloys can also exhibit totally different creep behavior from the Class II alloys and pure metals. These Class I alloys exhibit exactly the opposite material and structural characteristics of Class II systems, with relatively low moduli, large size misfits, and high stacking fault energies. Transient
creep may be very small, nonexistent or even inverse before reaching the steady state regime. Dislocations tend not to form networks or subgrain boundaries and, instead, are very homogeneously distributed, of mostly edge character, and smoothly curved due to the existence of a glide
resis-9
tance on a fine scale . The pertinent diffusion coefficient for these alloys is not the vacancy diffusion coefficient of the Class II alloys, but the diffusion coefficient of the solute atom, since it is the solute
atom which is imparting a dragging or pinning effect on the gliding or stationary dislocations. This coefficient is actually derived from a chemical potential gradient, and hence the chemical interdiffusion coefficient,
o ** Iny B
D = (DAX + DBXA) 1+ 2nYB) - (2.05) A B B A UXB
is the appropriate value for use in the Dorn equation.
Weertman derived an expression for the creep rate in Class I alloys of. the form
3 g=(l-v)a
(2.06)
s (91) 6G 2A'
"micro-creep" mechanism. A microcreep mechanism is basically any solute dis--location interaction which can reduce the rate of gliding of disdis--locations
12
on a glide plane to a value slower than the climb rate. The most
prevalent types of mechanisms are the Cottrell-Jaswon solute atmosphere,1 3 the Suzuki segregation of solute to a stacking fault and the Fisher
15
short range order interaction. These three mechanisms will be the center of the discussion on glide controlled creep in this study. A short
synopsis of the pertinent features for each of these mechanisms follows the defining of the microcreep constant, A'.
In evaluating the parameter A', Sellars and Quarrell16 showed that it is equal to the critical stress (a c) for break away from the dragging component, times the Burgers vector (b), and divided by vc, the dislocation
2
velocity at a stress just below a . The cgs units are dyne-seconds/cm2 The quantities to be evaluated for each mechanisms, then, are ac and vc.
11.3.1. Cottrell Atmospheres
Cottrell-Jaswon solute atmospheres are present in both substitutional and interstitial solutions. Substitutional solute atoms diffuse to the dislocations to lower their energy, with the larger solute atoms posi-tioning themselves in the dilatation field of an edge dislocation and the smaller atoms diffusing to the compressive portion of the stress field. This leads to a pinning of stationary dislocations and a drag force on moving dislocations because the solute atoms only move as fast as the chemical potential induced diffusion process allows. The solute atom interacts with a positive edge dislocation at rest, with a potential given by
V GEr b( ) +v sine (2.07)
3at -v r
where r and
e
are its coordinates relative to the dislocation, c is the fractional difference in atomic radii between the solvent and solute, ra is the solvent atom radius, and the rest have their usual meaning. The equilibrium concentration of the solute at r, 0 is given byc(r,O) = C exp-[V(r,e)/kT] (2.08)
where C is the average atomic solute concentration of the alloy. This formulation holds provided the atmosphere is not so concentrated that the local dilatation caused by the solute atoms is comparable to that caused by the dislocation. For moving dislocations, the non-symmetrical
dis-tribution of solute atoms about the core causes a viscous drag force to act on the dislocation in opposition to the applied force. This force increases with dislocation velocity, leading to a steady-state condition under constant applied stress13
At elevated temperatures, pinning becomes less prevalent since the solute atoms diffuse away more readily. Thus, the primary effect of solute atoms at high temperature is the formation of nonsymmetrical at-mospheres exerting a viscous drag force opposite to the applied force. On the other hand, if the solute atoms were randomly dispersed, a
dis-17
location would move almost as if in a pure metal . The critical velocity for escape of a dislocation from an atmosphere has been shown to be
pro-18
portional to D kT, where D is the solute diffusivity8. Mohamed and
8 5
Langdon defined the factor A', a function of the breakaway stress and velocity, as the following formulation:
e cb G2
A'- % (2.09)
kTD
where e is the solute-solvent size difference and c is the concentration
19
of solute . The quantity e is tabulated for a large number of binary solutions by King,20 and the other parameters are readily measurable for calculation of this factor and, subsequently, the calculation of the glide controlled creep rate.
