U.S. patent application number 10/395987 was filed with the patent office on 2004-03-11 for method for enhancement of grain boundary cohesion in crystalline materials and compositions of matter therefor.
This patent application is currently assigned to Northwestern University. Invention is credited to Freeman, Arthur, Geng, Wen-Tong, Kantner, Christopher, Olson, Gregory B..
Application Number | 20040047758 10/395987 |
Document ID | / |
Family ID | 31998999 |
Filed Date | 2004-03-11 |
United States Patent
Application |
20040047758 |
Kind Code |
A1 |
Olson, Gregory B. ; et
al. |
March 11, 2004 |
Method for enhancement of grain boundary cohesion in crystalline
materials and compositions of matter therefor
Abstract
A method for identifying additive components for polycrystalline
metals and materials that enhance grain boundary cohesion and
compositions of such materials comprises calculation of an
empirical value .DELTA..sub.B.sup.Awhich is dependent upon a
summation of various energy values associated with the matrix and
additives and identifying the additives having a negative value.
Formulations of alloys having improved physical properties and
their processing steps are also disclosed.
Inventors: |
Olson, Gregory B.;
(Riverwoods, IL) ; Freeman, Arthur; (Evanston,
IL) ; Geng, Wen-Tong; (Ibaraki, JP) ; Kantner,
Christopher; (Chicago, IL) |
Correspondence
Address: |
BANNER & WITCOFF, LTD.
TEN SOUTH WACKER DRIVE
SUITE 3000
CHICAGO
IL
60606
US
|
Assignee: |
Northwestern University
Evanston
IL
|
Family ID: |
31998999 |
Appl. No.: |
10/395987 |
Filed: |
March 25, 2003 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10395987 |
Mar 25, 2003 |
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09755821 |
Jan 5, 2001 |
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60174454 |
Jan 5, 2000 |
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60367293 |
Mar 25, 2002 |
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Current U.S.
Class: |
420/107 ;
148/328; 148/335 |
Current CPC
Class: |
C22C 38/002 20130101;
C22C 38/44 20130101; C22C 38/005 20130101; C22C 38/46 20130101;
C21D 1/18 20130101; C22C 38/52 20130101 |
Class at
Publication: |
420/107 ;
148/328; 148/335 |
International
Class: |
C22C 038/52 |
Goverment Interests
[0002] This development was supported by the Office of Naval
Research (Grant No. N00014-94-1-0188) and a grant of Cray-T90
computer time at San Diego Supercomputing Center and Cray-J90
computer time at the Artic Region Supercomputing Center.
Claims
What is claimed is:
1. An alloy, comprising in combination: a crystalline matrix of at
least one metal selected from the group consisting of iron and
nickel, wherein said matrix includes crystals with grain
boundaries, and at least an alloying element selected from the
group consisting of tungsten (W), rhenium (Re), osmium (Os),
niobium (Nb), iridium (Ir), technetium (Te), ruthenium (Ru),
platinum (Pt), tantalum (Ta), zirconium (Zr), hafnium (Hf),
vanadium (V) and titanium (Ti) in an amount that enhances cohesion
at said boundaries characterized by segregation of said alloying
element to the grain boundaries and the term .DELTA.E.sub.B.sup.A
being negative, said alloy being processed by low temperature heat
treatment to segregate said alloying element to a grain
boundary.
2. The alloy of claim 1 wherein said matrix is a nickel compound
and said alloying element is selected from the group consisting of
osmium (Os), rhenium (Re), ruthenium (Ru), tungsten (W) and niobium
(Nb).
3. The alloy of claim 1 wherein said matrix is an iron compound and
said alloying element is selected from the group consisting of
tungsten (W), rhenium (Re), niobium (Nb), and osmium (Os).
4. A generally solution heat treated alloy composition consisting
essentially of a formulation in weight percent of 0.18-0.40 C
15.0-20.0 Co 6.0-7.5 Ni 2.0-4.0 Cr 0-1.7 Mo 1-3.0 W 0-3.0 Re
Balance Fe and one or more additives in weight percent selected
from the group consisting of up to 0.05 % Ti, 0.010 % La, 0.02 %
Zr, 10-20 ppm B, combinations thereof and impurities, said alloy
solution heat treated in the range of 800.degree. C. for at least
one hour to form carbides characterized primarily as M.sub.2C and
to effect migration of Mo, W and/or Re to grain boundaries.
5. The alloy of claim 4 subjected to tempering in the range of
450.degree. C. to 550.degree. C. for at least one hour to increase
hardness.
6. The alloy of claim 4 having an M.sub.S temperature in the range
of about 225.degree. C. to 400.degree. C.
7. The alloy of claim 4 wherein the mole percent of M.sub.2C
carbides is greater than 0.030.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This is a continuation in part utility application based
upon pending utility application Ser. No. 09/755,821 filed Jan. 5,
2001 which is based upon provisional application Ser. No.
60/174,454, filed Jan. 5, 2000, entitled, "Method for Enhancement
of Grain Boundary Cohesion in Crystalline Materials and
Compositions of Matter Therefor", and is also based upon pending
provisional application Ser. No. 60/367,293 filed Mar. 25, 2002
entitled "Ultra High Strength Steels with Enhanced Grain Boundary
Cohesion", all of which are incorporated herewith by reference.
BACKGROUND OF THE INVENTION
[0003] Grain boundary cohesion is often the controlling factor in
limiting the ductility of high strength metallic alloys.
Understanding the influence of the transition metal alloying
additions is of great importance in predicting and controlling
grain boundary embrittlement (GBE) in metallic alloys since the
complexity of GBE behavior is often correlated with the presence of
substitutional alloying elements. Attempts to qualitatively explain
GBE on the electron-atom level go back to the 1960's.
Quantitatively, alloy designers, on the one hand, have built
various atomistic theories such as thermodynamic and semi-empirical
pair bonding models to understand and predict the influence of
segregants on the mechanical properties of the grain boundary (GB).
Electronic structure theorists, on the other hand, have employed
both empirical and first-principles quantum-mechanical methods in
their calculations to predict the influence of segregants. While
the atomistic treatments have traditionally served as the starting
point for materials design, the electronic level explorations,
which are numerically more accurate, are more demanding in their
complexity to predict precise effects in advanced materials.
[0004] In spite of the complexity of the mechanical behavior and GB
atomic structures, general trends in certain mechanical properties
can be correlated with specific features of the electronic
structure. First-principles computation have proved to be an
accurate and powerful tool in attacking the problem of the
mechanical properties of real materials such as GBE. An inherent
advantage of the first-principles electronic theory is that it is
independent of any adjustable perimeters. Therefore, the numerical
results of first-principles calculations formed a basis or starting
point for more advanced theories. Without such theories, one has to
repeat the full procedure of calculations to predict quantitatively
the effect of any substitutional element even on the same GB. In
this case, the exact mechanism by which segregation elements cause
embrittlement remains unclear, and in any event the desirability of
any expedient way to predict the qualitative impact of segregants
is deemed especially desirable for the custom design of alloys
having desired properties such as workability.
[0005] This work involves a new ultra-high strength, tough steel
with enhanced stress corrosion cracking resistance using a systems
approach to materials design. Special emphasis is given, in this
design, to the integration of quantum mechanical principles for the
enhancement of grain boundary cohesion.
[0006] More specifically, two ultra-high strength steels are
disclosed having enhanced grain boundary cohesion. Requirements for
a transformation toughened alloy were found to be contrary to those
for grain boundary cohesion enhancement. Therefore, transformation
toughening was not incorporated in the disclosed steels and
processing. One alloy, Fe-15Co-6Ni-3Cr-1.7Mo-2W-0.25C designated
alloy QSW, is considered a commercially viable alloy. The second
alloy, Fe-15Co-5Ni-3Cr-2.7Re-1.2W-0- .18C designated alloy QSRe
involves the effect of rhenium and tungsten, reducing site
competition by eliminating molybdenum from the design. Both alloys
are fully martensitic, M.sub.2C carbide strengthened without any
precipitated austenite.
SUMMARY OF THE INVENTION
[0007] Starting from first-principles quantum mechanical
calculations on the strengthening and embrittling effects of
alloying metals on the grain boundary cohesion of a crystalline
matrix metal, there has been developed a method to predict
quantitatively the effect of a substitutional alloying addition on
grain boundary cohesion of the matrix metal or material. Thus, with
the practice of the invention, using the bulk properties of the
alloying material and the matrix material or metal utilized as
input information, the mechanical behavior of a substitutional
metallic element (A) near the grain boundary can be predicted
without conduct of the first-principles calculations once the
atomic structure of the corresponding clean grain boundary is
determined. This model differs from the thermodynamic and atomistic
theories in that it is not only based on first-principles and
therefore displays an electronic level understanding of the grain
boundary embrittlement, but also in that it takes the grain
boundary volume expansion into account and hence yields a more
precise treatment and result. Examples include the effect of Ru, W,
and Re alloying metals on the Fe grain boundary and Ca alloying
metal on the Ni grain boundary. Cohesion effects predicted by the
method are confirmed by rigorous first-principles
quantum-mechanical calculations.
[0008] Thus, there has been developed a method and compositions of
matter wherein grain boundary cohesion is predicted as directly
enhanced for iron (Fe) and nickel (Ni) alloys by the addition of
specific additive materials including tungsten, rhenium, osmium,
niobium, iridium, technetium, molybdenum, ruthenium, platinum,
tantalum, zirconium, hafnium, vanadium, and titanium in amounts
which segregate to the grain boundaries as a result of alloy
processing. Such additive materials have a cohesive effect
regardless of other additive materials which, for example, may
foster or may inhibit cohesion. Such cohesive enhancing materials
may thus be used alone or in combination. Favored cohesion
enhancing additives for iron (Fe) include tungsten, rhenium,
niobium, and osmium. Specific iron (Fe) based examples are
disclosed. Favored cohesion enhancing elements for nickel include
molybdenum, rhenium and ruthenium.
[0009] The method of the invention provides a means by which the
embrittlement or cohesion potency of a substitutional atom in a
grain boundary can be predicted without carrying first-principles
calculations. The method is capable of prediction without solving
the quantum-mechanical Schrodinger equation and makes use of
atomic, or bulk quantities as inputs. This method has an
electronic, rather than an atomistic or thermodynamic basis, in
order to yield a quantum description of the mechanical behavior of
a substitutional element near the grain boundary.
[0010] Additionally, the method is considered applicable to any
crystalline system including those comprised of metals and/or
ceramics, wherein alloying elements or other substitute components
are added to the matrix or base crystalline material in the
polycrystalline matrix. Thus, the described method and the
resulting compositions of matter and processing methods, though
described in the context of certain specific metals and alloying
elements, i.e., iron (Fe), nickel (Ni) and transition metal
alloying elements as set forth in Tables 1 and 2, contemplates
applicability in any crystalline material or composition.
[0011] In general, therefore, as one feature of the invention, a
methodology is disclosed which comprises a formula or protocol for
efficiently predicting the desirable alloying elements (and their
quantitative effect) for enhancement of grain boundary cohesion in
crystalline materials, including metals and ceramics for structural
and electronic applications. A first step undertaken in the
development of the method is a rigorous quantum-mechanical (e.g.
FLAPW) (full potential linearized augmented plane wave (FLAPW)
method calculation of a high free volume (to be representative of
weakest boundaries) and high symmetry (for calculational speed)
grain boundary to define fundamental boundary parameters such as
free volume. This is then applied in an approximate general model
of the mechanical and chemical contributions to the effect of all
alloying elements on boundary cohesion based on known properties of
pure elements. The quantitative effect of predicted cohesion
enhancers is then determined or verified by a pair of rigorous
quantum-mechanical (e.g., FLAPW) calculations comparing the energy
of segregation from crystal to boundary determining the efficiency
with which the element can be specified for cohesion
enhancement.
[0012] The alloying element in the compositions proposed is thus
substituted in the crystalline matrix at the grain boundaries. The
method of the invention, as generally described above and for which
various examples are provided hereinafter, determines the identity
of alloying or additive materials which will enhance grain boundary
cohesion. Various techniques may be utilized to deliver the
alloying component to the grain boundaries or, in other words,
cause the alloy or additive component to segregate to the grain
boundaries. For example, low temperature heat treatment for various
metals is a useful technique to effect such segregation and thereby
enhance cohesion. The methodology used for delivery and the
quantities of additive to be delivered to the grain boundaries may
be within the scope of general materials knowledge or can be
determined for specific conditions by limited testing or
experimentation. However, the identity of such components is a
result of the method of the invention, and the practice of the
invention contemplates the identity and processing materials that
result from the practice of the method.
[0013] It is noted that the examples herein are directed to binary
systems. However, the methodology is considered applicable to more
complex systems and to systems wherein the additive material is
counteracted by other additives, e.g., a cohesion enhancer is
counteracted by hydrogen (H) embrittlement. Additionally, the
amount of additive component or the range of the amount of additive
component may be derived using techniques disclosed.
[0014] The reference citations set forth in this application are
incorporated by reference.
BRIEF DESCRIPTION OF THE DRAWING
[0015] In the description, reference will be made to the drawing
comprised of the following figures:
[0016] FIG. 1 (FS) is a schematic representation of the atomistic
array of a crystalline matrix material wherein the free surface
energy is to be defined for iron;
[0017] FIG. 1 (GB) is a schematic view representation of the
atomistic array of an alloy material at a grain boundary in a
matrix material for iron;
[0018] FIG. 2 (FS) is analogous to FIG. 1 (FS) but is
representative of nickel;
[0019] FIG. 2 (GB) is analogous to FIG. 1 (GB) but is
representative of nickel;
[0020] FIG. 3 is a graph of the empirical calculation results using
the method of the invention for iron and various additives; and
[0021] FIG. 4 is a graph of the empirical calculation results using
the method of the invention for nickel and various additives.
DESCRIPTION OF PREFERRED EMBODIMENTS
[0022] Grain Boundary Cohesion Considerations
[0023] A. Atomic Structure and Volume Effect
[0024] As is the case of alloys and solid solutions, the volume
effect of a segregant is of great importance for understanding many
of its physical and mechanical properties near the GB. As a
first-principles treatment, one has to fully relax the atoms near
the GB.
[0025] To address the problem of volume mismatch, the atomic size
of the segregant and also the size of the GB hole should be well
defined. Unfortunately, the geometric size of an atom has no
absolute meaning and its definition depends on the physical,
chemical, or mechanical problem under consideration. The problem of
defining the size of an atom in metallic solid solutions has been
discussed in detail by King, "AIME Symposium of the Alloying
Behavior and effects in Concentrated Solid Solutions" (Gordon and
Brach, New York 1965) in the study of substititional solid
solutions, and by de Boer et al. "Cohesion in Metals" (North
Holland, N.Y. 1988) in the study of energy effects in transition
metal alloys. One of these definitions uses the atomic volume in
the structure of the elemental crystals. In the case of metallic
solid solutions, this definition is applicable when Vegard's law
(i.e., the unit-cell volume equals the sum of elemental atomic-cell
volumes) is observed. However, in the problem of GB segregation,
there is no requirement to keep the bulk lattice symmetry.
Therefore, such a definition of the atomic size is free from the
limitation of Vegard's law. The atomic volume (VA) of each selected
element in its elemental crystal is listed in Column 6, Tables 1
and 2.
1TABLE 1 Model calculated embrittling effect .DELTA.E.sub.B.sup.A
(eV) for all of the transition elements on the Fe .SIGMA.3 grain
boundary cohesion. Also listed are elemental cohesive energies 1 E
Coh A and E Coh A ( eV ) , formation heat of alloy 2 AFe Heat A
,atomic volumes V.sup.A (a.u..sup.3), bulk moduli K.sub.A
(.times.10.sup.11 N/m.sup.2), volume mismatch correction
.delta..DELTA. Ev and also the work needed to change the ground fcc
(hcp is approximated by fcc) structure to bcc structure for an
element. 3 E B A = 1 / 3 ( E Coh A + E A Stru + E Heat A ) + E V A
. 4 E Coh A = E Coh A - E Coh Fe . G.sub.Fe = 0.816 .times.
