Turbo Machinery Dynamics Part 12 docx

Iron gradually disappeared over a period of time as an alloy base, to bereplaced by nickel and cobalt because of the more durable face-centered cubic structure.Although chromium may lead

According to Lubkin (1962), stresses in the x, y, and z directions are principal

stresses, and are defined by the maximum pressure at the center of the contact area asdefined by the expression

For an element on the z-axis the stresses are:

(10.37)

(10.38)

The equations given above also apply to the contact of a sphere and a plane surface or

to a sphere and an internal spherical surface For a plane surface use d= ∞ For an nal surface the diameter is expressed as a negative quantity

inter-A ball bearing’s inner raceway may be considered to be the segment of a sphere Therolling elements have a mating surface Hence, the two contacting surfaces may be ide-alized as spheres loaded against each other If the raceway diameter = 2.25 in, ball diam-eter = 0.775 in, and contact force F = 15 lb, determine the contact area and stress levels Use Young’s modulus E1= E2= 30 × 106lb/in2and Poisson’s ratio n1= n2= 0.3 for bothbodies

Solution The pressure within each sphere has a semielliptical distribution, as shown inFig 10.48 Maximum pressure occurs at the center of the contact area For an internalsurface, the diameter is negative Then the contact area and maximum pressure are cal-culated to be

Figure 10.49 provides variation in the stress components for a distance 3a below the surface Note that shear stress t reaches a maximum value slightly below the surface.

Maximum shear stress is considered to be the leading cause of surface fatigue failure incontacting elements A crack initiating at the point of maximum shear stress below thesurface and lubricant pressure flowing into the crack region may be enough to dislodgemetal chips

When the contacting surfaces are cylindrical the contact area is a narrow rectangle

of half width b, given by the equation

(10.39)

where l is the length of the contact area The pressure distribution across the width 2b is elliptical, and maximum pressure is given by pmax= 2F/pbl.

When applied to a cylinder and a plane surface, for the plane use d= ∞ For an

inter-nal cylinder d is negative To evaluate stresses, select the origin of a reference system

at the center of the contact area with x parallel to the axes of the cylinders, y ular to the plane formed by the two cylinder axes, and z in the plane of the contact force.

a

a z

424 COMPONENT DESIGN

FIGURE 10.49 Stress components below the surface of contacting spheres.

For elements on the z axis, principal stresses σx, σy, and σzexist Figure 10.50 shows a

plot of the stresses for depths up to 3b below the contact surface.

For the contacting spheres three different shear stresses are created, given by

ings the objective is to establish the median and the L10, or rated, life The L10impliesthat 90 percent of identical bearings operating at a constant speed and load will com-plete or exceed the test before the failure criterion develops When a number of batches

of bearings are under test, the median life is usually between four and five times the

L10life

The concept of probable survival of a batch of bearings also needs examination If a

machine uses N bearings with each bearing having the same reliability R, then the bility of all the bearings is (R) N The distribution of bearing failures can be approximated

relia-by the Weibull procedure By making adjustments to the Weibull parameters (Mischke,1965), the distribution of bearing failures takes the form

(10.41)

If a certain application requires a reliability of 98 percent for the bearing to last for 2500 h,determine the rated life

Solution Using L = 2500 and R = 0.98 in the above equation

Then the rated bearing life L10is calculated to be 10,262 h

Problem 10.3 Experiments indicate that identical bearings acting under different

radial loads F1and F2and operating at speeds n1and n2have lives L1and L2according

to the relation

(10.42)

where a= 3 for ball bearings and 10/3 for roller bearings A roller bearing can safely

accept a load of 4.5 kN at 650 rpm for an L10life of 1400 h Determine its life if the load

is reduced to 3.75 kN and the speed is increased to 725 rpm

Determine the load rating F2if the bearing is to have a reliability level of 95 percent.