A very recent paper byTakeuchi and Argon21 yields a creep rate for glide different by a factor of three from that of Weertman. Their model was based upon the dislocation behavior expected when both glide and climb of dislocations are governed by atmosphere dragging. They point out that the inclusion of the atmosphere dragging effect on dislocation climb better predicts the resultant dislocation structure observed in Class I alloys after creep. In particular, the theory requires that dislocation pile-ups should be unstable (as metallography has shown) because once a dislocation leaves a glide plane by climb, it is accelerated to climb continuously due
to repulsion from other dislocations of the same sign. The criterion defined in this paper, however, would not be applicable for alloys with low stacking fault energies (y/Gb<2x102) because no extension of the
dis-location is taken into account in the model. For low stacking fault materials, the next mechanism, Suzuki locking, should be more suitable
11.3.2. Suzuki Stacking Fault Segregation
14
Suzuki defines the interaction of dislocations with solute atoms in a material with extended dislocations as caused by the difference in crystal structure in the faulted region. Solute atoms segregate to the faulted area for thermodynamic reasons and, in the process, cause a more extended, weaker hardening pffect than the solute atmospheres. This is due to a diminished strain field for an extended dislocation compared to a perfect dislocation. Hendrickson22 derived a relation for this difference in composition between the matrix and fault of the form
x 2 x2 dy S.F.
S 2exp(- d /RT) (2.10)
(l-x)2 l-x
2 2
for less than ten atomic percent solute, where x2' is the mole fraction of solute in the fault at equilibrium and x2 is the mole fraction of solute in the alloy. This relation yields x2 >x2 when dy S.F./dx2 is negative, which is as it should be, and it gives a decreasing compositional difference with increasing temperature due to thermal motion. Solute additions
generally lower the stacking fault energy, therefore creating more fault area to segregate to. One study found a dependence of stacking fault energy on solute concentration of the form
Yalloy = Tsolvent exp [K{c2/ (l+c) 2 (2.11) where c is the ratio of solute concentration to the maximum solubility
23
limit of the solid solution2. The value of K will be negative and depend on characteristics of the system studied, in particular the
difference in the number of electrons per atom of the solute and solvent. The greater the difference, the stronger the tendency to segregate to
the extended dislocation, the larger the value of K, and, -for a given
com-position, the lower the stacking fault energy.17
Relating all of these observations to the strengthening potential for this mechanism, Dorn and Mote showed a linear dependence of ATon the solute concentration difference between the fault and the matrix and the dif-ference between the free energies of the solvent and the solute in the
18
fault and the matrix. But, more appropriate to the creep equation defined previously, the factor A' was defined by Sellars and Quarrell, from work by Flinn, to be
A 2 26 2 2.22RT + (+v ) ( 2 - (2.12)
As 9 1v ( )-8H
VD v/AB
where 6 =(V/2) (y BA) V is the molar volume, V/aX is the change in molar volume with mole fraction, AH1/2 is the enthalpy of mixing at X =X B 0.5, and h is the distance between slip planes.1 6
11.3.3. Fisher SRO Interaction
The last important microcreep mechanism is short range order hardening. This is of particular interest in concentrated solid
solutions. Fisher15 first qualitatively described the reason for
hardening in an alloy displaying deviation from randomness by reasoning that the passage of a dislocation through short range ordered material creates disorder in its wake. Since the system's thermodynamics favor certain bonding patterns over others, a stress increment is required to move the dislocation and exchange the preferred bonding arrangement for a higher energy, less ordered arrangement. Fisher quantitatively estimated this stress increment in the form,
T Y }(2.13)
b
where y is the energy of the disordered interface produced by the passage of a dislocation. Since then, several modifications and improvements on this simple equation have been formulated, the most notable being those
24 25
of Flinn and Cohen and Fine2. The former derived a relation between the shear stress and the short range order parameter, a, for relatively low temperatures, of the form,
/T
XAX wa
T1 - A6/ 3 (2.14) a where
W
- [ (WM~oBB)] (2.15)is the parameter relating bond energies. This relative bond energy can be calculated from an experimental a by the relation,
a e (Ref. 24) (2.16)
(1-a)2 XAXBI""exp - 1] (.6
(1-a) 2 AB k