10.sup.11 N/m.sup.2. At- om 5 - E Coh A 6 E Coh A 7 E Heat A 8 E A
Stru V.sup.A K.sub.A .DELTA.E.sub.v .DELTA.E.sub.B.sup.A Li 1.63
2.66 0.94 0.00 143.58 0.116 -0.04 1.16 Be 3.32 0.97 -0.20 0.03
55.77 1.003 0.44 0.71 Na 1.11 3.18 2.75 0.00 254.46 0.068 0.18 2.16
Mg 1.51 2.78 0.67 0.01 156.93 0.354 0.19 1.34 Al 3.39 0.90 -0.91
0.12 112.09 0.722 -0.07 -0.03 K 0.93 3.36 4.80 0.00 481.33 0.032
0.33 3.05 Ca 1.84 2.45 1.28 0.01 293.40 0.152 0.76 2.01 Sc 3.93
0.36 -0.52 0.04 158.04 0.435 0.26 0.22 Ti 4.86 -0.57 -0.74 0.02
119.22 1.051 -0.01 -0.44 V 5.30 -1.01 -0.29 0.00 93.46 1.619 -0.11
-0.54 Cr 4.10 0.19 -0.06 0.00 81.01 1.901 -0.02 0.02 Mn 2.98 1.31
0.01 * 82.49 0.596 -0.07 0.37 Fe 4.29 0.00 0.00 0.00 79.39 1.683
0.00 0.00 Co 4.39 -0.10 -0.02 0.20 75.23 1.914 0.07 0.10 Ni 4.44
-0.15 -0.06 0.06 73.83 1.86 0.09 0.04 Cu 3.50 0.79 0.50 0.01 79.86
1.37 -0.01 0.42 Zn 1.35 2.94 -0.14 0.07 103.02 0.598 -0.11 0.85 Rb
0.85 3.44 4.75 0.00 587.83 0.031 0.47 3.20 Sr 1.72 2.57 1.90 0.00
379.12 0.116 0.97 2.46 Y 4.39 -0.10 -0.06 0.09 223.45 0.366 0.92
0.90 Zr 6.32 -2.03 -1.17 0.01 157.30 0.833 0.47 -0.59 Nb 7.47 -3.18
-0.70 0.00 121.37 1.702 0.05 -1.24 Mo 6.81 -2.52 -0.09 0.00 105.11
2.725 -0.09 -0.96 Tc 6.85 -2.56 -0.13 0.19 95.85 2.97 -0.11 -0.94
Ru 6.62 -2.33 -0.20 0.53 91.68 3.208 -0.10 -0.77 Rh 5.75 -1.46
-0.23 0.36 92.95 2.704 -0.10 -0.54 Pd 3.94 0.35 -0.19 0.08 99.24
1.808 -0.11 -0.03 Ag 2.96 1.33 1.23 0.00 115.35 1.007 -0.04 0.81 Cd
1.16 3.13 0.42 0.04 145.43 0.467 0.15 1.35 Cs 0.83 3.46 5.21 0.00
745.67 0.020 0.40 3.29 Ba 1.86 2.43 2.12 0.00 421.77 0.103 1.04
2.56 La 4.49 -0.20 0.25 0.11 249.93 0.243 0.84 0.89 Hf 6.35 -2.06
-0.98 0.10 149.29 1.09 0.43 -0.55 Ta 8.09 -3.80 -0.67 0.00 148.31
2.00 0.61 -0.88 W 8.66 -4.37 0.00 0.00 107.11 3.232 -0.08 -1.54 Re
8.10 -3.81 -0.01 0.27 99.24 3.72 -0.11 -1.29 Os 8.10 -3.81 -0.17
0.85 94.51 4.18 -0.11 -1.15 Ir 6.93 -2.64 -0.38 0.64 95.58 3.55
-0.11 -0.91 Pt 5.85 -1.56 -0.59 0.16 101.93 2.783 -0.11 -0.77 Au
3.78 0.51 0.37 0.00 114.37 1.732 -0.03 0.26 Hg 0.69 3.60 0.69 *
158.41 0.382 0.22 1.65 Tl 1.87 2.42 1.06 0.00 192.80 0.359 0.55
1.71 Pb 2.04 2.25 0.95 0.00 204.49 0.430 0.81 1.88
[0026]
2TABLE 2 Model calculated embrittling effect .DELTA.E.sub.B.sup.A
(eV) for all of the transition elements on the Ni.SIGMA.5 grain
boundary cohesion. Also listed are elemental cohesive energies 9 E
Coh A and E Coh A ( eV ) , formation heat of alloy 10 ANi E Heat A
,atomic volumes V.sup.A (a.u..sup.3), bulk moduli K.sub.A
(.times.10.sup.11 N/m.sup.2), volume mismatch correction
.delta..DELTA. Ev and also the work needed to change the ground bcc
structure to fcc structure for an element. 11 E B A = 1 / 3 ( E Coh
A + E A Stru + E Heat A ) + E V A . 12 E Coh A = E Coh A - E Coh Ni
. G.sub.Ni = 0.839 .times. 10.sup.11 N/m.sup.2. At- om 13 - E Coh A
14 E Coh A 15 E Heat A 16 E A Stru V.sup.A K.sub.A .DELTA.E.sub.v
.DELTA.E.sub.B.sup.A Li 1.63 2.81 0.03 0.02 143.58 0.006 -0.04 0.99
Be 3.32 1.12 -0.22 0.00 55.77 1.003 0.27 0.57 Na 1.11 3.33 1.40
0.01 254.46 0.068 0.27 1.85 Mg 1.51 2.93 -0.25 0.00 156.93 0.354
0.36 1.25 Al 3.39 1.05 -1.39 0.00 112.09 0.722 0.06 -0.05 K 0.93
3.51 2.35 0.00 481.33 0.032 0.40 2.35 Ca 1.84 2.60 -0.37 0.00
293.40 0.152 0.91 1.65 Sc 3.93 0.51 -1.79 0.00 158.04 0.435 0.46
0.03 Ti 4.86 -0.42 -1.54 0.00 119.22 1.051 0.18 -0.47 V 5.30 -0.86
-0.75 0.17 93.46 1.619 -0.05 -0.53 Cr 4.10 0.34 -0.27 0.39 81.01
1.901 -0.05 0.10 Mn 2.98 1.46 -0.33 0.00 82.49 0.596 -0.06 0.32 Fe
4.29 0.15 -0.06 0.20 79.39 1.683 -0.05 0.05 Co 4.39 0.05 -0.01 0.00
75.23 1.914 -0.01 0.00 Ni 4.44 0.00 0.00 0.00 73.83 1.86 0.00 0.00
Cu 3.50 0.94 0.14 0.00 79.86 1.37 -0.05 0.31 Zn 1.35 3.09 -0.63
0.00 103.02 0.598 -0.02 0.80 Rb 0.85 3.59 2.59 0.01 587.83 0.031
0.54 2.60 Sr 1.72 2.72 -0.06 0.00 379.12 0.116 1.10 1.99 Y 4.39
0.05 -1.62 0.00 223.45 0.366 1.17 0.65 Zr 6.32 -1.88 -1.37 0.00
157.30 0.833 0.78 -0.30 Nb 7.47 -3.03 -1.36 0.36 121.37 1.702 0.29
-1.05 Mo 6.81 -2.37 -0.32 0.40 105.11 2.725 0.06 -0.70 Tc 6.85
-2.41 0.03 0.00 95.85 2.97 -0.04 -0.83 Ru 6.62 -2.18 0.02 0.00
91.68 3.208 -0.06 -0.78 Rh 5.75 -1.31 -0.04 0.00 92.95 2.704 -0.05
-0.50 Pd 3.94 0.50 0.00 0.00 99.24 1.808 -0.02 0.15 Ag 2.96 1.48
0.68 0.00 115.35 1.007 0.12 0.84 Cd 1.16 3.28 -0.24 0.00 145.43
0.467 0.33 1.34 Cs 0.83 3.61 2.84 0.01 745.67 0.020 0.46 2.61 Ba
1.86 2.58 0.01 0.00 421.77 0.103 1.16 2.02 La 4.49 -0.05 -1.46 0.00
249.93 0.243 1.03 0.53 Hf 6.35 -1.91 -2.04 0.00 149.29 1.09 0.76
-0.56 Ta 8.09 -3.65 -1.33 0.19 148.31 2.00 1.07 -0.53 W 8.66 -4.22
-0.14 0.52 107.11 3.232 0.10 -1.18 Re 8.10 -3.66 0.10 0.00 99.24
3.72 0.00 -1.19 Os 8.10 -3.66 0.06 0.00 94.51 4.18 -0.04 -1.24 Ir
6.93 -2.49 -0.07 0.00 95.58 3.55 -0.04 -0.89 Pt 5.85 -1.41 -0.22
0.00 101.93 2.783 0.02 -0.52 Au 3.78 0.66 0.33 0.00 114.37 1.732
0.17 0.50 Hg 0.69 3.75 0.04 0.00 158.41 0.382 0.41 1.67 Tl 1.87
2.57 0.14 0.00 192.80 0.359 0.77 1.67 Pb 2.04 2.40 0.08 0.00 204.49
0.430 1.08 1.91
[0027] Volume expansion is an important property in the atomic
structure of the GB. Its contribution to the space available for
the substitutional element has a significant influence on the
physical and mechanical behavior of this element. The existence of
GB volume expansion makes the problem of the volume effect in the
GB different from those in alloys and solid solutions, where the
otherwise undisturbed atomic structure is perfect. A local measure
for the GB expansion is the relative normal displacement of the two
nearest atomic planes (M(2)) across the boundary plane. This gauge
was adopted, e.g., by Lu et al. Phys. Rev. B59, 891 (1999), in
Ni.sub.3Al.SIGMA.5 (210), and by Chen et al. J. Mater Reg. 5,955
(1990) in pure Ni and Al 5 (210 studies).
[0028] This definition, however, is not appropriate for the
investigation of the volume mismatch between the substitutional
element and the GB hole, as the GB local environment is determined
by not only M(2) but also by M(3) and M(4). The volume of the GB
hole, V.sup.GB, can be taken as the summation of the displacements
of M(2), M(3), and M(4). The calculated V.sup.GB, for the Fe
.SIGMA.3 (111) GB is 27.4 a.u., for the Ni .SIGMA.5 (210), it is
18.6 a.u.
[0029] As pointed out by Geng et al., Phys. Ref. B62, 6208 (2000),
not all the expanded volume near the GB is of the standard type
available for the GB core atom. The GB core atom A/M (1) can form
bonds only with M (2) and M (4), but not with M (3). This means
that, near Fe .SIGMA.3 GB only two-thirds of the GB hole is
available for A/M (1) and near the Ni .SIGMA.5 GB only 70% is
available.
[0030] Now the volume mismatch .DELTA..sup.A between a segregant
and the GB can be defined,
.DELTA..sup.A.ident..sup.A-(.sup.M+.varies..sup.GB)
[0031] where .varies. is 67% for Fe .SIGMA.3 and 70% for Ni
.SIGMA.5.
[0032] To address the volume effect of a substitutional addition A,
one should compare the elastic energy of the clean and segregated
GB. This elastic energy is associated with the volume mismatch
between A/M (1) and the GB hole. Since the crystal lattice near the
GB is not perfect even without the volume mismatch between A/M (1)
and the GB hole, the bulk modulus and shear modulus (of M) near the
GB no longer retain the perfect bulk values and are not well
defined. As an approximation, these deviations are therefore
neglected in the method. The elastic energy is then calculated in
the framework of elasticity theory with the sphere and hole model
developed by Eshelby and Friedel. In this model, a spherical hole
with volume V.sup.M (atomic cell of metal M) in the matrix is
partly filled by a sphere of another metal with volume V.sup.A,
(dissolved atomic cell). The remaining volume, (V.sup.M-V.sup.A),
will disappear by elastic deformation of matrix and inclusion. If
this is a state of purely internal stress, the total volume is
unaffected. Both inclusion and hole are then subjected to a uniform
hydrostatic pressure. The pressure on the inclusion is related to
its bulk modulus K.sub.A, while that on the hole is related to an
effective bulk modulus equal to {fraction (4/3)} times the shear
modulus of the matrix, G.sub.M.
[0033] The elastic energy yields 17 E V A = K A ( V A ) 2 2 V A + 2
G M ( V M ) 2 3 V M
[0034] Where .DELTA.V.sup.A and .DELTA.V.sup.M are the volume
changes of sphere and hole due to the internal stress. The
pressures are adjusted such that they are continuous across the
interface between matrix and inclusion, which leads to an
expression for the elastic energy per mole of solute metal: 18 E V
A = 2 K A G M ( V M - V A ) 2 3 K A V M + 4 G B V A _ _
[0035] In the GB environment, the hole cut from the matrix has a
volume V.sup.M+V.sup.GB rather than V.sup.M. Therefore, to describe
the GB case E.sub.V.sup.A should take the form 19 E V A = 2 K A G M
( V A - V M - 2 3 V GB ) 3 K A V M + 4 G M V A _ _
[0036] The volume effect of a substantial addition A, is
therefore
.DELTA.E.sub.V.sup.A=E.sub.V.sup.A-E.sub.V.sup.M
[0037] The calculated 20 E A V
[0038] values for each alloying addition are listed in Column 8,
Tables 1 and 2.
[0039] B. Electronic Structure and Bonding Characters
[0040] The other factor even more important in general, in
determining the behavior of a segregant in the GB is its bonding
character in both the GB and free surface (FS) environments. At the
electronic level, a quantitative description of the chemical
bonding will generally employ the concepts of change transfer, or
electronegativity. Nevertheless, neither charge transfer nor
electronegativity is well defined in a non-elemental crystal and
therefore is not considered appropriate to be built into a unified
theory. The macroscopic quantity that can be a measure of the
bonding capacility of an element, as adopted in the thermodynamic
or atomistic theory of GBE, is the elemental cohesive energy. It is
also employed in the present method.
[0041] According to the Rice-Wang thermodynamic theory (Mat. Sci.
& Eng. A107 p. 23 (1989), the potency of a segregation impurity
in reducing the `Griffith work` of a brittle boundary separation is
a linear function of the difference in binding energies for that
impurity at the GB and the FS. For a substitutional addition, the
above binding energies should be binding energy differences between
the segregant and the host (GB core) atom. The first-principles FS
and GB (Fe .SIGMA.3) chemical energies, defined as the work needed
to remove the segregant while not permitting the hose (Fe) atoms to
relax, have a relation: 21 E Chem FS ( A ) = . 2 3 E Chem GB ( A )
.
[0042] The difference in binding energies for A at the GB and the
FS, 22 E Chem A ,
[0043] is 23 E Chem A = . 1 3 E Chem GB ( A ) . Also : E Chem GB (
A ) - E Chem GB ( M ) = . E Coh A - E Coh M .
[0044] Combining equations: 24 E Chem A E Chem A - E Chem M = . 1 3
( E Coh A - E Coh M ) .
[0045] This means that the embrittlement potency of a substantial
atom in the GB of FE is about 1/3 of the cohesive energy difference
between that element and the host Fe atom if the volume effect is
not significant. The factor 1/3 can be understood by the {square
root}{square root over (Z)} theory. The simplest expression of band
character is in the second-moment approximation to the
tight-binding model, in which the cohesive energy per atom varies
as {square root}{square root over (Z)}, where Z is the atomic
coordination which can range from one (diatomic molecule) to 12
(fcc crystal). For the segregant in the Fe .SIGMA.3 (111) GB, Z8,
and for that on the Fe (111) FS, Z4. Hence, by applying the {square
root}{square root over (Z)} rule one will get 25 E Chem FS ( A ) =
. 0.71 .times. E Chem GB ( A ) .
[0046] "", rather than "=", is used because in both FS and GB
systems the bond lengths of M(1)-M(n) (n=2, 3, 4) differ from the
bulk values. Taking the contributions from the volume effect and
the bonding characters together, the embrittling effect,
.DELTA.E.sub.B.sup.A, of an alloying addition A is 26 E B A = 1 3 (
E Coh A - E Coh M ) + E V A .
[0047] The heat of formation of metallic binary alloys must also be
considered. The heat of formation for alloys can be viewed as a
chemical shift of the bonding capability of the solute atoms.
Comprehensive thermodynamic data for the heat of formation of all
the A (A=Mo, Ru, Pd, and Re) in M (M=Fe and Ni) alloys is desired.
The existing experimental data is far less than complete and the
computational effort required for first-principles determination of
these quantities is significant. Thus, as an alternative, the
macroscopic atom model is employed, de Boer et al. "Cohesion in
Metals", (North Holland, N.Y., 1988) to estimate the heat of
formation of alloys with a specific concentration which is
determined by our slab model.
[0048] In the macroscopic atom picture, the heat of formation of an
ordered alloy A in M with a concentration c.sub.A is 27 E Heat A =
( 1 - C A ) [ 1 + 8 C A 2 .times. ( 1 - C A ) 2 ] .times. H _ AinM
.degree. Where C A is C A = c A ( V A ) 2 / 3 c A ( V A ) 2 / 3 + (
1 - c A ) .times. ( V M ) 2 / 3
[0049] and {overscore (H)}.degree..sub.A i n M is the heat of
formation of A in M in infinite dilution. In our first-principles
calculation, C.sub.A is {fraction (1/23)} for A in Fe, and
{fraction (1/21)} for A in Ni. The calculated values of 28 E Heat
A
[0050] within the macroscopic atom model are listed in Column 4,
Tables 1 and 2.
[0051] The last term that should appear in the above equation is
the one reflecting the preference for metallic elements to
crystallize in one of the main crystallographic structures, namely
bcc, fcc and hcp, depending on the number of their valence
electrons. We use 29 E Stru A
[0052] to denote the total energy difference of elemental crystal A
between its ground state structure and that of the host. To make
all (or, as many as possible,) contributions in our model to be
found from the same basis, we carried out full GGA (generalized
gradient approximation) calculations for all the elements under
consideration. In doing so, we approximate the hcp by the fcc
structure in order to save computational effort. This approximation
will introduce an error to 30 E Stru A
[0053] yielded by FLAPW-GGA are listed in Column 5, Tables 1 and
2.
[0054] Taking the above two corrections into account,
.DELTA.E.sub.B.sup.A becomes 31 E B A = 1 3 ( E Coh A - E Coh M + E
Heat A + E Stru A ) + E V A ) .
[0055] The embrittlement potency of each substitutional addition
calculated from this model is listed in Column 9, Tables 1 and 2.
For Mo and Pd in Fe, the model calculated values for
.DELTA.E.sub.B.sup.A are -0.96 and -0.03 eV, respectively. The
first-principles results are -0.90 and +0.08 eV, respectively,
(Geng et al. Phys. Ref. B 62, 6208 (2000)).
[0056] C. Confirmation of the Model
[0057] In order to verify the model, first-principles calculations
were performed on the effects of Ru, W and Re segregation on the
cohesion of the Fe .SIGMA.3 (111) GB and Ca on the Ni .SIGMA.3
(210) GB by using the same (FLAPW) method. As sketched in FIG. 1
for the Fe .SIGMA.3 GB case and FIG. 2 for the Ni .SIGMA.5 GB case,
both the FS and GB were simulated by a slab model, which minimizes
the impurity-impurity interactions inherent in the use of
superlattice cells.
[0058] In the FLAPW method, no shape approximations are made to the
change densities, potentials, and matrix elements. For both host
and alloying additions, the core states are treated fully
relativistically and the valence states are treated
semi-relativistically (i.e., without spin-orbit coupling). The GCA
formulas for the exchange-correlation potential are from Perdew et
al., Phys. Ref. Lett, 77, 3865 (1996).
[0059] For Ru, W, and Re on the Fe .SIGMA.3 GB, first-principles
results are -0.65, -1.31 and -1.31 eV, respectively. The values
calculated with the model of the invention are -0.77, -1.54 and
-1.29 eV, respectively. The largest discrepancy between the
first-principles and the model invention results in about 0.2 eV in
the case of W, whereas for Ca in the Ni .SIGMA.5 (210) GB, the
model gives +1.65 eV and the first-principles results show an
embrittlement potency of +1.4 (.+-.0.2) eV. In general, the
agreement between the semi-empirical invention method and
first-principles is quite good.