Solution Substituting the values gives F2= 4.51 kN

Problem 10.5 Data for a journal bearing are as follows: viscosity m= 3.95 × 10−6

reyn, speed N = 1800 rpm, radial load W = 525 lb, radius R = 0.875 in, clearance c = 0.0014 in, and length l= 1.625 in Determine the bearing’s characteristic number, min-imum film thickness, and its angular location

Solution Bearing l/d = 0.929 and pressure P = (W/2Rl) = 184.6 lb/in.2Equation (10.9)

provides the bearing Sommerfeld, or characteristic, number S= (.875/.0014)2× {3.95 ×

10−6× 1800/(184.6 × 60)} = 0.251 From charts for minimum film thickness and tricity ratio (Raimondi and Boyd, 1958), the ratio of minimum film thickness and clear-

eccen-ance h o /c = 0.54 and eccentricity ratio e = 0.46, and since clearance c = 0.0014, minimum film thickness h o = 0.00076 in and eccentricity e = 0.00064 in For no load, eccentricity e = 0.0 and film thickness h = 0.0014 As the load is increased the journal

is forced downward Figure 10.51 shows the distribution of hydrodynamic pressure inthe lubricant film

Problem 10.6 In Prob 10.5, determine the coefficient of friction, lubricant flow,film pressure, and temperature rise.

Solution From the chart for coefficient of friction (Raimondi and Boyd, 1958), the

value is (R/c)f = 5.2 Hence, the coefficient f = 0.00832 The torque required to come this frictional loss is T = fWR = 3.82 in⋅lb, which is equivalent to HP = TN/63000 = 0.1092 hp From the chart for lubricant flow, 60Q/RcNl = 4.08 and Q = 0.244 in3/s

over-Leakage at the two ends of the bearing is obtained from the charts, where Q s /Q= 0.54,

The maximum pressure developed in the film is obtained from the charts in the form

of pressure ratio P/Pmax= 0.47 Since P = 184.6, Pmax= 392.8 lb/in.2

REFERENCES

Allaire, P E., Li, D F., and Choy, K C., “Transient unbalance response of four multi-lobe journal

bearings,” Journal of Lubrication Technology, 1980.

Allison G., Turbine Division, TM # 55-2840-231-23, 1981.

ASME Report—Pressure/Viscosity in Rolling Element Bearings, Vol II, ASME Report, New York,

1954

Bailey, J K., and Galbato, A T., “Evaluating bearings for high speed operation,” Machine Design,

October 1981

Childs, D., Turbo-Machinery Rotor Dynamics, John Wiley & Sons, New York, 1993.

Childs, D., and Kleynhans, G., “Experimental rotor dynamic and leakage results for short (L/D = 1/6)

honeycomb and smooth annular pressure seals,” Proceedings of the 5th International Conference on

Vibrations in Rotating Machinery, Institute of Mechanical Engineers, London, 1992.

Darden, J M., Earhart, E M., and Flowers, G T., “Comparison of dynamic characteristics of smoothannular seals and damping seals,” ASME Paper # 99-GT-177, New York, 1999

Ehrich, F F., “The influence of trapped fluids on high speed rotor vibrations,” Journal of Engineering

for Industry 89(4):806–812, 1967.

Ehrich, F F., Handbook of Rotor Dynamics, Krieger Publishing Co., Malabar, FL, 1999.

Ferguson, J., “Brushes as high performance gas turbine seals,” ASME Paper # 88-GT-182, New York,1988

Forster, N H., “High temperature lubrication of rolling contacts with lubricants delivered from thevapor phase and as oil mists,” Ph.D Thesis, University of Dayton, Ohio, 1996

Friswell, M I., and Penny, J E T., “The choice of orthogonal polynomials in the rational fraction

poly-nomial method,” International Journal of Analytical Experimental Modal Analysis 8(3):257–262, 1993.

Greathead, S., and Bostow, P., “Investigations into load dependent vibrations of high pressure rotor on

large turbo-generators,” Proceedings of the Conference on Vibrations in Rotating Machinery,

Institute of Mechanical Engineers, Cambridge, pp 279–286, 1976

Gunter, E J., Barrett, L E., and Allaire, P E., “Design and application of squeeze film dampers for

turbo-machinery stabilization,” Proceedings of the 4th Turbo-Machinery Symposium, Texas A & M

University, College Station, Tex., pp 127–141, 1975

Hagg, A C., and Sankey, G O., “Some dynamic properties of oil film journal bearings with reference

to unbalance vibration of rotors,” Journal of Applied Mechanics 23(2):302–306, 1956.