Cohen and Fine showed a fluctuation of the short range order parameter with the number of units of slip which, in the case of a across the slip plane, approaches zero, while the overall order parameter approaches a
constant value with dampening fluctuations. From the change in ai for one Burgers vector of slip, they calculated the short range order strengthening to be
2X X sw C Aa - TAS
T - 3 1 (2.17)
b
where the summation is over i shells from a reference atom, C is the coordination number of the ith shell, AS is the entropy which is a complex
25 function of the a 's, and the rest have their already described meanings. Panin and co-workers qualitatively observed that, at small strains, this hardening will be present as theorized, but at larger strains, the
nature of the dislocation structure produced by order will actually
cause a loss of strength. Their hypothesis can be summarized by Fig. 2
which is a stress-strain curve for three hypothetical states of a material
26 27
leading to a range of values for a .2 Chen and Nicholson found that, for Au-Pd alloys, the strengthening increment derived by Flinn and Cohen and Fine was much larger than experimental values determined in their laboratory. Their modification of the theory took into account the drag effect on dislocations due to short range order and the maximum pinning stress. The relations derived for each effect are as follows:
2
Drag effect - r velocity(SRO) P -8 (2.18)
velocity (random) 2
T
where, p = exp(-b A *d/kT), s = exp(- Ag/kT),A - activation area and Ag is the energy to destroy an A-B bond.
1/2
Pinning stress - AT = 2.l[(Ag)3XAXB
cal/Gb
9] (2.19) The sum of these gives a value of hardening increment about one fifth of the values calculated from previous works.So far, these theories have primarily been concerned with room temperature or moderate temperature properties, where diffusion is not sufficiently rapid to affect the degree of short range order during the tests. At the temperatures of interest here, the order parameter has been shown to decrease in absolute value slowly with temperature. In
High
.o ot
strain
addition, examples of creep in short range ordered alloys display a thermally activated dislocation motion controlled by the rate of
diffusion, much like the other microcreep mechanisms.18, 28 Thus, the value of A' in the glide controlled creep rate relation must incorporate the equations for AT(a
)
with a diffusion controlled velocity component(vC ) to give,1 6, 24
4/6XAX a
A' - (2.20)
All of these parameters have been defined earlier.
II.4. Criterion for Crossover
Now that the three microcreep mechanisms in glide controlled creep and the relations important in dislocation climb controlled creep have been described, a relationship is needed to define the crossover point where the rate controlling mechanism switches from one to the other. By
equating the creep rate from the Dorn Eqn.(2.02), to that from the equation
derived by Weertman for dislocation glide, Eqn. (2.06), and assuming that the Cottrell-Jaswon solute atmosphere is the predominant microcreep mechanism, Mohamed and Langdon 9 arrived at the general equation,
- 5
DGb a - ,(l- )kTD a (221
A( ) )= ) (2.21)
Gt) G 6e 2cb5G 2'
3
The function $(y/Gb) was found equal to (y/Gb) by empirically relating s kT/DGb, at constant a/G, to y/Gb on a log-log plot and assuming
negligible dependence of the latter on temperature. Rearranging terms in the general equation and making it an inequality so that the glide component is slower, gives their final form,
2 3- 2
Ba 2
> (2.22)
2 Gb 2 26
k (1-v) D e cb
where k is Boltzmann's constant, c is the concentration of solute,
BN 8 x 10 12, and all the others have been given previously. Three things can be drawn from this inequality just by observing the effect of changing three of the variables, stress, composition and temperature. As stress and concentration increase, this formulation predicts a trend toward
glide controlled creep. As temperature increases, the tendency would be to favor climb creep. Other effects include: (1) an increase in yS.F. favors glide creep, (2) an increase in G favors climb creep, (3) a large size difference, e, favors glide creep, and (4) a large ratio of dif-fusion coefficients, 5 being much faster, would favor glide creep. These same authors29 plotted the right hand side of the inequality against the left on log-log paper to graphically portray the criterion for climb to glide transition. A reproduction of this plot for data on. alloys in the nickel-tungsten system, taken from several sources, is shown in Figure 3. The 45* line corresponds to values of each factor for the
equation, not the inequality. The results shown here indicate an expected tendency toward glide behavior with increased amounts of tungsten added.