[0060] In review, starting from first-principles, a semi-empirical
theory quantitatively predicts the mechanical behavior of a
substitutional metallic element in the grain boundary without
carrying out full first-principles calculations, once the atomic
structure of the clean grain boundary is determined. This model
displays an electronic level of understanding of the grain boundary
embrittlement. Also, it takes the grain boundary expansion into
account and hence yields a more precise treatment.
[0061] From the results, it is concluded that the strongest
cohesion enhancer in the Fe .SIGMA.3 (111) GB is W, followed by Re,
Nb, and Os. The strongest cohesion enhancer in the Ni .SIGMA.5
(210) GB is Os, followed by Re, W, and Nb. For both Fe based and Ni
based alloys (and therefore expected for most alloys based on
transition metals) the effective grain boundary cohesion enhancing
alloying elements are W. Re, Os, Nb, Ir, Tc, Mo, Ru, Pt, Ta, Zr,
Hf, V and Ti as suggested by FIGS. 3 and 4. Referring to FIGS. 3
and 4, those segregants having negative and positive
.DELTA.E.sub.B.sup.A are plotted as determined by the invention
method. Negative value segregants are direct cohesion enhancers.
Positive value segregants tend to cause embrittlement.
[0062] Table 3 summarizes the rigorous FLAPW calculations for both
.DELTA.E.sub.GB-.DELTA.E.sub.FS and the crystal/grain boundary
segregation energy .DELTA.E.sub.GB for the alloying elements Pd,
Mo, Ru, Re and W in Fe, validating the model predictions and
showing significant negative .DELTA.E.sub.GB values promoting
enhanced segregation to grain boundaries.
3TABLE 3 FLAPW Calculations of .DELTA.E.sub.GB - .DELTA.E.sub.FS
and .DELTA.E.sub.GB Alloying Elements in Fe based Alloys X
.DELTA.E.sub.GB - .DELTA.E.sub.FS (eV/atom) .DELTA.E.sub.GB
(eV/atom) Pd +0.08 -0.90 Mo -0.90 -0.76 Ru -0.65 -0.51 Re -1.31
-0.49 W -1.31 -0.68
[0063] To summarize the calculated FLAPW value
.DELTA.E.sub.GB-.DELTA.E.su- b.FS must preferably be a negative
number if the additive is to be effective as a cohesive material,
and the FLAPW value .DELTA.E.sub.GB must also be negative since it
represents the case with which the additive becomes transported to
the grain boundary. When both numbers are negative in a system,
then enhanced cohesion results. If one or both numbers are
positive, then there is a tendency toward embrittlement.
[0064] The method of the invention provides that a single number or
value (.DELTA.E.sub.B.sup.A), if negative for an additive,
represents a direct cohesion enhancer. The method employs
approximations or inputs of various energy states of the additive
(alloying element) and the matrix material including an energy
value based upon the volume effect of the additive.
[0065] The methodology is effective for any polycrystalline
material and calculations for iron (Fe) and nickel (Ni) are born
out by alternative (first-principles) calculations. The method is
not limited to Fe and Ni alloys, however. Also, the method of the
invention can be viewed as a process for identification of direct
cohesion additives in general, followed by utilization of FLAPW
calculations (See Table 3) to identify the separate .DELTA.E.sub.GB
and .DELTA.E.sub.GB-.DELTA.E.sub.FS calculations which further
identify subsets of additives that are especially effective as
cohesion enhancers and will be easily employed as enhancers because
they are identified as more easily diffused (e.g., tungsten).
EXAMPLES AND EXPERIMENTATION
[0066] A. Alloy Design--General Background
[0067] Alloys consisting of a Fe--Co--Ni martensitic matrix
strengthened by a fine carbide dispersion were studied. These
alloys are secondary hardening because the carbide dispersion can
be changed from a coarse, soft cementite to a fine, hard carbide
upon tempering at a proper temperature for a sufficient time. These
alloys are generally used in applications that require high
strength and toughness. Due to the environment that these alloys
are typically used, resistance to hydrogen embrittlement is also
needed. A flow block diagram describing the interplay between
processing-structure-properties of this class of steel is shown in
the following diagram:
[0068] As shown in FIG. 2.1 the Fe--Co--Ni lath martensitic matrix
is controlled by the solution treatment and tempering of the
material. Nickel additions are made to enhance cleavage resistance.
Cobalt is necessary to maintain a dislocation network by hindering
short-range order recovery. The dislocation forest is necessary to
promote heterogeneous nucleation of M.sub.2C carbides. Strength is
determined by the M.sub.2C carbide dispersion that is controlled by
the tempering process. In addition, the M.sub.2C carbides act as
hydrogen traps which slow hydrogen from degrading grain boundary
cohesion. Coarse carbide dispersions must be avoided because of
their detrimental effect on toughness and to optimize hardness.
[0069] Tempering can also allow an austenite dispersion to form.
This dispersion will soften the alloy due to the inherent softness
of face-centered cubic materials compared to martensite. However,
such dispersions may be desirable because of their beneficial
effects on toughness. Austenite dispersions can enhance toughness
if the dispersion is present in sufficient quantity, has the proper
stability, and has a large dilatation upon transformation from FCC
to BCC.
[0070] Solidification processing, hot working, and solution
treatment will affect grain size. To prevent excessive grain growth
during solution treatment, a grain refining dispersion is designed
in the materials. A desirable grain refining dispersion is stable
during solution treatment and is completely in solution before
melting. Such dispersions will avoid coarse primary carbides while
maintaining a fine dispersion to pin grain boundaries during
solution treatment. In addition, the grain refining dispersion
should have a high cohesive energy with the matrix to inhibit
micro-void nucleation at the interface.
[0071] Refining and deoxidation are processing steps to ensure
grain boundary chemistry. Clean start material and clean processing
will reduce tramp element impurities. In addition, small additions
are added to getter any impurities found in the material. Grain
boundary cohesion enhancers are added to the alloy to counteract
hydrogen embrittlement. These elements segregate to the grain
boundaries during solution and tempering treatments to enhance
grain boundary cohesion.
[0072] B. Martensitic Formation
[0073] The lath martensitic microstructure has the most desirable
combination of strength and toughness of any steel microstructure.
Therefore, it is necessary to maintain a sufficiently high
martensite start (M.sub.S) temperature to ensure a lath martensitic
structure and avoid retained austenite. The martensite
transformation occurs when high temperature austenite (FCC)
transforms to martensite (BCC). Minimum values for the M.sub.S that
ensure complete martensitic transformation upon quenching are
approximately 200.degree. C. As a general rule, alloying elements
act to reduce the M.sub.S temperature. Large amounts of alloying
elements are needed to achieve the desired properties of ultra-high
strength steels.
[0074] Ghosh and Olson have developed a model to predict the
compositional dependence of M.sub.S temperature in steel. Ghosh and
Olson have described the martensitic nucleus interface as a
combination of coherency and anti-coherency dislocations that
provide transformation strain and reduce the strain energy of the
system, respectively. Growth of the nucleus is governed by the
propagation of dislocations into the parent austenite. The motion
of dislocations into the parent austenite is hindered by
microstructural elements in the austenite. Microstructural
obstacles can interact with the long-range stress field and the
interfacial core of the martensite nucleus to hinder nucleus
growth. The interactions with the martensite nucleus must be
overcome by thermal activation and are, thus, highly temperature
dependent. Conversely, the interactions with the long-range stress
field are not temperature dependent. Therefore, the interfacial
frictional work term can be described as the summation of two
terms: a thermal term relating to interactions with the interfacial
core and an athermal term relating to interactions with the long
range stress field.
[0075] The nucleation criterion for martensitic transformation can
be described as the condition where the thermodynamic driving force
of the transformation (FCC.fwdarw.BCC) is equal to a constant plus
the interfacial frictional work term, as shown in the following
equation:
-.DELTA.G.sub.crit=K.sub.1+W.sub..mu.(X.sub.i) 2.1
[0076] -.DELTA.G.sub.crit is equal to the chemical driving force
for diffusionless transformation at a constant temperature. K.sub.1
is a constant that accounts for strain, interfacial energy, and
nucleating defect size. W.mu. is the athermal interfacial
frictional work term. The thermal term of the interfacial
frictional work term is negligible for M.sub.S temperatures greater
than 450 K, those typically found in UHS steels. The composition
dependence of W.mu. is given by the following equation: 32 W = i (
K i X i 1 / 2 ) 2 + j ( K j X j 1 / 2 ) 2 + k ( K k X k 1 / 2 ) 2 +
K Co X Co 1 / 2 2.2
[0077] The K.mu. terms represent values of the solid solution
strengthening coefficient where i=C and N; j=Cr, Mn, Mo, Nb, Si,
Ti, and V; k=Al, Cu, Ni, Re, and W. The values are separated by
their relative strengths. Cobalt is treated separately because it
lowers the interfacial frictional work term.
[0078] Alloying elements will affect the M.sub.S temperature in two
ways. First, alloying additions will change the interfacial
frictional work term as demonstrated above in 2.2 Secondly,
alloying elements will change the chemical driving force for
nucleation, as shown above in equation 2.1.
[0079] C. Carbide Strengthening Dispersion
[0080] The carbide dispersion in UHS steels dominates the strength
of the alloy. The carbide dispersion controls plastic flow via
Orowan dislocation bypass. The strength of the material is
inversely proportional to the mean distance between strengthening
particles. For a given particle volume fraction, finer particles
will yield a smaller spacing between strengthening particles.
However, if the particles are too small, dislocations will shear
the particles instead of looping them. Therefore, the most
desirable particle size is at the transition between particle
shearing and Orowan looping.
[0081] Jack and Jack provide a review of carbides in steel. There
are four stages of it tempering in UHS steels. First stage
tempering results in the formation of iron based epsilon carbides
during quenching or tempering up to 200.degree. C. Second stage
tempering describes the decomposition of retained austenite.
Cementite (Fe.sub.3C) forms during third stage tempering between
250.degree. C. and 450.degree. C. The fourth stage of tempering,
between 450 and 700.degree. C., results in the formation of alloy
carbides (M.sub.2C, M.sub.23C.sub.6, M.sub.6C, and M.sub.7C.sub.3
where M=Cr, Mo, V, and W). The type of carbide found after stage
four tempering depends on the kinetic and thermodynamic stability
of the various carbides.
[0082] The thermal and mechanical history of a UHS steel determines
the nature of the carbide dispersion. The solution treatment and
quench produces a super-saturated lath martensite structure. Prior
to the fourth stage tempering; the carbide that forms is
para-equilibrium cementite The composition of metal sites in
para-equilibrium cementite is equal to the overall alloy
composition because its formation occurs before metal diffusion can
occur. Although this carbide is not the most thermodynamically
stable, it is kinetically favorable because it only requires the
diffusion of carbon. After sufficient time, para-equilibrium
cementite dissolves due to formation of more energetically
favorable carbides as carbide forming elements have time to
diffuse. In an optimal case, all para-equilibrium cementite is
dissolved at the point where peak carbide distribution is achieved.
In practice, however, alloys need to be tempered beyond peak
hardness to dissolve all para-equilibrium cementite. Dissolution of
para-equilibrium cementite is necessary because of its detrimental
effects on toughness.
[0083] Of the carbides that form during stage 4 tempering, the
M.sub.2C is most desirable. M.sub.2C carbides are metastable with
respect to other carbides such as M.sub.6C and M.sub.23C.sub.6.
M.sub.2C nucleates heterogeneously on dislocations, grain
boundaries, lath boundaries, and martensite/cementite interfaces.
This class of steel must maintain a large density of dislocations
during tempering to ensure a fine dispersion of coherent
carbides.
[0084] Langer and Schwartz modeled precipitation at high
supersaturation. They showed that the average particle size is
always close to the critical particle size for growth or
dissolution at high supersaturation. Further, they defined high
supersaturation by the condition:
.delta.W*.ltoreq.10kT 2.3
[0085] where .delta.W* is the work of formation of a critical
nucleus and kT is the Boltzmann factor. At high supersaturation,
the nucleation rate is very high causing the supersaturation to
drop rapidly. Since the critical particle size is inversely
proportional to the degree of supersaturation, the critical
particle size increases greatly during precipitation. The decrease
in supersaturation can cause smaller particles to dissolve because
they are no longer larger than the critical nucleus size. The
competition between nucleating particles and critical nucleus size
inhibits growth of the particle distribution. The average particle
size is initially governed by the nucleation process and smoothly
transitions to a regime governed by coarsening. The growth stage is
bypassed because all the supersaturation is consumed during
nucleation and coarsening. This analysis shows the critical
particle size and coarsening rate as the parameters that control
particle size and, thus, strength. The critical particle size
varies directly with particle/matrix interfacial energy and
inversely with thermodynamic driving force.
[0086] Montgomery, Olson and coworkers have completed a
comprehensive study of M.sub.2C carbide precipitation in AF1410, a
commercially available Co--Ni UHS steel. The alloy was austenized
at 830.degree. C. for one hour and tempered at 510.degree. C. The
following graphs (2.2) present the results from the AF 1410
studies.
[0087] The top graph shows the M.sub.2C carbide particle size
represented as the diameter of a sphere of equal volume to the
rod-shaped carbides. The second plot shows that the aspect ratio of
the carbides increase from 2 to 4 as the carbides evolve from
nucleation to coarsening. The third plot shows the evolution of
particle number density and volume fraction. The plot shows a
smooth transition from nucleation to limited growth to coarsening.
The number density remains constant from approximately 0.5 to 1.0
hr showing that nucleation has been completed and the particles are
growing. From 1.0 hr to 2.0, the number density increases
corresponding to re-nucleation. After re-nucleation, the carbide
size increases due to coarsening. Volume fraction data show that
precipitation is nearly complete after 10 hours. The fourth plot
shows measured lattice parameters of the carbides. Coherency of the
M.sub.2C particles is maintained during early stages of tempering
by carbide composition shifts to reduce the lattice parameter. The
particles are coherent with the matrix up to about 10 hours and
incoherent after 100 hours. The final plot shows the evolution of
hardness. The material is hardest after 0.5 hours, corresponding to
an equivalent particle size of approximately 3 nm.
[0088] Similar studies have been conducted on AerMet100. Aermet100
is a commercially available Co--Ni UHS steel which has superior
properties to AF1410. Yoo, et al. have shown the aspect ratio of
M.sub.2C carbides to be nearly constant at 3:1 during tempering in
AerMet100, as seen in the following graph 2.3.
[0089] Results from a SANS study of the AerMet100 carbide
dispersion, conducted by Jemian are shown in the following graphs
2.4.
[0090] The alloy was tempered at 485.degree. C. up to 20 hours. The
results show similar behavior as those seen in the AF1410 study.
One notable exception is the absence of a re-nucleation stage. The
particle distribution is much finer than that found in AF1410 due
to chemistry changes and lower tempering temperature. In addition,
the carbide volume fraction is greater in AerMet100 compared to
AF1410, accounting for the increase in strength in AerMet100.
[0091] In order to accurately predict carbide evolution, a
multi-component coarsening model is needed to predict tempering
response. Lee has expanded the classical "LSW" binary coarsening
theory to treat multi-component coarsening of shape preserving
particles in a dilute solution matrix. The form of the rate
equation has the same form as that from classical LSW theory, given
in the following equation 2.4. 33 R _ 3 ( t ) - R _ 3 ( 0 ) = 4 9 K
( t - t 0 ) ( 2.4 )
[0092] The rate constant, K, is modified to account for the
multi-component nature of carbide coarsening. Lee applied a model
that is analogous to electrical resistance of series resistors. The
inverse of the rate coefficient is equal to the sum of the inverses
of the individual element rate constants, as shown in the following
two equations 2.5, 2.6 34 1 K = M 1 K M ( 2.5 ) K M = 2 V m B RT ln
( 2 A s ) D M ( k M - k Fe ) ( k M - 1 ) X M 2.6
[0093] In the second equation, .sigma. is the interfacial energy,
V.sub.m.sup.B is the molar volume of the dispersed phase, A.sub.s
is the particle aspect ratio, D is the bulk diffusivity of element
M in BCC iron, k is the partitioning ratio of the various elements,
and X is the mole fraction of element M in the matrix. In this
model, the slowest diffusing element dominates the coarsening
coefficient. The model is to be used as a guide to alloy
design.
[0094] Umantsev approached the problem of multi-component
coarsening in non-dilute solutions using partial derivatives of
chemical potentials with respect to mole fractions to derive his
theory rather than equilibrium partitioning coefficients. This
model addresses a minor error Lee made in assuming equal activities
in both phases at equilibrium. In spite of the differences in the
models, both calculate similar coarsening coefficients.
[0095] Grain Refining Dispersion
[0096] Small additions are added to alloys to form a carbide
dispersion stable during austenization. The dispersion is necessary
to pin grain boundaries and prevent excessive grain growth during
solution treatment was described in general prior to this example.
A small volume fraction of fine particles is optimal, as
illustrated in the following graph 2.5.
[0097] The graph shows the volume fraction of grain refiner needed
at a particular particle size to maintain an average grain size of
10 .mu.m. A volume fraction of large particles needed to maintain
constant grain size is independent of solution temperature whereas
a larger volume fraction of small particles is needed for higher
solution temperatures due to thermally activated de-pinning.
Additions of up to 0.04 wt. % titanium are added to form a
desirable TiC grain refining dispersion. Such additions create
dispersions stable at solution temperatures but soluble below the
melting temperature. It is necessary to avoid primary carbide
formation to ensure a fine distribution of carbides.
[0098] E. Transformation Toughening Strategy
[0099] Work on UHS steels has created a microstructure that is
strong and tough. Improvements in composition and processing have
eliminated previous fracture modes. For instance, brittle cleavage
fracture has been inhibited by the addition of nickel. As one
fracture mode is eliminated through progress, another fracture mode
dominates and limits the uses of the material.
[0100] Low toughness ductile fracture modes have been seen in
nickel containing UHS steels. Garrison has explored the role of
primary inclusions on primary void nucleation and coalescence. The
resistance to primary void formation and coalescence is
proportional to inclusion spacing. Therefore, it is desirable, for
a given volume fraction of inclusion, to have very few, large
particles. Similarly, it is desirable to reduce the volume fraction
of inclusions. Clean processing and tight composition control have
successfully eliminated primary void nucleation as the dominant
fracture mode in UHS steels.