Harris, T A., Rolling Bearing Analysis, John Wiley & Sons, New York, 1984.

Hertz, H., “The contact of elastic solids,” J Reine Angew Math 92:156–171, 1881.

Jones, A B., “Analysis of stress and deflections,” New Departure Engineering Data, Bristol, Conn.,

1946

Holmes, R., and Box, S., “On the use of squeeze film dampers in rotor support structures,” Machine

Vibration 1:71–92, 1992.

Kirk, R G., “Oil seal dynamics: Considerations for analysis of centrifugal compressors,” Proceedings

of the 15th Turbo-Machinery Symposium, Texas A & M University, College Station, Tex., 1986.

Kirk, R G., “A Method for Calculating Labyrinth Seal Inlet Swirl Velocity,” Rotating Machinery

Dynamics, Vol 2, pp 345–350, ASME, New York, 1987.

Liao, N T., and Lin, J F., “A new method for the analysis of deformation and load in a ball bearing

with variable contact angle,” ASME Journal of Mechanical Design, New York, NY., 1999 Lubkin, J L., “Contact problems,” in W Flugge (ed.), Handbook of Engineering Mechanics, Sec 42-1,

McGraw-Hill, New York, 1962

Lund, J W., “Spring and damping coefficients for the tilting pad journal bearing,” Transactions

7(4):342–352, 1964

Lund, J W., and Thomsen, K K., “A calculation method and data for the dynamic coefficients of oil

lubricated journal bearings,” Topics in Fluid Film Bearing and Rotor Bearing System Design and

Optimization, ASME, New York, pp 1–28, 1978.

Marquette, O R., Childs, D W., and San Andres, L., “Eccentricity effects on rotor dynamic

coeffi-cients of plain annular seals: Theory versus experiment,” Journal of Tribology 119:443–448, 1997 Mischke, C., “Bearing reliability and capacity,” Machine Design 37(22):139–140, September 1965.

Orcutt, F K., “The steady state and dynamic characteristics of the tilting pad journal bearing in

lami-nar and turbulent flow regimes,” Journal of Lubrication Technology 89(3):392–404, 1967.

Padavala, S., Palazzolo, A B., Vallely, D P., and Ryan, S G., “Application of an improvedNelson-Nguyen analysis to eccentric arbitrary profile liquid annular seals,” Workshop on RotorDynamic Instability Problems in High Performance Turbo-machinery, Texas A & M University,Tex., pp 113–115, 1993

Raimondi, A A., and Boyd, J., “A solution for the finite journal bearing and its application to design

and analysis, Parts I, II, and III,” Transactions of ASLE, Vol 1, Lubrication Science and Technology,

Pergamon, New York, No 1, pp 159–209, 1958

Redmond, I., “Rotor dynamic modeling utilizing dynamic support data obtained from field impact

tests,” Proceedings of the 6th International Conference on Vibrations in Rotating Machinery, Paper

# C500/055/96, Oxford, 1996

Santhanan, C K., and Koerner, J., “Transfer function synthesis as a ratio of two complex

polynomi-als,” IEEE, Transactions Automatic Control, SME, Bethel, Conn., pp 56–68, 1963.

Santiago, O., San Andres, L., and Oliver, J., “Imbalance response of a rotor supported on open endintegral squeeze film dampers,” ASME Paper # 98-GT-6, New York, 1998

Sawyer, T., Gas Turbines, Vols I, II, and III, International Gas Turbine Institute, ASME, Atlanta,

1982

Sedy, J., “Improved performance of film-riding gas seals through enhancement of hydrodynamic

effects,” ASLE Transactions 23(1):35–44, 1979.

Shemeld, D., “A history of development in rotor dynamics—A manufacturers viewpoint,” Rotor

Dynamic Instability Problems in High Performance Turbo-Machinery, NASA Report # CP 2443,

pp 1–18, 1986

Soto, E A., and Childs, D W., “Experimental rotor dynamic coefficient results for (a) a labyrinth sealwith and without shunt injection and (b) a honeycomb seal,” ASME Paper # 98-GT-8, New York, 1998.Spakovszky, Z S., Paduano, J D., Larsonneur, R., Traxler, A., and Bright, M M., “Tip clearance actu-ation with magnetic bearings for high-speed compressor stall control,” ASME Paper # 2000-GT-528,New York, 2000

Stephenson, R W., and Rouch, K E., “Generating matrices of the foundation structure of a rotor

sys-tem from test data,” Journal of Sound and Vibrations 154(3):467–484, 1992.