11.5. Series Summation of Creep Rates
In a very recent two-part paper by Chin and co-workers,30, 31 the Al-Zn system was studied in detail up to 60 atomic percent zinc at two temperatures above 0.5 TM. Part one primarily dealt with defining the appropriate diffusion coefficients for climb and glide controlled creep,
106
10
5
T
2eZcb
6 1050 K, 10i-6
10-2
(MN m-2
2Figure
3:
Graphical
display
of climb to glide transition as per
referenc*(29).
Ni-4 wt% W
Ni-15
wt%W
NI-25wt%W
Ni-26.4wt%W
10~
(r/GO'
(4/D.)
quantities used to determine them, were plotted as a function of composi-tion at both temperatures and compared to the corresponding steady-state creep rates at a constant stress. Since the two mechanisms give very
differently shaped curves of the appropriate diffusion coefficients (due
to a large variation in the thermodynamic factor), a qualitative comparison was easily made. The creep data correlated well to D g. In part two,
the formulas defined here for e cl and E gl were evaluated with all the parameters and properties known as a function of composition at the two
test temperatures. Again, the Cottrell atmosphere model was used as the microcreep contribution to E . Activation energies for creep were
compared to the corresponding activation energies for glide and climb over the entire composition range and stress exponents, n, were plotted to
show the transition from climb (nr5) to glide (n,3). To relate the
meas-ured steady-state creep rates at a given stress level to the theoretical values calculated from the equations given, these authors assumed the relationship,
10
1+ (2.23)
total ccl Egl
All values but the constants in each equation were known, so values of c /A and Be /A', where A, A' and B are constants, were plotted and
cl
g
summed to fit the data points. In the process, these constants were determined from the fit of the sequential summation to the data. A
11.6. Grain Size and Environmental Effects
The correlations described so far have had the inherent assumption throughout that dislocation glide and dislocation climb are the only two active -deformation modes.79 11 Relegated as insignificant, for the
purpose of deriving intragrain creep rate relations, are the contributions to creep strain due to grain boundary sliding and associated accommodation mechanisms. In reality, grain boundary contributions to the overall
creep strain are not insignificant. However, it has been shown that this contribution remains at a low constant value for grain sizes greater than a certain minimum value.3, 32 In a study on Ni-6 w/o W, Johnson and co-workers showed virtually no change in creep rate with increasing grain size, above a grain size of approximately 140 U, tested at constant
32
stress and temperature in vacuum. Sherby and Burke calculated this contribution for polycrystalline pure copper as a function of grain size
and found a variation from 34% of the total strain at a 40 p grain size,
to 15% for grain sizes of 100 p or larger. They concluded that the doubling of the creep rate with decreasing grain size was attributable
to the increasing importance of grain boundary sliding as a deformation mechanism.3
Two recent papers have taken the concept presented by Ashby of deformation mechanism maps and expanded their applicability to solid
33, 34
solutions over a range of grain sizes. Instead of plotting
a/G vs. T/TM, these maps plot d/b vs. a/G for a given homologous tem-perature, where d is the grain size. Again, the constitutive equations are related to give mechanism fields and boundaries, but with the
additional capacity to relate series processes as well as parallel (independent) processes. The slope of the boundaries between fields is given by An/Am, where An is the change in stress dependence and Am is the change in grain size dependence upon crossing the boundary.33 Grain boundary sliding is a series mechanism, according to these authors, but the relationjship between it and other mechanisms is not well known.