[0101] Shear localization by microvoid nucleation is found to be
one of the dominant fracture modes in clean steels. Microvoids
nucleate on the grain refining dispersion, carbide strengthening
dispersion, prior austenite structure, martensite lath and packet
structure, and the dislocation structure. Studies have shown that
fine particle dispersions with coherent interfaces are optimal for
controlling microvoid nucleation. Inhibiting microvoid nucleation
is difficult in UHS steels due to the microstructure needed to
achieve other properties. The most promising microstructure
modification is achieved by nucleating a transforming austenite
dispersion. Certain austenite dispersions increase toughness by
suppressing microvoid nucleation to higher strain levels
[0102] Leal and Stavehaug examined the use of TRansformation
Induced Plasticity (TRIP) to delay microvoid nucleation in fully
austenitic steels. The flow behavior of TRIP steels is understood
based on the interactions between stress and strain on the
martensitic transformation. Applied stress initiates the
martensitic transformation through the interaction of applied
stress with the transformation strain. This mechanism is called
stress-assisted transformation. A second mechanism for martensitic
transformation is called strain-induced transformation. In this
regime, plastic strain assists the transformation by creating
heterogeneous nucleation sites at the intersections of shear bands.
In the stress-assisted transformation, yielding of the material is
governed by the transformation of the parent austenite and all
initial plastic strain is the result of the transformation. In the
strain-induced transformation, initial yield of the parent
austenite is caused by slip resulting in the formation of
martensite nuclei at the intersection of shear slip bands.
[0103] Olson and Azrin have shown that the boundary between
stress-assisted and strain-induced transformation can be determined
by testing the temperature dependence of yield strength. The
temperature at which transformation mechanism changes is typically
called M.sub.s.sup..sigma. shown qualitatively in the following
graph 2.6.
[0104] Below M.sub.s.sup..sigma. the transformation-controlled
yield stress rises because the stability of the parent austenite
increases as temperature rises and more stress is required for
transformation. Above M.sub.s.sup..sigma., the slip-controlled
yield stress decreases because of thermal activation of dislocation
motion.
[0105] Control of the austenite stability is critical to achieving
optimal transformation toughening. Leal and Stavehaug demonstrated
that the optimal toughening enhancement occurs at the
M.sub.s.sup..sigma. temperature for the crack-tip stress state.
Leal controlled the stability of the austenite by varying test
temperatures. Stavehaug conducted similar experiments controlling
austenite stability by varying composition, as seen in the
following graph 2.7;
[0106] The driving force for transformation at the crack-tip is
compared to the driving force at M.sub.s.sup..sigma.. Stavehaug
showed that toughening enhancements up to a factor of 5, compared
to non-transforming austenite, were achieved when the crack-tip
driving force equaled that at M.sub.s.sup..sigma..
[0107] Haidemenopolous explored the effect of austenite dispersions
on toughness in two martensitic steels. He examined the effect of
retained austenite in 4340 steel. No toughening enhancement was
seen due to insufficient austenite stability. The
M.sub.s.sup..sigma. was estimated to be approximately 150.degree.
C. for the crack-tip stress state so no toughening was observed at
room temperature tests. No tests were conducted near the
M.sub.s.sup..sigma. due to its proximity to the tempering
temperature.
[0108] Haidemenopolous studied the effects of a precipitated
austenite phase in AF1410. He determined that austenite dispersions
could be stabilized by composition enrichment and size refinement.
ThermoCalc calculations predicted an austenite dispersion nucleated
at 510.degree. C. would have adequate stability to provide a
toughening enhancement at room temperature. Contrary to
expectations, no toughening enhancement was seen in AF1410 after
tempering at 510.degree. C. for 8 hours. A non-equilibrium
interlath austenite was found in the material instead of the
predicted austenite dispersion. The interlath austenite lacked the
needed stability because of its coarse size (.about.200 nm films)
and composition. The composition of the interlath austenite was
Fe-14Ni-13.2Co-2.8Cr-1Mo compared to the calculated equilibrium
composition of Fe-38.5Ni-4.1Co-1Cr-0.25Mo. The lack of nickel in
the interlath austenite is the primary reason the austenite was too
unstable at room temperature.
[0109] Haidemenopolous was successful in achieving a toughening
enhancement in AF1410 by altering the heat treatment. A two-stage
heat treatment consisting of a brief high temperature step (15
minutes at 600.degree. C.) followed by normal temperature step (8
hours at 510.degree. C.) was used. Analysis of the austenite
dispersion revealed fine particles (.about.20 nm) of composition
Fe-29.1Ni-10.5Co-4.2Cr-1.9Mo- . Toughness of the two-stage
condition was 40% higher than the normal condition at equivalent
strength levels.
[0110] Haidemenopolous applied the Olson-Cohen classical
heterogeneous martensitic model to describe the transformation of
the austenite particles. The result of this approach is given in
the following equation 2.7:
.DELTA.G.sup.Ch+W.sub.f=-[f(1nV.sub.p).sup.-1+.DELTA.G.sup..sigma.+E.sup.S-
tr] (2.7)
[0111] .DELTA.G.sup.Ch is the transformation chemical free energy
and W.sub.f is the athermal frictional work term mentioned in
section 2.2. .DELTA.G.sup.Ch is temperature and composition
dependent while W.sub.f is composition dependent. It is important
to note that W.sub.f will vary with tempering temperature due to
changes in the austenite composition. The first term on the right
side of the equation accounts for the particle size, defined by
particle volume V.sub.p, effect on stability. .DELTA.G.sup..sigma.
is set by the stress state and E.sup.str is elastic strain energy
per unit volume associated with the semi-coherent nucleus
structure. The optimal austenite dispersion for a given set of
conditions or optimum service temperature for a given austenite
dispersion can be determined from this relationship.
[0112] Kuehmann conducted a study to thermally optimize AF1410,
AerMet100, and a series of experimental alloys designated MTL.
Multi-step tempering treatments were performed on all alloys in an
attempt to nucleate a toughness enhancing austenite dispersion.
Kuehtnann was unable to achieve high toughening enhancements in
AF1410 due to the poor cleanliness of the particular heat.
Toughness enhancements of 15-20% were seen in overaged AerMet100.
Unfortunately, the high temperature short temper overaged the
carbide strengthening dispersion and resulted in unacceptable
decreases in hardness. Based on these results, Kuehmann determined
that a ratio of austenite/carbide kinetics must be maintained to
ensure proper microstructure. Carbide kinetics were reduced in two
MTL alloys providing a kinetically favorable situation for both
carbide and austenite dispersions. However, tramp element impurity
segregation during tempering degraded grain boundary cohesion to
the point where the fracture mode changed from ductile fracture to
brittle intergranular fracture. No toughening enhancement was then
seen due to the change in fracture modes.
[0113] In addition to controlling austenite stability, it is
desirable to maximize the volume change of transformation from
austenite to martensite. While data is limited, Young has shown
that the transformation toughening efficiency is proportional to
the transformation volume change to the third power, as shown in
the following graph 2.8.
[0114] This graph shows the toughening increment as a function of
the relative volume change. The two curves represent two levels of
hardness difference between austenite and martensite. The
difference in the two curves shows that the toughening effect due
to strain hardening is minor compared to that from the
transformation volume change. Based on this result, an expression
for the toughening efficiency parameter (TEP) for dispersed
austenite is given in the following equation 2.8. 35 TEP = V f ( V
V ) 3 ( 2.8 )
[0115] V.sub.f is the volume fraction of austenite present and
.DELTA.V/V is the relative volume change. The relative volume
change is related to the lattice parameters of the BCC and FCC
phase by the following equation 2.9: 36 V V = 2 [ BCC FCC ] - 1 (
2.9 )
[0116] Models to predict the composition dependence of the FCC and
BCC lattice parameters have been developed. Ghosh has developed a
model using known lattice parameters to predict the BCC lattice
parameter at room temperature. The following equation 2.10 gives
the model based on least squares fitting and linear superposition
of Fe--X (X=C, Co, Cr, Mo, and Ni) binary systems. 37 BCC ( nm ) =
0.34906 X C + 0.28258 X Co + 0.28847 X Cr + 0.28665 X Fe + 0.31417
X Mo + 0.27801 X Ni + X Co X Fe [ 0.00346 - 0.00269 ( X Co - X Fe )
] + X Cr X Fe [ 0.00024 - 0.00224 ( X Cr - X Fe ) ] + 0.00757 X Fe
X Mo + X Fe X Ni [ 0.00778 + 0.00743 ( X Fe - X Ni ) ] ( 2.10 )
[0117] The model expresses the lattice parameter in nm as a
function of the mole fraction of each element.
[0118] Prediction of the FCC lattice parameter is more difficult
due to strongly non-linear compositional dependence arising from
the INVAR magnetic anomaly in FCC Fe.
[0119] The INVAR effect is problematic because the FCC lattice
parameter is non-monotonic with its maximum near the composition of
the austenite particles in the Co--Ni martensitic steels of
interest. The effect will reduce the transformation dilatancy of
the austenite and, therefore, the transformation toughening
efficiency. The INVAR effect manifests itself in abnormal
thermodynamic, magnetic, and thermal expansion behavior in certain
alloys. Well-studied alloying elements that cause INVAR anomalies
are nickel, palladium, and platinum
[0120] The two-gamma states model assumes that there are two
distinct magnetic states of FCC Fe. The two states have different
thermodynamic quantities, magnetic moments, and atomic volumes.
Applying the two-gamma states description of the INVAR effect is
advantageous to predicting the FCC lattice parameter. The
mathematical formalism can be extended to multi-component alloys
using the thermodynamic model developed by Miodownik and Hillert.
In addition, many binary and ternary iron based alloys have been
modeled using the two-gamma states framework
[0121] The INVAR anomaly is described by the relative amount of
iron atoms in each state. The relative amounts of iron atoms in
each state vary as composition or temperature are changed. The
variations in iron atom distribution result in the unconventional
physical properties. While the iron atom distribution is in dynamic
equilibrium, a Schottky two-level excitation model can be used to
describe the relative population of each state, as shown in the
following equation 2.11. 38 f 1 f 2 = g 1 g 2 exp ( - E k T ) (
2.11 )
[0122] The fractions of elements in each state are given by f.sub.1
and f.sub.2, g.sub.1 and g.sub.2 are the degeneracies of each
state, .DELTA.E is the energy difference between each state, and kT
is the Boltzman factor. The energy difference between states does
not vary with temperature but is dependent on composition.
Miodownik determined the cobalt and chromium effects on the energy
difference while Kuehmann modeled the effect of nickel using
Redlich-Kister polynomials, as shown in the following two graphs
2.9 and 2.10.
[0123] Kuehmann described the degeneracy in a functional form that
accounts for the transition due to magnetic effects, expressed in
the following equation 2.12. 39 g 1 g 2 = A + B 2 - A - B 2 tanh [
D ( T T C - 1 ) ] ( 2.12 )
[0124] A is a fitting parameter above the Curie point, B is a
fitting parameter below the Curie 1 point, D is related to the
sharpness of the transition, and T.sub.C is the Curie point. Using
existing room temperature and high temperature data Kuehmann found
values of A=1.05, B=3.10, and D=1.0 best fit the data. The
following graph 2.11 presents the value of the degeneracy ratio
from Kuehmann's model.
[0125] The following equation 2.13 presents Kuehmann's model for
predicting FCC lattice parameters in Fe--Co--Cr--Ni systems.
.alpha..sub.FCC=(f.sub.1.alpha..sub..gamma..sub..sub.1+f.sub.2.alpha..gamm-
a..sub..sub.2)X.sub.Fe+X.sub.Co.alpha..sub.Co+X.sub.Cr.alpha..sub.Cr+X.sub-
.Ni.alpha..sub.Ni (2.13)
[0126] The values of f.sub.1 and f.sub.2 are described by the two
equations preceding the above equation with the added constraint
that f.sub.1 and f.sub.2=1. The following Table 3 presents
properties of each state extrapolated from alloy data to the pure
state.
4TABLE 3 Properties of the two gamma states FCC Fe Room Temperature
Magnetic Moment Nel or Curie State Lattice Parameter (.ANG.) per
Atom (.mu..sub.B) Temperature (K) .gamma.1 3.57 .+-. 0.01 0.5 80
.gamma.2 3.64 .+-. 0.01 2.8 1800
[0127] Cullity presented room temperature FCC lattice parameters of
cobalt and nickel as 3.5440 .ANG. and 3.5239 .ANG., respectively.
The FCC Cr lattice parameter is inferred from high temperature
Fe--Cr--Ni ternary data as 3.57 .ANG.. The Cr FCC lattice parameter
must be inferred because chromium is not stable in the FCC crystal
structure.
[0128] F. Thermodynamic Calculations
[0129] ThermoCalc is a thermodynamic database and calculation
package developed at the Royal Institute of Technology in
Stockholm, Sweden The database is comprised of information from
binary, ternary, and quaternary systems used to extrapolate to
higher order systems. The Scientific Group Thermodata Europe (SGTE)
database, included with ThermoCalc, contains data on more than 2000
condensed compounds. Solution temperature calculations used the
SGTE database.
[0130] Two databases, developed by the Steel Research Group at
Northwestern University, were used in the alloy designs. The MART4
database is a fourth generation database used to calculate
martensite start temperature. The database includes modified low
temperature thermodynamic parameters for FCC and BCC phases for
iron based systems. The database modifications are used to
accurately predict martensite start temperature because the
parameters in the SGTE database are based on high temperature data.
The COHERENT3 database is used to predict the tempering response of
the ultra-high strength steels. The database includes elasticity
energy for coherent M.sub.2C carbides with an aspect ratio of
3.
[0131] C. Grain Boundary
[0132] The fracture resistance of ultra-high strength steels is
greatly reduced in an aqueous environment due to hydrogen-assisted
cracking. Toughness reductions of up to 80% are possible due to the
transition of fracture mode from ductile to intergranular a
brittle. The transition to intergranular fracture is promoted by
impurity segregation to grain boundaries.
[0133] Rice and coworkers developed a theoretical model describing
the effect of grain boundary segregation on intergranular fracture.
Their model postulates that embrittlement arises from a competition
between crack tip blunting via dislocation emission and interfacial
cleavage. According to this model, crack extension by dislocation
emission will happen if the work for dislocation emission,
G.sub.dis1, is less than the Griffith work for intergranular
fracture, 2.gamma..sub.int. Ductile fracture is observed if
G.sub.dis1 is less than 2.gamma..sub.int while brittle fracture is
seen if 2.gamma..sub.int is less. The crack extension force,
G.sub.dis1, is set by the strength of the material. However, the
intergranular Griffith work term can be altered by the composition
of the grain boundary, as described by the following equation
3.1
2.gamma..sub.int=(2.gamma..sub.int).sub.0-(.DELTA.g.sub.b-.DELTA.g.sub.s).-
GAMMA. (3.1)
[0134] Equation 3.1 shows that the Griffith work is modified from
an inherent value associated with the "clean boundary" by the,
solute concentration, .GAMMA., on the boundary. The embrittling
effect of the solute, .DELTA.g.sub.b-.DELTA.g.sub.s, is the
difference in segregation free energy of a solute atom on the grain
boundary and free surface. If a solute atom has a lower free energy
on the free surface compared to the grain boundary, the solute will
reduce the Griffith work term and increase susceptibility to
intergranular fracture. Conversely, it is possible to increase
resistance to intergranular fracture by segregating a solute that
has lower free energy on the grain boundary compared to the free
surface. For equilibrium at a temperature T, the equilibrium
concentration, .GAMMA., of a solute is given in the following
equation 3.2: 40 0 - = X bulk exp ( - g b R T ) ( 3.2 )
[0135] where .GAMMA..sup.0 is the number of sites at the grain
boundary, X.sub.bulk is the content of the solute in the bulk, and
.DELTA.g.sub.b is the grain boundary segregation energy of the
solute. Since grain boundary segregation involves the transport of
solute to the boundary, equilibrium may not be reached and kinetics
must be considered. Equation 3.3 gives the concentration on the
boundary as a function of time, as modeled by McLean 41 t - X bulk
- X bulk = 1 - exp ( 2 D t d ) 2 erfc ( 2 D t d ) ( 3.3 )
[0136] .GAMMA..sub.t is the concentration at time t, and r is the
equilibrium solute segregation at a given temperature, defined by
equation 3.2. D is the diffusivity of the solute at the temperature
of interest while d is the interplanar spacing. Finally, .alpha. is
the ratio of equilibrium grain boundary concentration to the bulk
concentration.
[0137] Combination of equations 3.2 and 3.3 make it possible to
predict the grain boundary concentration after processing. Lower
temperatures promote grain boundary segregation by increasing the
thermodynamic driving force for segregation. However, kinetics is
reduced as temperature is lowered because of slower diffusivity.
Therefore, grain boundary concentration exhibits a C-curve behavior
when plotted as a function of time and temperature. A temperature,
thus, exists where kinetic and thermodynamic effects are balanced
to maximize grain boundary segregation at a given time.
[0138] H. Grain Boundary
[0139] Many studies have examined the effects of specific solutes
on grain boundary cohesion. It is well known that elements, such as
phosphorus, tin, sulfur, and antimony segregate to grain boundaries
and degrade the cohesion of the grain boundaries [58]. Segregation
is commonly measured by Auger electron micro-analysis that requires
intergranular fracture in ultra-high vacuum. Boundary
concentrations are compared to bulk concentrations to determine the
partitioning ratio. Determining the bulk concentration and boundary
concentration make it possible to calculate the free energy of
segregation for a given temperature. There are discrepancies
between data from different researchers, in part, because of
different Auger data conversion methods. The segregation energy of
phosphorus in iron at 500.degree. C. is calculated to be
approximately -50 kJ/mol based on data from Erhart and Grabke
whereas, the segregation energy at 480.degree. C. is calculated to
be approximately -38 kJ/mol based on data from YuQing and McMahon.
Briant determined the segregation enthalpy to be approximately
-51.5 kJ/mol. Temperature dependence of the segregation free energy
can be described by adding the segregation entropy term. The
estimated segregation entropy term is between 0.02-0.03
kJ/molK.
[0140] Control of sulfur and phosphorus content is very important
in ultra-high strength steels. The Griffith work term for brittle
fracture is reduced by 10% if phosphorus atoms occupy 25% of grain
boundary sites. Reductions of the Griffith work term of 30% are
possible if sulfur occupies one quarter of the grain boundary.