Stribeck, R., “Ball bearing for various loads,” Vol 29, ASME, New York, pp 420–463, 1947.Van Treuren, K W., Barlow, D N., Heiser, W H., Wagner, M J., and Forster, N H., “Investigation

of vapor phase lubrication in a gas turbine engine,” ASME Paper # 97-GT-3, New York, 1997.Vazquez, J A., Barrett, L E., and Flack, R D., “Flexible bearing supports using experimental data,”ASME Paper # 00-GT-404, New York, 2000

Weigl, H., Paduano, J., Frechette, L., Epstein, A., Greitzer, E., Bright, M., and Strazisar, A., “Active

stabilization of rotating stall and surge in a transonic single stage axial compressor,” ASME Journal

of Turbo-Machinery 120:625–636, 1998.

Wilcox, D F., and Booser, E R., Bearing Design and Application, Mc-Graw-Hill, New York, 1957.

Zeidan, F Y., San Andres, L., and Vance, J M., “Design and application of squeeze film dampers in

rotating machinery,” Proceedings of the 25th Turbo-Machinery Symposium, Texas A & M

University, College Station, Tex., 1998

BIBLIOGRAPHY

AFBMA Standards for Ball and Roller Bearings, Revision # 4, June 1972.

American Petroleum Institute, “Centrifugal compressors for petroleum, chemicals and gas service

industries,” API Standard, Vol 617, 6th ed., 1995.

Bently, D E., “Monitoring rolling element bearings” 3(3):2–15, 1982

Boto, P A., “Detection of bearing damage by shock pulse measurement,” Ball Bearing Journal, 1971.

Eshelman, “The role of sum and difference frequencies in rotating machinery fault diagnosis,” Paper

# C272/80, Institute of Mechanical Engineers, London, 1980

Lees, A W., Friswell, M I., Smart, M G., and Prells, U., “The identification of foundation vibration

parameters from running machine data,” Proceedings of the 7th International Symposium on

Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-7, SME, Honolulu, Bethel,

Conn., pp 715–724,1998

Mathew, J., and Alfredson, R J., “The condition monitoring of rolling element bearings using

vibra-tion analysis,” ASME Journal of Vibravibra-tion and Acoustics 106:447–453, 1984.

Monk, R., “Vibration measurement gives early warning of mechanical fault,” Process Engineering,

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MATERIALS AND MANUFACTURE

P ● A ● R ● T ● 3

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SUPERALLOYS FOR TURBINES

11.1 INTRODUCTION

Among the many different technologies that have made possible the development and ation of gas turbines at very high temperatures, superalloys stand at the forefront Thealloys used in the manufacture of jet engines and industrial and marine gas turbines repre-sent the leading edge in materials, and in turn these engines have been the primary drivingforce for the development of superalloys Rocket engines, nuclear reactors, submarines,steam power plants, and space vehicles also extensively use superalloys

oper-Turbine inlet temperatures have gone up by nearly 450°C in the last 30 years.Approximately 70 percent of this increase has been gained from improved design of cool-ing of blades and vanes by taking advantage of serpentine passages, turbulators, pin fins,film cooling, and thermal barrier coatings (TBC) The remaining 30 percent gain in inlettemperature is derived from improved superalloys and casting processes Significantadvances in metal temperature, stress, and environmental capabilities for turbine airfoilshave been obtained from the development of directionally solidified, columnar grain andsingle-crystal casting processes Casting and solution heat treatment of directionally solid-ified materials is less expensive, and the production of single and multiairfoil vane seg-ments with a large platform is not complex