Nontheless, assuming sliding to be Newtonian viscous (n-l) and a function of Dg.b., constitutive equations were derived for gbs and acc, an
-intragranular accommodation mechanism in series, as follows:
A D Gb
S kg.b. (b) ) (2.24)
and
A2DGb b n
acc kT ( (2.25)
The constants A and A2 were determined by relating these equations to experimental data for grain boundary sliding rate.34 Figure 4 gives a hypothetical example of this mapping technique based on actual plots for aluminum and Al-3% Mg. The dashed curve between the sliding and glide fields indicates uncertainty exists in defining its shape.
A comprehensive review of grain boundary sliding by Bell and Langdon summarizes the effect of several important variables on the ratio cgb/ to Lowering the stress or initial grain size (below a certain value of
grain size) will increase this ratio. The sliding rate has been shown to be proportional to am, where m is less than n for the steady-state total creep rate. Temperature effects are uncertain due to the inability to
II
I
m.
10
'I0
d/b
10
l0
Nabarro-Herring
Coble
4
I
1076
I
10-4
Figure 4: Deformation mechanism map for a solid solution alloy.
Harper-Dorn
-7
10~
Climb
Glide
I
I
I
I
energies for sliding have been reported to be near the activation energy for self diffusion. As strain increases, this ratio remains nearly constant for low strains before dropping off slowly at strains near the end of the secondary creep stage.35 Finally, Gifkins proposed a rate equation for the contribution of grain boundary sliding and its accommo-dation, in the dislocation climb controlled regime, of the form
-2 0 4.5
2
b 5xl02b3. (1+2Fya/d ) (2.26)where F is a stress concentration factor, y is the width of a triple-edge fold and their product is 2.3 x 10-1 mm when d, the grain size, is greater than a, the subgrain size. This equation was derived assuming that the rate of accommodation of grain boundary sliding controls the rate of grain boundary sliding, which is in conformity with observation and theory.3 6
Johnson and co-workers tested for the effect of environment on the measured steady-state creep rates. They postulated that intergranular cavitation and fracture may be very sensitive to the environment due to environmental effects on grain boundary sliding and migration. They tested electropolished Ni-6 w/o W samples at 900C (1173*K) and 5,000 psi in vacuum and in commercial purity Ar. The grain sizes varied from 50 p to 250 p. Their results showed a marked positive deviation of the creep rate in Ar as compared to tests in vacuum, above approximately
140 p grain size. This was thought to be due to the failure of the Ar tested samples before reaching the true steady-state region, as a result of oxidation induced early cavitation failure in the large grained
prove deleterious to rupture life and steady-state creep rate due to reduction of the effective cross-sectional area during the test. Also, some studies have actually shown improvement in creep properties due to the oxide scale forming a load bearing entity which inhibits
inter-crystalline cracking of the metal deforming beneath it. 3 7, 46 The nickel-molybdenum system was thought to be prone to accelerated or catastrophic oxidation38 due to the volatile and hazardous species, MoO3, formation. However, work done by Brenner39 in stationary and flowing air atmospheres up to 1000C showed that alloys containing up to 19.7 a/o Mo, with traces of W, C and Fe , did not exhibit accelerated oxidation. In fact, in alloys containing greater than 12 a/o Mo, the parabolic oxidation rate decreases. His model of the process includes an outside NiO layer, an intermediate, high melting point, solid NiMoO4 layer, and a layer of
internally oxidized matrix, with MoO2 as the oxide formed. The rate determining step is the diffusion of Ni ions in NiO. The decrease in oxidation rate at higher molybdenum content is due to densification of
the subscale MoO2, which hinders the migration of the Ni ions. As temperature increases, the probability of formation of volatile MoO3 increases as more Mo is soluble in the NiO and hence more able to react
39
directly with the 02 in the air. Nickel-tungsten alloys show an increasing oxidation rate with increased tungsten content, with Ni-17.6 a/o W exhibiting a parabolic rate constant an order of magnitude greater than pure nickel at 1000*C. The layering is identical to that for Ni-Mo alloys except that the authors of this study40 hypothesize WO *as the dispersoid in the nickel-tungsten matrix. As tungsten content increases, the outer NiO scale becomes thinner and more porous, and the tendency
for internal oxidation diminishes. Increasing the temperature thins the outer NiO scale as well as decreases the tendency to form a roughened alloy/scale interface. Thus, both alloy systems are susceptible to
relatively rapid oxidation kinetics, particularly at the higher
tem-peratures, and care needs to be taken to ensure that this environmental effect is taken into account in describing the measured creep rates.