Although many processing improvements have been made to increase
the cleanliness of melts, it is desirable to reduce the amount of
sulfur and phosphorus on grain boundaries to zero. Adding elements
that form stable compounds with the impurities can further reduce
bulk concentrations of impurity elements. Additions of manganese
will form sulfides and reduce sulfur segregation to grain
boundaries. Recent research has shown stable lanthanum oxy-sulfides
and lanthanum phosphate compounds to form in rapidly solidified
steels.
[0141] Equilibrium segregation can increase as temperature is
increased The abnormal behavior arises from an increase in bulk
concentration due to dissolution of second phase particles. Going
to more stable compounds such as the lanthanum oxysulfide,
La.sub.2O.sub.2S, minimizes this effect.
[0142] A second way to reduce grain boundary impurity concentration
is by site competition. Since there are a finite number of grain
boundary sites, elemental additions can reduce the concentration of
phosphorus and sulfur on the boundary by reducing the number of
available sites. The beneficial effects of certain elements are
two-fold because they provide a direct cohesion enhancement and
limit phosphorus and sulfur concentrations. Carbon has been shown
to compete with sulfur and phosphorus for grain boundary sites. In
addition, carbon provides a direct cohesion enhancement
[0143] The segregation free energy of carbon at 800.degree. C. is
approximately -80 kJ/mol. The necessity of carbon is apparent when
one considers a common technique for inducing intergranular
fracture is decarburizing samples in hydrogen gas,
[0144] Liu and coworkers have examined the effects of boron on
grain boundary segregation in high purity Fe--P alloys. Samples
with bulk composition up to 5.4 ppm boron showed no boron grain
boundary segregation and phosphorus grain boundary concentration
remained constant. The concentration of dissolved boron is strongly
dependent on the presence of carbon, nitrogen, and oxygen. The
impurity levels in the alloys tested were sufficient to trap all
boron, thus, reducing the effect bulk boron composition to zero.
Alloys with boron concentration between 5.4 and 12.5 wt. ppm showed
a decrease in phosphorus grain boundary concentration and an
increase in boron grain boundary concentration. Maximum boron
segregation, corresponding to minimum phosphorus segregation, was
seen at 12.5 wt. ppm boron concentration. Quantities greater than
12.5 wt. ppm did not show added benefits due to formation of
borides in the alloys. Liu and coworkers determined the segregation
free energy of boron to be approximately -100 kJ/mol at 800.degree.
C. This value is significantly higher than that of carbon.
[0145] Intergranular fracture was suppressed in all samples
exhibiting boron segregation. Improvements to intergranular
fracture were quantified by decreases in the intergranular ductile
to brittle transformation temperature (DBTT). Two mechanisms are
responsible for the reduction in DBTT. DBTT is reduced by the
exchange of boron for phosphorus on the grain boundaries due to
site competition. The reductions in DBTT are too great to be solely
due to benefits from site competition. A direct grain boundary
cohesion effect of boron is partly responsible for the improved
fracture properties. Liu and coworkers concluded that the cohesion
enhancing effect of boron is the predominant reason intergranular
fracture was suppressed.
[0146] In an effort to fully understand the embrittling effects of
alloying additions, first principles full-potential linearized
augmented plane-wave method (FLAPW) calculations have been
performed. Initial calculations examined the effect of phosphorus
and boron impurities on the Fe.SIGMA.3[110]( 111) grain boundary
and the corresponding Fe(111) free surface. shows a schematic of
the Fe.crclbar.3 grain boundary used in the calculation.
[0147] substitutional grain boundary sites labeled #1, and
interstitial sites are designated by the small, solid atom.
[0148] The difference in energy between the two structures,
.DELTA.E.sub.b-.DELTA.E.sub.s, was calculated to determine the
embrittling effect. In the case of phosphorus,
.DELTA.E.sub.b-.DELTA.E.su- b.s was found to be +0.79 ev/atom,
which is in good agreement with experimental data. The same study
found boron to be a slight cohesion enhancer. Since the first
principles calculations are demonstrated to predict embrittling
effects accurately, more systems of interest have been examined.
Experimental results show qualitatively that carbon is a cohesion
enhancing element. The first qualitative theoretical determination
of the cohesion enhancing effect of C was found to be
.DELTA.E.sub.b-.DELTA.E.sub.s=-0.61 ev/atom by first principles
calculations. Re-optimized structure calculations of the Fe--B
system have found the enhancing effect of boron to be
.DELTA.E.sub.b-.DELTA.E.su- b.s=-1.30 ev/atom. Based on these
results, boron is approximately twice as effective as carbon for
cohesion enhancement.
[0149] Most research on grain boundary embrittlement has focused on
the effect of impurities. The impurity atoms typically occupy
interstitial sites. Recently, work has examined the alloying
effects of transition metals on grain boundary cohesion. Transition
metal segregation is different from impurity segregation because
the metal atoms occupy substitutional sites, instead of
interstitial sites. Advanced FLAPW calculations have examined the
effect of substitutional segregation of molybdenum and palladium on
grain boundary cohesion in the Fe.crclbar.3(111) grain boundary
[70]. Molybdenum was found to be an effective cohesion enhancer
(.DELTA.E.sub.b-.DELTA.E.sub.s=-0.90 ev/atom) primarily due to its
strong bonding characteristics arising from its half-filled d band.
Conversely, palladium was found to be a mild embrittler
(.DELTA.E.sub.b-.DELTA.E.sub.s=+0.08 ev/atom) due to its weak
bonding capability associated with its full d band. A model, based
on the first-principles calculations of molybdenum and palladium,
has been proposed to predict the alloying effect on grain boundary
cohesion without carrying out complex first-principles
calculations, for each case. Once the atomic structure of the clean
grain boundary is determined, the embrittling potency can be
predicted with simple inputs of "handbook" properties of the
alloying element and matrix. Model predictions of the embrittling
effect of metal alloy additions on the Fe.SIGMA.3(111 ) grain
boundary are shown in the following graph (3.2) which is the
teaching set forth prior to the examples herein:
[0150] Tungsten and rhenium are the most effective cohesion
enhancing elements. Cobalt, an important alloying element, is
predicted to be a weak embrittler. In order to test the accuracy of
the model, first-principles calculations were conducted for cobalt,
rhenium, ruthenium, palladium, and tungsten and compared to the
values from the simple model prediction, as shown in the following
Table 4:
5TABLE 4 Predicted embrittling effects and segregation enthalpies
from quantum mechanics calculations. Grain Boundary Embrittling
Effect Embrittling Effect Segregation (Model Prediction) (1.sup.st
Principles Calc.) Enthalpy Element (ev/atom) (ev/atom) (ev/atom) Co
+0.10 +0.05 Mo -0.96 -0.90 -0.76 Pd -0.03 +0.08 -0.90 Re -1.29
-1.31 -0.49 Ru -0.77 -0.65 -0.51 W -1.54 -1.31 -0.68
[0151] The largest discrepancy is 0.23 ev/atom in the case of
tungsten. Based on these results, the model is effective in
predicting the effect of transition metal alloying elements on
grain boundary cohesion.
[0152] Grain boundary segregation enthalpies relative to the bulk
solution were also determined from first-principles calculations as
shown in the above. Of elements that will act as significant
cohesion enhancers, molybdenum has the highest segregation energy
while rhenium has the lowest. From this information, one predicts
that molybdenum will have the greatest driving force for
segregation and displace other atoms, such as rhenium, that have
lower segregation energies.
[0153] I. Grain Boundary--Multi-Component Grain Boundary Cohesion
Model
[0154] A dynamic model to predict the grain boundary cohesion of
multi-component alloys has been developed integrating the results
of the first-principles calculations and prior research. A grain
boundary cohesion model is desired in the design of material
susceptible to hydrogen-assisted stress corrosion cracking. The
model is able to predict total grain boundary cohesion by summing
the effects of substitutional and interstitial atoms. In addition,
the model is able to predict cohesion enhancement in
non-equilibrium conditions by including kinetic parameters.
Modeling the grain boundary with a two-site sub-lattice model
separates substitutional and interstitial segregation. Simply
stated, all elements that segregate to substitutional sites are
treated separately from elements that segregate to interstitial
sites. A system of equations, similar to the above equations, is
used to predict the equilibrium composition of multi-component
systems, as expressed in the following equation 3.4: 42 i 1 - i i =
X bulk i exp ( - G R T ) ( 3.4 )
[0155] Equation 3.4 accounts for site competition by multiple
species and will be identical to equation 3.2 if only one element
segregates. For the interstitial case, i=B, C, P, and S. A second
system of equations, identical to equation 3.4, is solved for the
substitutional elements. For the substitutional case, i=Mo, Re, and
W.
[0156] Equation 3.4 can also account for any "co-segregation."
Co-segregation is described as one segregant attracting (or
repelling) another segregant to the grain boundary. A non-metal
atom may be attracted to dissolved metal atoms and form compounds
at the interface. This was first described for grain boundary
segregation by Guttman and recently applied to surface segregation.
Inclusion of co-segregation effects into the grain boundary model
can be accomplished by viewing the attraction (or repulsion)
effects as modifying the segregation free energy, as described in
equation 3.5. 43 G = G 0 + i i i ( 3.5 )
[0157] .alpha. is a binary interaction parameter between
segregants, .GAMMA..sub.i is the same as above, and .DELTA.G.sub.0
I is the inherent segregation energy of the component of interest.
Higher order interaction parameters could be added to equation 3.3
if necessary. Guttman originally assumed identical parameters as
the bulk solution, but the predicted degree of co-segregation is
not supported by experiment. Misra and Rama Rao found that
segregation energies of carbon and phosphorus in a multi-component
alloy were nearly the same as those found in simple binary alloys.
Based on the results from Misra and Rama Rao and the lack of strong
co-segregation observations, it is apparent that segregation energy
data determined from simple binary systems is sufficient and no
interaction parameters are needed to reasonably predict grain
boundary segregation.
[0158] The system of equations presented by equation 3.4 describes
the equilibrium grain boundary composition, but does not address
kinetics. Slow diffusers, such as tungsten, will not reach
equilibrium during normal tempering treatments. No diffusivity
information is available for rhenium in iron, but it is assumed
that the diffusivity is similar to that of tungsten. Some
enrichment of molybdenum will occur during tempering. Equation 3.3
is incorporated into the model to add kinetic parameters for each
solute in order to predict the grain boundary segregation during
tempering.
[0159] Segregation during solution treatment must be addressed
because substitutional segregation can only achieve equilibrium
quantities at high temperatures. Description of interstitial
segregation dynamics during solution treatment is not essential
because near equilibrium conditions will be reached during
tempering. FLAPW calculations of grain boundary segregation
enthalpy in FCC iron have been limited to tungsten and found to be
0.80 ev/atom. Table 5 summarizes all data used in the grain
boundary cohesion model.
6TABLE 5 Grain boundary cohesion model data. BCC BCC Segregation
Cohesion Diffusivity Energy, .DELTA.G Enhancement (.DELTA.g.sub.b -
.DELTA.g.sub.s) (cm.sup.2/sec) (J/mol) (J/m.sup.2 * monolayer) B
-75,000 - 25T -1.463 C -55,000 - 25T -0.686 P 1.38e5 exp -34,300 -
21.5T +0.214 (-332,000/RT) S 34.6 exp -51,500 - 25T +0.99
(-231,500/RT) Mo 0.44 exp -73,203 - 25T -1.013 (-238,000/RT) Re 25
exp -47,197 - 25T -1.474 (-298,000/RT) W 25 exp -65,495 - 25T
-1.474 (-298,000/RT)
[0160] The grain boundary cohesion model predicts the improvement
in the Griffith work term, shown in equation 3.1. Spaulding has
measured experimentally the effect of grain boundary cohesion on
fracture strength in the Ni--Co secondary hardening steels
considered here. Graph3.3 shows the effect of the Griffith work
term on fracture strength at various steel hardness levels.
[0161] It is important to note that more negative values of
Griffith work are superior. In addition, the figure shows that
improvements in grain boundary cohesion are needed to maintain
constant fracture strength as hardness is increased. levels of
approximately 16,000 J/mol for the M.sub.2C phase and 1,100 J/mol
for the FCC phase. Based on this model, all design calculations
here will include capillary energy additions in order to more
accurately predict non-equilibrium alloy microstructure which arise
from standard tempering practices.
[0162] J. The Alloys Tested
[0163] The objective of this design is an ultra-high strength alloy
with enhanced toughness and superior hydrogen resistance. The
desired microstructure is a fully martensitic, M.sub.2C carbide
strengthened steel with a fine austenite dispersion. In addition,
superior grain boundary cohesion enhancement is desired to limit
impurity embrittlement. Properties of the design alloy include
hardness levels greater than HRc 57, corresponding to an ultimate
tensile strength greater than 325 ksi, fracture toughness of 75
ksi{square root}in, and K.sub.ISCC/K.sub.IC=0.5.
[0164] The alloy design optimizes composition by considering
M.sub.s temperature, carbide fraction, austenite dispersion, and
grain boundary cohesion. In order to achieve a fully martensitic
microstructure, the M.sub.s temperature is required to be at least
220.degree. C., matching the M.sub.s of AerMet100.
[0165] Calculations, including capillary energy, of AerMet100
tempered at 455.degree. C. predict a carbide fraction of 0.0277 and
grain boundary cohesion enhancement of 1.656 J/m.sup.2.
[0166] The carbon content of alloys is 0.25 wt. % that provides
sufficient M.sub.2C carbide fraction. vanadium and molybdenum
contents are fixed at 0.11 wt. % and 1.5 wt. %, respectively, to
ensure high carbide volume fraction. Vanadium additions are limited
by increases in solution temperature arising from the stability of
VC carbides. Molybdenum content is set by constraints on
segregation during processing. Chromium is added to ensure a
minimum 2:1 mole ratio of carbide forming elements to carbon. In
addition, tungsten additions enhance M.sub.2C carbide formation.
Limits on tungsten are set by dissolution of M.sub.6C during
solution treatment. Carbide fraction calculations with capillary
energy corresponding to peak hardness microstructure, where
M.sub.2C particle size is equal to 3 nm, are used.
[0167] Tungsten and rhenium are added to enhance grain boundary
cohesion beyond levels found in AerMet100. Grain boundary cohesion
in AerMet100 is due to the segregation of molybdenum and carbon to
the grain boundaries. Rhenium and tungsten are considered because
they have the greatest enhancing effect. Rhenium is considered
because of its high solubility in BCC at tempering temperatures.
Tungsten has low solubility in BCC because of its high carbide
formation driving force. Molybdenum additions are necessary to
saturate all substitutional grain boundary sites, as additions of
tungsten and rhenium will not fill all sites. Carbon segregation
can be reduced if large quantities of carbide forming elements are
present, thus reducing its BCC solubility. Additions of boron can
replace carbon on the boundary and provide greater cohesion
enhancement. However, control of boron composition between heats is
difficult because of its low solubility in iron. Excess additions
of boron can form deleterious borides while a shortage of boron
will not provide any segregation. The window of boron composition
is between 5 and 15 ppm.
[0168] Since substitutional segregation does not reach equilibrium
conditions during tempering, tempering time is incorporated into
the design to more accurately predict grain boundary segregation.
Kuehmann and Olson have examined the correlation between
precipitation half-completion time and the coarsening rate constant
evaluated at half-completion. The half-completion coarsening rate
constant is calculated from the thermodynamic properties, using the
Lee model discussed previously the carbide fraction is half of the
equilibrium value. The study examined a number of different 0.24
wt. % carbon alloys tempered at 510.degree. C. and found the values
to be correlated over two decades, as shown in the following graph
4.4:
[0169] The austenite dispersion must have sufficient stability and
proper formation kinetics to ensure optimum toughening enhancement.
After satisfying primary considerations, toughening efficiency is
maximized by optimizing dilatancy and austenite fraction. The
stability of the austenite particle is related to its size and
composition. Size is controlled by matching the ratio of austenite
to carbide kinetic rate constants to that of prior alloys. The
austenite rate constant is normalized by the carbide rate constant
to predict final austenite precipitate size to final carbide size.
Kinetic parameters are determined by calculating the Lee coarsening
rate constants, shown in equations 2.5 and 2.6, for the predicted
three-phase microstructure including capillary energy. The ratio of
austenite to carbide rate constants of AerMet100 at 455.degree. C.
is calculated to be 3.6. Similar calculations for AF1410 tempered
at 510.degree. C. predicted a rate constant ratio of approximately
5. Since both conditions produced successful transformation
toughened alloys, the target kinetic ratio is between 3 and 6.
[0170] The composition dependence of austenite stability is
manifest in a chemical and mechanical term. The chemical term-is
evaluated by determining the difference in free energy between FCC
and BCC at service temperature, generally room temperature. The
composition used is determined from a three-phase calculation
incorporating capillary energy at the tempering temperature. The
mechanical term is identical to the athermal frictional work of
interfacial motion represented by equation 2.2. The calculated
austenite stability of AerMet100 tempered at 455.degree. C. is 6.37
kJ/mol. It is important to note that equilibrium three-phase
calculations predict a value of 4.35 kJ/mol. The large difference
arises from the inclusion of capillary energy. Prior designs set a
target of an increase in austenite stability of 0.5 kJ/mol to
account for the increased strength level. The target austenite
stability of the design alloy will have a lower bound of 6.87
kJ/mol, maintaining the same increment as prior designs. An upper
bound will be set at 7.25 kJ/mol maintaining a constant percentage
increase in austenite stability as the prior designs.
[0171] The alloy uses the constraints presented previously to fix
the alloy composition as Fe--Co--Cr--Ni--W-1.5Mo-1.5Re-0.11V-0.25C.
Initial calculations examine two levels of chromium and tungsten
content and 4 levels of cobalt to determine the effect on austenite
stability, grain boundary cohesion, carbide fraction, and kinetics.
Chromium content varies between 2 wt. % and 3 wt. %, tungsten
content varies between 0.5 wt. % and 1.5 wt. %, and cobalt varies
between 15 wt. % and 21 wt. %. Nickel content for each alloy
composition is set by the M.sub.s temperature constraint. All
three-phase calculations were performed at 455.degree. C. with
capillary energy additions of 16,000 J/mol for M.sub.2C and 1,100
J/mol for FCC using the COHERENT3 database.
[0172] Graph 4.7 shows the alloy nickel content vs. cobalt content
for each series of alloys that results in an M.sub.s temperature of
220.degree. C.
[0173] The calculations were performed using the MART4 database
with an accuracy of .+-.25.degree. C. for this class of steel.
Increases in cobalt content allow higher nickel contents.
Reductions of chromium from 3 wt. % to 2 wt. % allow an increase of
approximately 1.5 wt. % nickel. Nickel content increases
approximately 0.5 wt. % as tungsten is reduced from 1.5 wt. % to
0.5 wt. %.
[0174] Austenite stability is determined by summing the chemical
free energy term and a thermal frictional work term, as shown in
Graph 4.8.
[0175] Nickel partitions strongly to FCC and acts as an FCC
stabilizer. Cobalt has no direct effect on FCC stability but
increases in cobalt will yield more stable austenite due to the
higher nickel content of the alloys. While a large percentage of
chromium is expected to partition to the M.sub.2C, some of the
excess chromium will partition to the FCC and decrease the chemical
stability of FCC relative to BCC. Tungsten behaves in a similar
manner as chromium but its effect is much milder. At high cobalt
content, the 3 wt. % chromium series has slightly higher stability
compared to the 2 wt. % series. While this result is unexpected, it
can be explained by examining each component of the austenite
stability, as shown in Graphs 4.9 and 4.10.
[0176] The athermal frictional work term decreases as cobalt
increases for both of the 2 wt. % chromium series. As cobalt
content increases, the M.sub.2C fraction increases and consumes
more chromium. The effect is not seen at higher chromium levels
because M.sub.2C fraction is maximized for all cobalt contents.
Graph 4.11 shows the carbide fraction of each series.
[0177] In order to improve stress-corrosion cracking resistance,
the design alloy must have greater grain boundary cohesion than
that of AerMet100. Grain boundary cohesion was calculated for each
design series in two manners. Graph 4.12 shows the predicted grain
boundary cohesion without boron additions and graph 4.13 shows
predictions when 10 ppm boron is added. All calculations assumed
sulfur content to be 10 ppm and phosphorus content to be 50
ppm.
[0178] The interstitial site grain boundary cohesion behavior is
dramatically different if boron is included. When boron is not
included, increases in cobalt slightly reduce grain boundary
cohesion because carbon solubility decreases. However, cohesion
enhancement increases as cobalt increases when boron is added. The
increase in cohesion enhancement is also due to a reduction in
carbon solubility. As carbon solubility decreases, the boron grain
boundary composition increases because there is less site
competition. Boron is nearly twice as potent per atom as carbon in
enhancing grain boundary cohesion. It is clear that boron must be
added to the alloys to maximize grain boundary cohesion at the
possible expense of ease of processability.
[0179] Chromium and tungsten content are the primary factors
controlling substitutional site grain boundary cohesion
enhancement. Increasing tungsten content directly increases grain
boundary cohesion by increasing the number of tungsten atoms in
solution. Increasing chromium content has a similar effect because
chromium and tungsten compete for sites in M.sub.2C carbides.
[0180] All of the alloys have carbide fractions greater than
AerMet100 suggesting that the strength requirement can easily be
achieved. However, none of the alloy calculations yielded austenite
stability in the target range. The 2Cr-0.5W series approached the
target at high cobalt levels. Unfortunately, the same series has
the lowest grain boundary cohesion enhancement when boron is added.
None of the alloys examined in this study meet the criteria
necessary to produce a transformation toughened alloy.
[0181] A second study examined the feasibility of transformation
toughened alloys of high cobalt content. It is clear from the
previous results that high cobalt contents are needed to assure
proper austenite stability. Cobalt content was fixed at 22 wt. % to
maximize nickel content while maintaining reasonable material cost.
Higher cobalt contents were not examined because of the high raw
material cost of cobalt. Chromium, molybdenum, and tungsten
contents were varied to examine the effect on grain boundary
cohesion and austenite stability. Rhenium, vanadium, and carbon
were fixed at the same content as the previous study. Nickel
content was determined by the constraint that M.sub.s temperature
be 220.degree. C. Table 6 presents the compositions of the designs
examined.
7TABLE 6 Composition of design alloys. Cr content Mo content W
content Ni content Alloy (wt. %) (wt. %) (wt. %) (wt. %) A 3.0 1.5
1.8 9.52 B 3.2 1.5 2.0 9.09 C 3.2 0.5 2.0 9.38 D 3.2 1.1 2.1 9.14 E
3.2 1.1 2.3 9.02 F 3.2 1.5 2.3 8.91 G 3.3 1.5 2.3 8.76 H 3.5 1.5
2.4 8.41
[0182] Carbide fraction was not an issue with the second set of
design alloys because each had at least 20% more carbide than
AerMet100. Cohesion enhancement predictions included boron in order
to achieve the highest possible values. Graph 4.14 shows a
cross-plot of cohesion enhancement vs. austenite stability in order
to determine the alloys that meet both criteria.
[0183] All of the alloys have significant improvements in grain
boundary cohesion compared to AerMet100. The highest enhancement
corresponds to the alloy with the lowest molybdenum content. More
tungsten and rhenium are able to segregate to the boundary because
of reduced site competition. However, molybdenum must be present in
order to saturate all substitutional sites.
[0184] Five alloys meet or exceed the minimum austenite stability
while exceeding grain boundary cohesion requirements. The ratio of
FCC to M.sub.2C precipitation rate constant must be examined to
determine if formation kinetics are favorable. In addition, FCC
mole fraction is also examined to ensure that a large enough
fraction is present to provide toughening enhancement. Graph 4.15
shows a property cross-plot of FCC mole fraction vs. kinetic ratio
of the five alloys that met both criteria in FIG. 4.14.
[0185] All alloys have at least 25% less austenite than that of
AerMet100 indicating that the toughening enhancement will be less
than that of AerMet100 unless the transformation volume change is
enhanced by 10%. Typical transformation volume changes of 3% would
have to be increased to 3.3%.
[0186] In addition to the reduction in toughening efficiency, the
kinetic ratio does meet specified goals. The crosshatched region of
graph 4.15 represents the target region for kinetic ratio. The
minimum kinetic ratio of the five alloys is approximately twice the
target value. It is thus expected that the austenite dispersion of
each alloy will exceed the desired size and not yield desired
properties. The kinetic ratio is much too high because of slow
carbide kinetics arising from the presence of tungsten. Removing
tungsten from the system will lower the kinetic ratio to the
desired values. However, removal of tungsten will result in
inferior grain boundary properties. Based on these results, this
study will not pursue the design of a transformation toughened
alloy.
[0187] K. Non-Transformation Toughened Alloy Design
[0188] In order to ensure high strength in the alloy, no retained
or precipitated austenite is desired in the alloys. Retained or
precipitated austenite will not have properties leading to
transformation toughening. Therefore, presence of austenite will
lower strength without any toughening enhancement. The overall
alloying additions will be limited by the constraint that M.sub.s
temperature be greater than 220.degree. C. However, this constraint
will not be used to determine nickel content, as in the previous
design. Nickel content will be limited by the constraint that no
precipitated austenite forms. Graph 4.16 shows a plot of predicted
precipitated austenite fraction vs. alloy nickel content.
[0189] The data plotted are from predictions from the previous
alloy design. Added to the data are linear and second-order
polynomial fits. The critical nickel content is predicted to be
between 5 wt. % and 6.5 wt. %.
[0190] L. Tungsten Steel
[0191] The Fe--Co--Ni--Cr--Mo--W--C alloy system is examined as a
candidate for an ultra-high strength steel. Carbon content is set
at 0.25 wt. % to produce a carbide dispersion meeting the strength
requirement. Cobalt is set at 15 wt. % in order to enhance M.sub.2C
driving force and maintain dislocation recovery resistance. Nickel
content is set at 6 wt. % to minimize austenite precipitation.
Rhenium grain boundary composition is minimized in the presence of
molybdenum and tungsten because of its low segregation energy
compared to molybdenum and tungsten. Since rhenium has a very high
cost and limited effectiveness, rhenium is excluded from this
design. Chromium, molybdenum, and tungsten variations are examined
to determine their effects on alloy properties. Chromium content is
varied from 2 wt. % to 4 wt. %, molybdenum content is varied
between 0 wt. % and 1.5 wt. %, and tungsten content is varied
between 1 wt. % and 3 wt. %. A full-factorial design with three
levels for each variable is examined. Among the properties examined
are M.sub.s temperature, solution temperature, grain boundary
cohesion, M.sub.2C fraction, and M.sub.6C to M.sub.2C driving force
ratio.
[0192] Calculations determining fraction M.sub.2C and cohesion
enhancement were conducted at 455.degree. C. using the COHERENT3
database. 16,000 J/mol was added to the M.sub.2C phase to account
for capillary energy at peak hardness. The SGTE database was used
to determine solution temperature, and M.sub.6C to M.sub.2C driving
force ratio. The MART4 database was used to predict the M.sub.s
temperature.
[0193] Graph 4.17 presents the effect of composition on Ms
temperature.
[0194] All M.sub.s temperatures in the design series exceed the
minimum value of 220.degree. C. Increases of 1 wt. % molybdenum
reduce the M.sub.s temperature by approximately 4.degree. C. 1 wt.
% increases of tungsten reduce the M.sub.S temperature by nearly
10.degree. C. while 1 wt. % increases of chromium reduce the
M.sub.s temperature by approximately 27.degree. C.
[0195] Proper solution treatment of the alloy is crucial to
optimize strength, toughness, and stress-corrosion cracking
resistance. Solution treatments must dissolve all large carbides,
such as M.sub.23C.sub.6 and M.sub.6C, to limit void nucleation
sites. In addition, all carbon must be in solution to maximize the
M.sub.2C strengthening dispersion. In addition, the majority of
tungsten grain boundary segregation occurs during solution
treatment. Therefore, solution temperature should be designed to
maximize grain boundary segregation while dissolving all
undesirable carbides. Solution time will be fixed at one hour to
prevent excessive grain growth. Solution treatment tungsten
segregation vs. temperature, for 1-hour treatment in an Fe-2 wt. %
W alloy, is shown in FIG. 4.18 to predict optimum solution
temperature. The BCC tungsten diffusivity is extrapolated to high
temperature in the model.
[0196] Graph 4.18 shows that solution temperatures above
900.degree. C. will result in complete tungsten segregation after 1
hour. An upper limit on solution temperature is placed at
1100.degree. C. due to processing concerns. Graph 4.19 shows the
effect of composition on predicted solution temperature.
[0197] Nearly all predicted solution temperature of all alloys
falls within the desired range. As expected, solution temperature
rises as additions are made to molybdenum and tungsten. Increases
in chromium do not affect the solution temperature greatly because
the low chromium M.sub.6C phase is the last carbide to dissolve.
Typical solution treatments require an increase in temperature
between 50.degree. C. and 100.degree. C. over the predicted
equilibrium value to account for the kinetics of dissolution of the
carbides. Including such a temperature allowance for kinetic
effects causes alloys with high molybdenum and tungsten contents to
exceed the desired solution treatment temperature.
[0198] The majority of tungsten grain boundary segregation occurs
during solution treatment while some molybdenum segregation will
occur during tempering. Calculations assumed a solution treatment
temperature of 1050.degree. C. and a tempering temperature of
455.degree. C. Tempering time was fixed at 8 hours.
[0199] Graph 4.20. shows the predicted grain boundary cohesion
enhancement of the design series.
[0200] Increases in tungsten content enhance grain boundary
cohesion because more tungsten is in solution. As chromium content
increases, small increases in cohesion occur because tungsten
solubility increases during tempering. Small tungsten enrichment
(or depletion) occurs during tempering. As molybdenum is added to
the alloy, the predicted cohesion enhancement decreases. The
decrease arises from depletion of grain boundary tungsten content
due to site competition with molybdenum. While it appears that
additions of molybdenum are not beneficial to grain boundary
cohesion, molybdenum additions are included in the design because
it segregates to lath boundaries during tempering. Since lath
boundaries form after quenching, boundary enhancement will only
occur during tempering. Therefore, molybdenum must be included to
enhance lath boundary cohesion because sufficient tungsten
enrichment will not occur at these boundaries.
[0201] Additions of tungsten will stabilize M.sub.6C carbides and
increase the nucleation driving force to levels higher than those
of the M.sub.2C carbide. Fortunately, kinetic considerations favor
M.sub.2C carbides causing them to form before M.sub.6C carbides.
However, it is desirable to limit the M.sub.6C stability to ensure
that the M.sub.2C carbide will remain stable over any possible
tempering range. Graph 4.21 shows the dependence of
M.sub.6C/M.sub.2C driving force ratio on composition.
[0202] The driving force ratio does not vary greatly as molybdenum
and chromium are changed. The carbide ratio increases as tungsten
content is raised. However, the driving force for M.sub.6C
formation is not significantly greater than that of M.sub.2C
formation and is not a concern in the examined composition
range.
[0203] As a final consideration, the M.sub.2C fraction must be high
enough to ensure strength properties are achieved. The M.sub.2C
carbide fraction of each design series is shown in Graph 4.22.
[0204] Other than alloys with low chromium and low tungsten, all
design alloys have carbide fractions nearly 30% greater than that
of AerMet100.
[0205] Based on the results of the alloy design, an alloy
composition of Fe--15Co--6Ni--3Cr-1.7Mo-2W-0.25C has been chosen.
The alloy has a predicted M.sub.S temperature of 273.degree. C. and
predicted solution temperature of approximately 975.degree. C. The
predicted grain boundary cohesion is approximately 2.3 J/m.sup.2
that is approximately 12% improvement over AerMet100. In addition,
the alloy will have sufficient molybdenum content to segregate to
lath boundaries during tempering. The carbide dispersion is
predicted to consist of fine M.sub.2C precipitates and avoid
M.sub.6C carbides. This alloy is expected to meet minimum strength
requirement while having good toughness. The stress-corrosion
cracking resistance is predicted to be higher than existing
alloys.
[0206] M. Rhenium Steel
[0207] A second alloy has been designed to quantify the effect of
rhenium on grain boundaries. In order to enhance rhenium
segregation, an alloy has been designed with reduced site
competition and reduced solution temperature. Reducing the carbon
content from 0.25 wt. % to 0.18 wt. % lowers solution temperature.
Molybdenum is excluded from the design in order to minimize site
competition. Cobalt and chromium content are fixed at the same
levels as in the tungsten quantum steel of 15 wt. % and 3 wt. %,
respectively. Nickel content is reduced from 6 wt. % to 5 wt. %.
The reduction of nickel content will ensure no austenite forms and
allow a qualitative determination of the importance of nickel on
alloy properties. The rhenium content is fixed at 2.7 wt. % by cost
constraints. Finally, 1.2 wt. % tungsten is added to enhance grain
boundary cohesion by occupying sites that have not been occupied by
rhenium. The addition of tungsten is limited by the constraint that
predicted rhenium grain boundary site fraction is greater than
0.20. Graphs 4.23 and 4.24 show the predicted grain boundary site
fraction of tungsten and rhenium.
[0208] Two diffusivity estimates are used to bracket tungsten and
rhenium grain boundary site fraction. The high diffusivity estimate
extrapolates the tungsten BCC diffusivity to high temperature. The
low diffusivity estimate applies the same FCC/BCC diffusivity ratio
as that of chromium. Rhenium diffusivity is estimated to be equal
to that of tungsten. The large dependence of diffusivity on
tungsten site fraction illustrates the need for accurate
diffusivity data for tungsten and rhenium.
[0209] Tungsten segregation is limited by thermodynamics above
1000.degree. C. for both diffusivity estimates. Rhenium segregation
increases over the entire temperature range because of reduced site
competition at higher temperatures.
[0210] N. Materials
[0211] The designed compositions are Fe-15Co-6Ni-3Cr-1.7Mo-2W-0.25C
for alloy QSW and Fe-15Co-5Ni-3Cr-2.7Re-1.2W-0.18C for alloy QSRe.
Allvac, an Allegheny Technologies Company, in Monroe, N.C.,
produced the alloys as 150 pound heats alloy, by vacuum induction
melting. The heats were re-melted by vacuum arc re-melting to
produce a 6" round ingot. Table 7 shows the measured compositions
of each alloy.
8TABLE 7 Chemical compositions of design alloys. Composition (wt.
%) QSW QSRe Fe Balance Balance Co 15.61 15.67 Ni 6.01 4.92 Cr 3.02
2.96 Mo 1.72 -- W 2.00 1.18 Re -- 2.69 Ti 0.04 0.04 La 0.009 0.006
C 0.249 0.179 B 0.002 0.002 S 0.0012 0.0010 P 0.005 0.004 O 0.0008
0.0008 N 0.0004 0.0005
[0212] small elemental additions were added for grain refinement
and impurity gettering. 0.04 wt. % titanium was included in melt
de-oxidation to form small amounts of TiC. TiC is stable during
solution treatment and provides an effective grain refining
dispersion with good interfacial adhesion for toughness.. A target
value of 0.01 wt. % lanthanum was added as a late melt addition to
getter oxygen and sulfur as La.sub.2O.sub.2S. The boron content of
the melts met the target of 15 ppm for grain boundary cohesion. A
target value of 0.015 wt. % zirconium was added to each melt to
getter phosphorus as ZrP. However, no residual zirconium was
detected during chemical analysis.
[0213] Each ingot was homogenized for 12 hours at 1190.degree. C.
The alloys were upset to 6.9" round at a temperature of
1175.degree. C. Alloys were re-heated if the temperature dropped
below 1010.degree. C. The alloys were press forged to 6" round
ingots at 1175.degree. C. (minimum T=1010.degree. C.). The alloys
were upset a second time under identical conditions as the first
upset. The alloys were press forged to 2.5" square at 1093.degree.
C. The minimum temperature allowed during the forging was
927.degree. C. The ingots were air cooled upon completion of press
forging.