11.7. Creep Studies on Ni-W and Ni-Mo
Turning now to specific creep studies of these two systems, a
brief sunmary of the findings of Pelloux is in order. Figure 5 gives
the results of the high temperature creep testing performed at 8150C (1088*K) on the three nickel alloy systems. A sharp increase in both
aIHR and a100HR rupture life values is readily observed above about ten atomic percent molybdenum. The other alloy systems show only moderate continuous increases over their solid solution ranges. In addition, room temperature tensile tests of solid solution alloys with high solute content showed a yield point which was explained in terms
14
of the Suzuki hardening mechanism. The Ni-Cr alloys showed a larger increase in flow stress at E - 0.2 percent for a given change in lattice parameter than Ni-Mo and Ni-W, both of which displayed a common linear
40
30
Stress
(1000 psi)
20
10
-
15000 F
Limits of Solubility for W
.1Cr
-I
I
Hour
Rupture Life -l \ % % % 0Ni-Cr\
+ Ni-Mo
0 Nl-W
+-0,Hou+-
Solid Solution Alloys
---- Two-Phase Alloys
Rupture Life
I
-
I
--
I
-
I
I
I
I
10
20
30
40
ATOMIC
PERCENT OF SOLUTE ELEMENT
Figure 5: Creep strength vs. atomic percent solute, from (1).
50
0
position in the periodic chart of the solute atoms to show that the change in room temperature flow stress, for a change in lattice parameter of 0.01 kX units, should be greatest for the solute giving the largest difference in valency. These trends at room temperature
were then assumed to be true for 650*C (923*K ) and 8150C (10880K) tests, up to ten atomic percent, because the relative change of lattice parameter with solute content was thought to be nearly equivalent to
the room temperature values at these temperatures. Rubin then
performed stress rupture tests on several other nickel solid solutions
at 8150C (10880K) and tested Pelloux's alloys at 982*C (12550K). The
results are summarized in Table 1. Only the.Ni-17.5 a/o W alloy is two phase at the latter temperature.