[0214] O. Experimental Procedures
[0215] 1. Dilatometry
[0216] The dilatometry was performed on a computer controlled MMC
Quenching Dilatometer. An induction furnace performs sample heating
and jets of helium gas rapidly quench samples. Cylindrical samples
10 mm long and 3 mm wide are placed inside an induction coil and
held in place by two low expansion quartz platens. The platens are
spring loaded allowing the sample to expand or contract during
thermal cycling. The length change is transmitted to an LVDT
transducer via two quartz rods in contact with the platens.
Temperature control is achieved with a thermocouple spot welded
directly to the sample surface. The sample stage is enclosed in a
vacuum chamber connected to a turbo-molecular pump and mechanical
backing pump capable of quickly achieving a vacuum of 10.sup.-4
torr.
[0217] Dilatometry specimens were prepared by EDM machining 3 mm
diameter rods from bar stock material. The 3 mm rods were cut to 10
mm length by EDM machining. The surfaces were sanded to remove
surface oxide resulting from machining. The thermocouple was
attached to the sample midway along its length.
[0218] Under computer control, the samples were heated to
1050.degree. C. at a rate of approximately 3.degree. C./sec. and
held for 5 minutes. Quench rate is controlled by a needle valve
monitoring the flow of helium gas onto the sample. The samples were
cooled from 1050.degree. C. at approximately 15.degree. C./sec. The
test results in a data file containing time, temperature, and
length information. Austenite start temperature was determined as
the temperature at which the sample started contracting upon
heating. Similarly, martensite start temperature was determined as
the temperature at which the sample started expanding upon
cooling.
[0219] 2. Rockwell C Hardness Testing
[0220] Rockwell C hardness testing determines the hardness of a
material by the depth of penetration of the indenter under a
constant load. The measurement consists of the additional depth the
indenter travels upon application of a large load beyond the small
indentation of the preload. A small preload is used to remove
backlash in the loading apparatus and remove bias due to any
surface layer effects. The Rockwell C scale uses a preload of 10
kg, a load of 150 kg, and a Rockwell C diamond indenter. The
testing apparatus used was a standard Wilson Rockwell hardness
tester.
[0221] Before testing any samples, the machine was calibrated using
R.sub.c 45 and R.sub.c 61 standard blocks. 5 to 7 indentations were
randomly distributed along the sample. All indentations were at
least 3 indentation diameters away from an edge or other
indentation. Each indent consisted of preloading the sample,
zeroing the indicator, and performing the test. Results were
measured to the nearest 0.1 R.sub.c and the average and standard
deviation of each sample was determined.
[0222] 3. Tensile Testing
[0223] Round tensile specimens were cut from bar stock material
parallel to the longitudinal direction according to ASTM standard
E-8. Samples had a gage diameter of 0.25" and a gage length of
1.00". Samples were encapsulated in quartz under vacuum less than 5
mtorr. Samples were quenched in oil after solution treatment by
breaking the quartz tube and quickly immersing in oil. Samples were
cryogenically cooled in liquid nitrogen for two hours. The samples
were encapsulated a second time in pyrex, under similar vacuum, and
tempered. Upon completion of tempering, samples were air cooled in
the pyrex tubes.
[0224] Testing was conducted on a Sintech 20G tensile machine
controlled by the Testworks software package at a rate of 1 mm/sec.
An extensometer was attached during testing to generate
load-displacement curves. Area reduction and extension were
measured manually upon completion of the test.
[0225] 4. Fracture Toughness Testing
[0226] K.sub.IC samples were prepared from bar stock material in
the longitudinal configuration. Oversized blanks were abrasive cut
from the billet and solution treated in air. Samples were cooled in
liquid nitrogen for 2 hours after oil quenching. Final tempering
was done in air. Upon completion of heat treatment, the surfaces of
the blanks were ground parallel to final thickness. EDM machining
was used to machine the final specimen shape.
[0227] The method for determining K.sub.IC is outlined by ASTM
standard E-399 Sample geometry was identical to that used by
Kuehmann Kuehmann performed combined J.sub.IC and K.sub.IC tests
which require samples to be machined to specifications listed by
ASTM standard E-813. Diagram 5.1 shows the compact tension specimen
geometry used to measure fracture toughness.
[0228] Specimen surfaces were polished to 6 .mu.m finish in order
to observe crack propagation during pre-cracking. Pre-cracking was
accomplished on a servo-hydraulic MTS load frame. Pre-cracking was
accomplished at 20 Hz with a stress ratio of 0.1. Load control was
accomplished by constraining maximum strain levels. Load is
controlled by strain because as crack propagation occurs, stress
levels decrease. If constraints are placed on maximum stress,
samples may fracture prematurely because specified peak stress may
exceed fracture stress of the sample after the crack has
propagated. Initial peak load was 1000 pounds. Samples underwent
10,000 cycles at the initial load. If no crack initiation is
observed, the peak stress level is increased 200 pounds. The
process is increased until crack initiation is observed.
Pre-cracking is terminated when the notch and fatigue crack are
between 0.5" and 0.55" depth. Pre-cracked samples were fractured on
a Sintech 20G tensile machine controlled by the Testworks software
package generating a load vs. crack opening displacement curve.
Crack opening displacement was measured with an MTS model
632.03E-30 clip gage with a gage length of 0.1" attached to the
knife edges of the sample.
[0229] K.sub.IC was determined from fractured samples according to
ASTM standard E-399. First, the K.sub.Q value is determined by
equation 5.1. 44 K Q = ( P Q B W 1 / 2 ) f ( a W ) ( 5.1 )
[0230] B is the sample thickness, W is the sample width, and
a.sub.0 is the initial crack length. Measuring the crack length of
five points evenly spaced along the sample and taking their average
determines initial crack length. The functional form represents a
geometry dependent calibration factor. A 95% secant construction on
the load vs. crack opening displacement curve determines the value
of P.sub.Q, as shown in graph 5.2.
[0231] The K.sub.Q values are equal to K.sub.IC if the relation in
equation 5.2 is met. 45 2.5 ( K Q YS ) 2 < B and a 0 ( 5.2 )
[0232] K.sub.Q is determined by equation 5.1, .sigma..sub.YS is the
0.2% offset yield stress, B is the sample thickness, and a.sub.0 is
the initial crack length. separate the overlapping peaks, and the
background-subtracted integrated intensities were obtained using
Desktop Spectrum Analyzer (DTSA 2.01) software from NIST.
[0233] Samples were ground to a thickness of approximately 50
microns. Transmission sections were polished using a Twin Jet
electropolisher at a temperature below -50.degree. C. The
electrolyte used was 20% percholoric acid in methanol.
[0234] 5. Electron Microscopy
[0235] A Hitachi 3500 scanning electron microscope with a tungsten
wire filament was used to investigate the fracture surfaces of the
compact tension specimens. The microscope uses Quartz PCI Image
Management Software through a Windows 95 interface. Fractured
samples were mounted using graphite tape and examined in the
scanning electron microscope with a 20 kV electron beam.
Examination was conducted at a vacuum level of 10.sup.-4 torr.
Fracture surfaces were examined and micrographs of characteristic
features were taken at 500.times. and 1000.times..
[0236] Auger electron microanalysis was conducted at Oak Ridge
National Laboratory on a Physical Electronics PHI G80 Auger
Nanoprobe. Voltage was set at 10 kV and current was set at 10 nA.
Specimens were examined under vacuum of 1.78.times.10.sup.-9 torr.
Samples were fractured under vacuum on a cold fracture stage. The
fracture stage was capable of quickly reaching -100.degree. C. by
liquid nitrogen cooling. Auger spectra were taken on all features
of the fracture surface.
[0237] Auger specimen rods were machined from heat-treated material
by EDM machining. Samples were cut to length by abrasive saw. A
grinding wheel was used to machine required notches into the
samples.
[0238] Analytical electron microscopy was performed in a Hitachi
HF-2000 cold-field emission gun equipped with a Gatan 666 parallel
electron energy-loss spectrometry detector, an ultra-thin window
Link EDS detector and processor, and a Gatan charge-coupled device
camera for high-resolution imaging. The electron microscope was
operated at 200 kV with a beam size of 3 nm. The x-ray spectra were
deconvoluted, to
[0239] P. Test Results
[0240] The final aspect of this study attempted to examine the
grain boundaries of the Two experimental methods were used to study
the composition of the grain boundaries. First, Auger electron
microanalysis of fracture surfaces was conducted to determine if
any enrichment of boron, tungsten, and rhenium is present. Samples
were fractured under high vacuum (10.sup.-9 torr) at -100.degree.
C. Samples were fractured at low temperature in order to induce
brittle fracture. The second method used high-resolution,
analytical electron microscopy to examine prior austenite grain
boundary composition. The composition of the grain boundary is
compared to the bulk composition to determine if any enrichment is
present.
[0241] 1. Dilatometry
[0242] A dilatometry study was conducted to determine the
martensite start temperature of the design alloys. Graph 6.1
presents the heating and cooling curves showing the relative length
of the sample vs. temperature for alloy QSW.
[0243] In addition to the experimental curve, polynomial fits of
the heating and cooling curves are presented. The martensite start
temperature is determined by comparing experimental sample length
to that predicted by the cooling curve. Experimental length values
do not differ from the polynomial fit by more than 1.9% at
temperatures greater than 300.degree. C. The martensite start
temperature is chosen as the temperature at which experimental
values differ from the polynomial fit by more than 5%. The
martensite start temperature of alloy QSW is 296.degree. C. The
Ghosh-Olson model predicts a martensite start temperature of
273.degree. C.
[0244] Graph 6.2 presents the dilatometry trace for alloy QSRe.
[0245] The martensite start temperature of alloy QSRe is
353.degree. C. The Ghosh-Olson model predicts a martensite start
temperature of 350.degree. C.
[0246] 2. Solution Treatment Study
[0247] A study was conducted on both design alloys in order to
determine the optimal solution treatment condition and confirm
ThermoCalc predictions. 8" bars of stock material were treated in a
gradient heat furnace, at Allvac research laboratories, up to a
temperature of 1125.degree. C. As-quenched hardness measurements
were taken along the length of the bar. Bars were treated for 1
hour, 1.5 hours, and 2 hours to determine any effect of solution
treatment time.
[0248] Solution treatment behavior of alloy QSW is predicted by
ThermoCalc calculations. The calculation allowed M.sub.23C.sub.6,
M.sub.6C, M.sub.7C.sub.3, M.sub.2C, and MC carbides to form Graph
6.3 shows the predicted equilibrium carbide fraction as a function
of temperature.
[0249] Graph 6.4 shows the results of the gradient heat treat study
for alloy QSW.
[0250] A rapid increase in hardness is seen over the temperature
range of 750.degree. C. to 825.degree. C. corresponding to
dissolution of M.sub.23C.sub.6 carbides. The 1-hour sample has
lower hardness than that of the longer treated samples indicating
that 1 hour is not sufficient time to reach equilibrium. Over the
temperature range of 825.degree. C. to 1000.degree. C., a gradual
increase in hardness is observed in samples treated for 1.5 and 2
hours. This behavior is attributable to the gradual dissolution of
M.sub.6C carbides. Once again, 1 hour is not sufficient to reach
equilibrium. At temperatures above 1000.degree. C., hardness does
not vary as solution time is increased suggesting that complete
solution treatment is accomplished within 1 hour. No drop in
hardness is observed as solution temperature increases. This
indicates that 0.04 wt. % addition of Ti forms an effective grain
refining dispersion preventing excessive grain growth. The peak
solution hardness approaches HR.sub.c 55. Any 1 hour solution
treatment between 1000.degree. C. and 1050.degree. C. will achieve
this condition. The experimentally determined minimum solution
temperature of 1000.degree. C. is similar to the predicted solution
temperature of 975.degree. C.
[0251] In addition to optimizing solution treatment, the gradient
heat treat study provided information about anneal softening. In
order to improve machinability, material is generally shipped in a
softened condition. A 2-hour heat treatment at 725.degree. C. drops
the hardness of alloy QSW below HR.sub.c 35.
[0252] The results of the ThermoCalc solution treatment
calculations on alloy QSRe are shown in Graph 6.5.
[0253] Alloy QSRe shows a rapid increase in hardness over the
temperature range 780.degree. C. to 870.degree. C. corresponding to
dissolution of carbides. The temperature at which carbide
dissolution occurs drops 30.degree. C. as solution time is
increased from 1 to 2 hours corresponding to kinetic effects. The
hardness remains relatively constant over the temperature range
900.degree. C. to 1100.degree. C. indicating that excessive grain
growth is prevented by an effective grain refining dispersion. The
solution treatment condition for alloy QSRe is 1 hour at
870.degree. C. The predicted solution temperature is approximately
800.degree. C.
[0254] The predicted equilibrium carbides are M.sub.6C carbides and
M.sub.7C.sub.3 carbides.
[0255] The results of the gradient heat treat study conducted on
alloy QSRe are shown in Graph 6.6. that is nearly identical to the
experimentally determined solution temperature of the 2-hour
sample.
[0256] 3. Isothermal Tempering Study
[0257] An isothermal tempering study was conducted on both design
alloys to determine their tempering characteristics. Alloy QSW was
solution treated at 1050.degree. C. for 1 hour while alloy QSRe was
solution treated at 870.degree. C. for 1 hour. Samples were
tempered at 482.degree. C. and 510.degree. C. for times up to 40
hours to determine the tempering response of each alloy. Graph 5.7
shows the tempering response of alloy QSW.
[0258] The solution treated hardness of the samples was
approximately HR.sub.c 52.5. Alloy QSW reaches a peak hardness of
HR.sub.c 58.9 after tempering for 20 hours at 482.degree. C. Upon
tempering 40 hours at 482.degree. C., the hardness shows a small
drop to HR.sub.c 58. The alloy shows strong coarsening resistance
as expected from the presence of tungsten. As shown in Chapter 2,
one slow diffusing element, such as tungsten, will impart
significant coarsening resistance.
[0259] Tempering at 510.degree. C. allows the alloy to reach peak
hardness after 2 hours. However, the maximum hardness achieved at
510.degree. C. is HR.sub.c 57.9. In addition, a reduction of
approximately HR.sub.c 1.5 is seen after tempering 4 hours. The
hardness drops to values comparable to the solution hardness after
10 hours.
[0260] The reduction in peak hardness is expected because the
driving force for M.sub.2C nucleation is inversely related to
tempering temperature. Lower tempering temperature will increase
the maximum peak hardness because finer particles will nucleate.
However, tempering times will dramatically increase because of the
relatively high activation energy of tungsten-diffusion-controlled
precipitation. Time to peak hardness in alloy QSW increases from 2
hours to 20 hours, as tempering temperature is reduced 28.degree.
C. While superior properties are attainable as tempering
temperature is reduced, the increase in tempering time is
undesirable because of added processing time. An optimal compromise
should be attainable at an intermediate tempering temperature.
[0261] Graph 6.8 presents the results of the isothermal tempering
study of alloy QSRe.
[0262] The tempering response of alloy QSRe is similar to that of
alloy QSW. Tempering at 482.degree. C. yields higher peak hardness,
but takes longer to achieve. The peak hardness of HR.sub.c 53.3
occurs after 12.5 hours at 482.degree. C. This value represents an
increase of approximately HR.sub.c 6.5 over the solution treated
condition. The hardness does not drop significantly after tempering
for 24 hours at 482.degree. C. Tempering at 510.degree. C. reduces
the peak hardness to HR.sub.c 52.2 and the time to peak hardness to
4.5 hours. Tempering treatments of 10 hours reduce the hardness to
HR.sub.c 50.5.
[0263] 4. Fracture Toughness Testing
[0264] Fracture toughness testing was conducted on both alloys to
determine the optimum combination of strength and toughness. Alloy
QSW was solution treated at 860.degree. C. for 2 hours and
1050.degree. C. for 1 hour. One sample was tempered at 200.degree.
C. for 1 hour to complete stage one tempering. Other samples were
tempered at 482.degree. C. between 5 and 160 hours. Graph 6.9
presents the results of the fracture toughness study of alloy QSW
by showing the fracture toughness vs. hardness trajectory during
tempering.
[0265] The fracture toughness of alloy QSW follows the anticipated
pattern. At short tempering times, an increase in hardness is
accompanied by a significant decrease in fracture toughness. The
decrease is the result of precipitation of coarse para-equilibrium
cementite. As tempering continues, para-equilibrium cementite is
dissolved as M.sub.2C carbides form. At the longest tempering
times, toughness is increased as all para-equilibrium cementite is
dissolved. Hardness drops as M.sub.2C carbides coarsen to particle
sizes exceeding optimum size. Points in parentheses are estimates
of samples that failed during pre-cracking due to load spikes. The
max load during the spike was used to estimate the fracture
toughness. Results from a prior fracture toughness test, denoted by
a triangle marker on FIG. 6.9, suggest that the fracture toughness
after tempering 20 hours is approximately 35 ksi{square root}in.
This information suggests that the estimates err on the low
side.
[0266] Samples undergoing solution treatment for 1 hour at
860.degree. C. were also tested. The solution treated strength and
toughness of these samples were lower than that of the sample
solution treated at 1050.degree. C. The decrease in strength and
toughness is due to an incomplete solution treatment. Un-dissolved
carbides reduce the strength by decreasing the amount of carbon in
solution. Fracture toughness decreases because the relatively
coarse carbides acts as microvoid nucleation sites. One sample aged
12 hours fractured during pre-cracking. The premature fracture is
the result of inferior fracture toughness arising from a
combination of para-equilibrium cementite and undissolved alloy
carbides. A sample tempered for 24 hours has a fracture toughness
of approximately 30 ksi{square root}in. at a hardness of HR.sub.c
55.4. This combination of properties is inferior and confirms that
incomplete solution treatment will result in poor strength and
toughness.
[0267] Micrographs were taken of the fracture surfaces to determine
the mode of fracture. Ductile fracture was observed in the stage
one tempered (200.degree. C./1 Hr), 1050.degree. C. solution
treated condition, as shown in graph 6.10.
[0268] The fracture surfaces of samples tempered between 5 and 20
hours are quite different from the surface of the solution treated
sample, as shown in a representative micrograph in graph 6.11.
[0269] The fracture surface exhibits faceting on a fine scale
indicating that the failure mode is quasi-cleavage. Quasi-cleavage
is similar to normal cleavage except the length scale is greatly
reduced due to the lath martensite microstructure. Notably absent
from the figure are large facets indicative of intergranular
fracture.
[0270] As tempering time increases, hardness drops and fracture
toughness increases. Fracture surfaces of samples tempered between
40 and 160 hours show a combination of quasi-cleavage and ductile
microvoid fracture. The majority of the 40-hour fracture surface is
quasi-cleavage with small regions of ductile fracture, as shown in
graph 6.12. After 160 hours, the majority of the fracture surface
shows ductile fracture, similar to the stage one tempered sample,
as shown in graph 6.13.
[0271] Fracture toughness samples of alloy QSRe were solution
treated at 1050.degree. C. for 1 hour. One sample was tempered at
200.degree. C. for 1 hour to complete stage one tempering. Samples
were tempered at 510.degree. C. for up to 8 hours. In addition, one
sample was double-austenized at 1050.degree. C. for 1 hour and
860.degree. C. for 2 hours. The double-austenized sample was
tempered at 510.degree. C. for 8 hours. Graph 6.14 shows fracture
toughness vs. hardness for alloy QSRe.
[0272] The fracture toughness drops dramatically after tempering at
510.degree. C. for 1 hour due to precipitation of para-equilibrium
cementite. Hardness increases at relatively constant fracture
toughness as M.sub.2C carbides precipitate at the expense of
para-equilibrium cementite after tempering up to 4 hours. Hardness
decreases after tempering 8 hours due to carbide coarsening. Double
austenizing increases fracture toughness by at approximately 12%,
as seen in samples tempered at 510.degree. C. for 8 hours. The
increase in fracture toughness is attributed to finer grain size
resulting from re-crystallization during the 860.degree. C.
austenizing step.
[0273] Unlike alloy QSW, fracture toughness does not increase as
hardness drops in the over aged condition. The lack of fracture
toughness enhancement in the over aged condition indicates that
fracture mode changes as tempering time increases. Graph 6.15 shows
ductile fracture of alloy QSRe in the stage one treated condition.
Graph 6.16 shows quasi-cleavage with large facets, possibly
indicating intergranular fracture, after tempering 8 hours at
510.degree. C.
[0274] Fracture surface studies show that the primary mode of
fracture is quasi-cleavage in both alloys. Alloy QSW has superior
fracture toughness compared to alloy QSRe, indicating better
resistance to quasi-cleavage. Improved quasi-cleavage resistance is
likely due to the higher nickel content in alloy QSW. The nickel
content in alloy QSW is 6 wt. % compared to 5 wt. % in alloy QSRe.
The alloy nickel contents were set in order to maintain high
strength by avoiding precipitated austenite. Comparing fracture
toughness of the two samples suggests that maximizing solution
nickel content will have strong positive effects on fracture
toughness.
[0275] Intergranular fracture is suppressed in alloy QSW, but
present in alloy QSRe. Molybdenum is included in alloy QSW but
excluded in alloy QSRe. Tungsten and rhenium are predicted to
segregate to austenite boundaries during solution treatment.
Molybdenum is predicted to segregate to boundaries during solution
and tempering treatments. Lath martensite boundary cohesion is not
enhanced in alloy QSRe because no molybdenum is present to
segregate during tempering. The lack of lath martensite boundary
cohesion enhancement is likely responsible for the intergranular
fracture contribution limiting the fracture toughness in alloy
QSRe.
[0276] 5. Tensile Properties
[0277] Tests were performed on both alloys to determine tensile
properties. Heat treat conditions were chosen based on the results
of the hardness and fracture toughness study. Alloy QSRe was
solution treated at 860.degree. C. for 2 hours and aged at
482.degree. C. for 20 hours. Tensile bars of alloy QSW were
solution treated at 1050.degree. C. for 1 hour and tempered at
482.degree. C. Specimens tempered 20 and 40 hours were examined.
The load-displacement curve of alloy QSW tempered for 40 hours is
shown in graph 6.17.
[0278] Table 8 summarizes the results of tensile testing.
9TABLE 8 Tensile properties of design alloys. Ultimate Reduction
Yield Strength Tensile % in Alloy (ksi) Strength (ksi) Elongation
Area (%) QSRe 240 274 17 59 QSW-20 Hr 297 335 15 53 QSW-40 Hr 293
328 12.8 55.6
[0279] Both alloys show reasonable ductility in all tested
conditions. Tensile properties of alloy QSW compare favorably to
typical ultra-high strength alloys. Graph 6.18 shows a tensile
property comparison of alloy QSW to several commercial ultra-high
strength steels [84].
[0280] The ultimate tensile strength of alloy QSW (Quantum 335 on
chart) is greater than that of any commercial alloy. In addition,
the yield strength of alloy QSW is greater than the ultimate
tensile strength of most commercial alloys.
[0281] 6. Auger Electron Microanalysis
[0282] Composition analysis of fracture surfaces from alloy QSRe
was conducted by Auger electron microanalysis. The goal of this
study was to determine if predicted rhenium and tungsten enrichment
occurs on prior austenite grain boundaries by examining
intergranular fracture surfaces. Alloy QSRe was chosen because its
fracture surface exhibited large facets indicative of possible
intergranular fracture. Alloy QSW was not examined because it did
not exhibit intergranular fracture.
[0283] Two solution treatments and two tempering treatments were
examined by Auger electron microscopy. All samples were solution
treated 1 hour at 1050.degree. C. and tempered 8 hours at
510.degree. C. In addition, two samples were solution treated 2
hours at 860.degree. C. One sample from each solution treatment
condition was post-tempered at 370.degree. C. for 1 hour. The heat
treatment conditions were chosen to determine the effect of
solution temperature on grain boundary segregation. The post-temper
treatment was designed to enhance boron grain boundary
concentration.
[0284] Samples were fractured under vacuum at -100.degree. C. All
samples exhibited similar fracture surfaces, as shown in graph
6.19.
[0285] Three different regions are evident on the fracture surface.
The majority of the fracture surface exhibits fine faceting
indicative of quasi-cleavage. A dimpled region indicative of
ductile fracture is present in small quantities. Finally, a large
facet suggests intergranular fracture. Auger spectra were taken
from each region to determine the composition along the fracture
surface. The spectra from each region were nearly identical, as
shown in graph 6.20.
[0286] Iron, cobalt, nickel, carbon, and oxygen were present on all
regions of the fracture surface. No tungsten, rhenium, or boron
peaks were discernible from the background noise. The absence of
tungsten, rhenium, and boron in the Auger spectra suggest that the
facets seen on the fracture surface are not from prior austenite
intergranular fracture. The large facets are more likely from
fracture along lath boundaries. Since tungsten and rhenium are only
expected to segregate during solution treatment, lath boundary
cohesion was not enhanced in alloy QSRe. Auger analysis on the
fracture surface was unable to provide any evidence of grain
boundary segregation because fracture could not be achieved on
prior austenite grain boundaries.
[0287] Evidence of successful oxygen and sulfur gettering suggest
the presence of oxygen on the fracture surface is most likely due
to contamination in the Auger chamber. This may have limited the
detectability of expected segregants such as boron. Graph 6.21
shows the fracture surface and Auger spectrum indicating the
presence of an La.sub.2O.sub.2S particle.
[0288] The area indicated by the arrow has an apparent lanthanum
concentration of 23%, sulfur concentration of 12.6%, and oxygen
concentration of 27.9%. The remainder of the area consists of iron,
cobalt, and nickel from the matrix. The La:O:S ratio is nearly
identical to the expected stoichiometric ratio of
La.sub.2O.sub.2S.
[0289] 7. Analytical Electron Microscopy
[0290] Analytical electron microscopy was used to analyze prior
austenite grain boundaries. A prior austenite grain boundary was
found in alloy QSRe solution treated 1 hour at 1050.degree. C. and
tempered 1 hour at 200.degree. C., as shown in graph 6.22.
[0291] Since many lath packets terminate at the boundary, it is
concluded that the boundary is a prior austenite grain
boundary.
[0292] X-ray spectra were taken at seven points along the grain
boundary and two points in the bulk. For each point, W M radiation
peaks were normalized by the Fe K, Cr K, Co K, and Ni K radiation.
The grain boundary points were averaged and compared to the average
of the bulk points to determine if any grain boundary enrichment
occurred. The spectrum from each grain boundary point consists of
contributions from the grain boundary region and bulk region due to
beam size. The analysis assumes a grain boundary thickness of 0.1
nm and a beam diameter of 5 nm. Based on these assumptions, the
grain boundary region will comprise approximately 27% of the total
beam area. The relation given in equation 6.1 determines the grain
boundary partition ratio. 46 Spectrum G . B . Spectrum bulk = X
bulk i A G . B . + X bulk i ( R 2 - A G . B . ) X bulk i R 2 ( 6.1
)
[0293] R is the beam radius, X.sup.i.sub.bulk is the alloy
composition of element i, A.sub.G.B. is the area of the grain
boundary region, and .alpha. is the grain boundary partition ratio.
Values greater than 1 correspond to grain boundary enrichment.
Grain boundary composition is determined by multiplying bulk
composition by the partition ratio. Table 9 gives the site fraction
of tungsten and rhenium when normalized by each element.
10TABLE 9 Site fraction data from analytical electron microscopy.
Normalization Element Tungsten Site Fraction Rhenium Site Fraction
Fe 0.0416 0.186 Co 0.0384 0.179 Cr 0.0354 0.165 Ni 0.0362 0.171
[0294] The results presented in table 9 show that enrichment of
rhenium is approximately 60% of the model predicted value of 0.29
shown in chapter 4. The grain boundary site fraction of tungsten is
approximately 0.04 which corresponds to an enrichment of
approximately 10 times the bulk. However, this site fraction is
significantly lower than the model predicted value of 0.66.
[0295] Based on the assumption that grain boundary segregation is
not kinetically limited at 1050.degree. C., segregation free
energies and enthalpies were determined for tungsten and rhenium
based on the experimental data. The segregation free energy of
tungsten at 1050.degree. C. was determined to be approximately
-27,300 J/mol while the segregation free energy of rhenium at
1050.degree. C. was -36,500 J/mol.
[0296] Graph 6.23 shows tungsten grain boundary segregation energy
as a function of temperature in FCC and BCC iron.
[0297] The figure shows the quantum mechanics estimates of grain
boundary segregation energy at 0 K. The straight line connects the
FCC quantum mechanics estimate with the experimental data point,
corresponding to a segregation entropy of -37.6 J/molK. This
segregation entropy is of similar magnitude but opposite sign to
that used in the original grain boundary cohesion model, which was
based on interstitial element data rather than substitutional
elements. BCC segregation energy is calculated from experimental
site fraction data from Lee, et al. over the temperature range 773
K to 873 K. The dashed line represents a fit through the Lee data
using the same segregation entropy of -37.6 J/molK estimated for
FCC. The experimental data are consistent with the quantum
mechanics prediction that the energy of tungsten segregation is
larger in FCC than BCC.
[0298] Q. Toughened Tungsten Steel
[0299] Composition modifications should enhance cleavage resistance
because the fracture mode at peak hardness was quasileavage. The
first alloy design limited nickel content to 6 wt. % to avoid
precipitated austenite. The re-design will not place any
constraints on nickel content related to austenite precipitation.
Since the carbide dispersion in alloy QSW meets the requirements,
chromium, molybdenum, and tungsten compositions will not change in
the modified alloy. In addition, cobalt is held constant to that of
alloy QSW. Carbon content will increase from 0.25 wt. % to 0.27 wt.
%. Carbon is increased to provide a slight boost in carbide
fraction. The increased carbide fraction is intended to maintain
strength levels comparable to alloy QSW by offsetting possible
softening from precipitated austenite. Nickel content is maximized
within the constraint that martensite start temperature must not
drop below 225.degree. C. in order to limit retained austenite. The
re-designed composition (in wt. %) is Fe-15Co-3Cr-1.7Mo-7.3Ni-2W-
0.27C. The predicted martensite start temperature is 232.degree.
C., which allows for slight composition variations (.+-.0.1 wt. %)
that may arise during melting.
[0300] In order to increase ultimate tensile strength from 335 ksi
to 375 ksi, alloy carbon content must be raised to increase
M.sub.2C carbide fraction. Graph 7.1 plots ultimate tensile
strength vs. M.sub.2C fraction for both quantum steels and
commercial AerMet100. Carbide fraction is calculated with additions
of 16,000 J/mol added to the M.sub.2C phase for each alloy to
account for capillary of 3 nm particle.
[0301] Three fits were used to extrapolate to higher strength
levels. First, a liner fit was placed through the data. Two fits
were used based on previous models. One assumed a relationship
based on carbide fraction to the V.sub.2 power. The other assumed a
y-intercept of 81.6 ksi an fit an exponential dependence on carbide
fraction. The three equations are shown on graph 7.1. An ultimate
tensile strength of 375 ksi will require a minimum carbide fraction
of 4.16% based on the linear fit or 4.24% based on the other two
fits. The three nearly identical over the strength range of
interest and can be used interchangeably.
[0302] ThermoCalc calculations using the composition of alloy QSW
and varying carbon content were performed to determine the minimum
alloy carbon content needed to ensure required carbide fraction.
Calculations added 16,000 J/mol to the coherent M.sub.2C phase to
account for capillary energy at the optimal particle size of 3 nm.
Graph 7.2 shows the effect of alloy carbon content on M.sub.2C
fraction tempered at 482.degree. C.
[0303] The minimum alloy carbon content in alloy QSW needed to
ensure sufficient M.sub.2C carbide fraction is 0.298 wt. %. The
carbon content is set at 0.32 wt. % for the alloy re-design of
Quantum 375. Excess carbon was intentionally set to allow
significant overaging of the alloy in order to fully dissolve
cementite.
[0304] In addition, graph 7.2 shows that alloy QSW has an excess of
M.sub.2C carbide forming elements relative to alloy carbon contents
up to 0.4 wt. %. Since alloy QSW has ample carbide forming elements
at a carbon level of 0.32 wt. %, the Quantum 375 re-design
maintains the same chromium, molybdenum, and tungsten contents to
maintain grain boundary cohesion enhancements designed in alloy
QSW.
[0305] The design examined the effect of cobalt compositions
between 15 wt. % and 20 wt. % on allowed nickel content, solution
temperature, and carbide fraction. Nickel content was set by the
constraint that martensite start temperature be at least
225.degree. C. Graph 7.3 shows the effect of cobalt on nickel
content, carbide fraction, and solution temperature.
[0306] Increasing cobalt has positive effects on all three
properties. Increasing cobalt causes a minor increase in carbide
fraction. Solution temperature drops nearly 20.degree. C. as cobalt
is increased from 15 wt. % to 20 wt. %. As cobalt content is
increased, allowable nickel content is increased. The design alloy
will have a cobalt content of 19 wt. % to lower solution
temperature to that of alloy QSW and increase the alloy nickel
content to 7.1 wt. %. The design composition is then
Fe-19Co-3Cr-1.7Mo-7.1Ni-2W-0.32C.
[0307] Tungsten and rhenium primarily segregate during solution
treatment while molybdenum and interstitial elements segregate
during tempering.
[0308] A study of the heat treatment optimization has investigated
the response of both design alloys to various solution and
tempering treatments. The solution treatment study examined the
effect of solution temperature and time on as-quenched hardness.
The optimum solution treatment of alloy QSW is 1 hour at
1050.degree. C. corresponding to predicted complete dissolution of
Cr-rich and W-rich carbides. The optimum solution treatment of
alloy QSRe is 2 hours at 860.degree. C., also consistent with model
predictions.
[0309] The tempering study examined the effect of two tempering
temperatures on strength. Alloy QSW reached a peak ultimate tensile
strength of 335 ksi (HR.sub.c 58.8) after 20 hours at 482.degree.
C. The fracture toughness in the peak strength condition is 35
ksi{square root}in. Tempering 40 hours at 482.degree. C., to more
fully dissolve cementite, increases fracture toughness to 47
ksi{square root}in with minimal reductions to strength. Alloy QSRe
reached peak ultimate tensile strength of 274 ksi (HR.sub.c 53.3)
after 20 hours at 482.degree. C. Samples tempered for 8 hours at
510.degree. C. achieved hardness of HR.sub.c 51.6 and fracture
toughness up to 44 ksi{square root}in. Fracture surfaces of alloy
QSW showed no evidence of intergranular fracture suggesting
effective cohesion enhancement.
[0310] Analytical electron microscopy examined a prior austenite
grain boundary in alloy QSRe. Results show a grain boundary site
fraction of rhenium of approximately 0.175 corresponding to an
enrichment of nearly 20 times the bulk. The model predicted rhenium
site fraction is 0.29. Grain boundary tungsten site fraction is
approximately 0.0375 corresponding to an enrichment of
approximately 10 times the bulk. The experimental value differs
significantly from predicted tungsten site fraction 0.664. The
large discrepancy between experimental and predicted tungsten site
fraction emphasize the need for accurate tungsten diffusion and
segregation information.
[0311] Low toughness in alloy QSRe arises from a combination of low
nickel content and intergranular fracture along lath boundaries.
Since molybdenum was excluded from the design, no lath boundary
cohesion enhancement is expected in alloy QSRe. Auger microanalysis
did not reveal any evidence of tungsten or rhenium enrichment along
intergranular fracture surfaces. Since analyticaI electron
microscopy showed tungsten and rhenium enrichment along prior
austenite grain boundaries, it is concluded that intergranular
fracture does not occur along prior austenite grain boundaries.
[0312] Two alloy compositions have been proposed to improve
mechanical properties of the prototype alloys. One alloy
composition seeks to maximize nickel content relative to alloy QSW
within the constraint that martensite start temperature be greater
than 225.degree. C. Carbon content is increased slightly to
anticipate potential reduction in strength that may arise from
precipitated austenite.
[0313] The second alloy composition is designed to reach an
ultimate tensile strength of 375 ksi. The carbon, nickel, and
cobalt contents of alloy QSW are modified to achieve this goal.
Carbon content is raised from 0.25 wt. % to 0.32 wt. % in order to
raise carbide fraction. Cobalt and nickel content are optimized
within the constraint that martensite start temperature be greater
than 225.degree. C. Cobalt content is raised from 15 to 19 wt. % to
reduce solution temperature and increase alloy nickel content to
over 7 wt. %.
[0314] While a preferred embodiment of the method and compositions
have been set forth, the invention is limited only by the following
claims and equivalents thereof.
* * * * *