Several Japanese studies have looked at the nickel-tungsten system in some detail at compositions somewhat lower in tungsten than
this research. Monma and co-workers tested alloys containing up to 9.2 a/o W in an argon atmosphere between 750C and 12000C and 2,000 and 12,800 psi (13.8 to 88.3 MPa). They found that strain to fracture decreasedwith increasing tungsten content, and that a sudden increase in creep rate occurs at short times, before leveling off again, in the highest
tungsten content alloy. This was not explained, but a conjecture that this was due to recrystallization was made based on previous literature. Calculations of the stress exponent, n, at these temperatures yielded a peak at 7.2 for 1.7 a/o W before decreasing to a value of 3.9 for 9.2 a/o W. Activation energies also peak, but at 5 a/o W, where a value of 84 kcal/
Table 1 a/o solute 2.7 Ti 5.6 Ti 7.9 Ti 5.9 V 11.7 V 17.4 V 1.9 Nb 3.1 Nb 4.3 Nb 1.3 Ta 1.9 Ta 2.3 Ta 9.7 Mo 13.5 Mo 15.6 Mo 17.3 Mo 18.7 Mo 7.4 W 11.0 W 14.7 W 17.5 W a100 hr (psi)
4,800
6,300 7,000 2,500 4,300 11,2004,600
5,8006,500
3,800 3,9004,100
5,000 4,600 4,800 5,500 5,200 3,000 3,500 7,000 7,500 Temp. 8150C 815*C 815*C 8150C 9820C 982*C Solubility limit 8.3 Ti 17.6 V 5.0 Nb 2.6 Ta 22.9 Mo 16.4 Wmole was reported. Finally, plotting e against tungsten content at 5
constant stress gave a continuous decrease in creep rate with increasing atomic percent tungsten.41
Suto and Yamada42 used Sherby's equationEqn. (2.01),to determine
the most important factor affecting high temperature strength in nickel-tungsten alloys containing up to ten atomic percent nickel-tungsten. Stacking fault energies were measured by using an X-ray texture technique on deformed material, using a standard calibration curve. Creep rates were plotted against atomic percent solute, and the log of equation 2.01 was
taken to give the relative strengthening effects of each parameter. The equation used was of the form
log c'/c - log D'/D + 3.5 logy'/y - 5 log E'/E (2.27)
s 5
where the prime values are for the alloy and the plain values are for pure nickel. The e' calculated in this fashion, at a constant stress
5
and temperature, were plotted against atomic percent solute, along with the observed creep rate and the relative contributions from the three parameters. Figure 6 gives an example of this plot from this reference. The difference betweer the calculated and experimental curves was
postulated to be due to the Suzuki effect or an ordering effect, or both. The most important contributions to strengthening of nickel-tungsten alloys were concluded to be the diffusion coefficient and the stacking
42
fault energy.
Two related works on Ni-10.3 a/o W gave values of n=3.2 and n=3.6 for 800-950*C and 10000C respectively. The activation energy was determined to be 60 kcal/mole. Dislocation climb was concluded to be
102
10(*//h r)
10
I0
5
10
Atomic Percent W
Figure
6t
Contributions of Eqn. 2.01 parameters
to(,
reference
(42).
-.
%D
4
E
.E
-. 92N
--
":4 kg/mm
2(obs)
T =923*C
0
I Isaw----t
l
I
43
rate controlling in this alloy, despite the low values of n. This was demonstrated by using the effective stress criterion and measuring
*
internal stress, a,, and m in the equation * m*
v - B(C-) (2.28)
* *
where a is the effective stress, m is one for glide and greater than one for climb, v is dislocation velocity, and B and C are constants.
-*
The value of m was around two to three, and the internal stress varied
with applied stress, signifying a dislocation climb mechanism.
Sukhovarov found three anomalies in the temperature dependence of
the deformation resistance of a Ni-10 a/o M alloy. In order of increasing
temperature, these anomalies were categorized as due to: (1) Cottrell atmospheres with interstitial impurities such as C and N, (2) Cottrell atmospheres with the substitutional Mo solute atoms, and (3) the K-state,
45
or short range order hardening. Guseva and Egiz studied the creep characteristics of Ni-6.2 a/o Mo and Ni-5.8 a/o W in comparison with other nickel solid solutions. The results for fully annealed samples at 825 to 950*C, in vacuum, yielded activation energies for Ni-Mo of 70 kcal/mole up to 900*C and 61 kcal/mole at higher temperatures. The Ni-5.8 a/o W activation energy was not calculated. To check the effect of environment on the creep rate, tests were run in air at 8500C. The creep rate was lower in air than in vacuum in all alloys except the nickel-tungsten. In addition, the elongations through stage II were greater in air.46 Their later work tested these alloys at a constant homologous temperature of 0.66 Tm. Stacking fault energy values were determined from fault density values for nickel and the alloys, and a