Ever since man constructed mechanical devices, it has been observed that the efficiency

in performing useful work is related to making use of high temperatures With the opment of the thermodynamic Brayton cycle (in conjunction with decreased rejection tem-perature), the basic principle that higher operating temperatures achieve improved efficiency

devel-is brought out Relatively advanced steam turbines based on the principle were developed inthe 1800s and gas turbines in the 1900s for power generation With the progress of newertechnologies in jet propulsion and power generation, the need for materials to withstand theelevated temperatures became apparent The definition of disks, airfoils, and combustionchambers became inexorably intertwined with the development of superalloys Metallurgyprogressed from the days when iron and copper were the primary components to the dis-covery of austenitic stainless steel in the 1910–1920 time period In the 1930s small amounts

of aluminum were added to titanium- and nickel-chromium alloys to obtain improvements

in creep strengthening Carbide-strengthened austenitic cobalt-based alloys later made theirappearance and could be cast into complex shapes From the 1940s onward the superalloyshave gone through a series of refinements and improvements through the formation of newcomposition for the alloys and manufacturing processes Military aircraft engines were theinitial beneficiaries of the new technology, but application to other gas turbines did not lagtoo far behind

Chromium is added to iron and nickel base to obtain resistance to oxidation, whilesmaller amounts of aluminum, titanium, and columbium provide enhanced creep-resistance

CHAPTER 11

433

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characteristics Iron gradually disappeared over a period of time as an alloy base, to bereplaced by nickel and cobalt because of the more durable face-centered cubic structure.Although chromium may lead to some level of deterioration in strength, considerable reduc-tion of this element can cause corrosion at high temperatures, leading to its more balanced

use in IN-738 Excessive use of aluminum, titanium, and columbium for forming g′ can alsopose a variety of structural problems Addition of molybdenum, initially in M-252, providedadditional strengthening through solid solution and carbide effects Other refractory ele-ments, tungsten, tantalum, and rhenium also later found their way to enhance the mechani-cal properties Carbon remains as a complexing agent, with matrix carbides providing pointstrengthening in several solid-state reactions Zirconium and boron improve on grain bound-ary effects, but are not needed in single-crystal alloys since the boundaries are absent (Sims,Stoloff, and Hagel, 1987)

The matrix of an alloy is made of densely packed face-centered cubic austenite, as

shown in the g′ field of Fig 11.1 for a simple ternary, a quaternary, and a polar phase gram The austenite is produced from the reduced field in the iron-chromium system,enlarged by nickel or cobalt Since iron is deleted in a large number of cases, superalloysmay be considered to evolve from stainless steel Mechanical capabilities of the alloy areobtained from solution strengthening of the matrix Carbides of the M23C6 and M6C formspresent in the nickel and cobalt alloys are readily heat treatable

dia-An important aspect in the preparation of alloys is to avoid undesirable elements such

as mu, sigma, and Laves by the use of phase control tools Phase diagram metallurgy mits sophisticated understanding and practice in developing eutectic superalloys that may

per-be strengthened by eutectic lamellae formed by freezing from the melt

Silicon carbide (SiC) and silicon nitride (Si3N4) are considered good candidates forhigh-temperature applications in gas turbines But satisfactory solutions to some of theproblems experienced have yet to be developed at a reasonable cost SiC suffers from itsinherent low thermal shock resistance, and Si3N4experiences degradation due to oxidationand creep The effect of type and amount of sintering additives, purity of the material com-ponents, and processing conditions on the developing microstructure and resulting proper-ties have yet to be understood

FIGURE 11.1 Face-centered cubic g′ field for austenitic superalloys (Sims, Stoloff, and Hagel, 1987).

FCC

BCC

BCC HCP

A

Cr (4.66)

V (5.66) Ni

(0.66)

Co (1.71)

Fe (2.66)

Cr-low

Mn (3.66) Ni

Co

FCC austenite

Cr

Polar diagram of Cr-low vs first long period elements

dis-In considering the effect of solutes on physical properties such as elastic modulus and

lattice parameter, Mott and Nabarro (1948) developed a model to yield stress t = 2Gec for

a dilute solution Here G is the shear modulus, c is the concentration of solute atoms, and e

is a misfit generated by the difference ∆a between the lattice parameter aoof the pure

matrix a is the lattice parameter of the solute atom, and is given by e = (1/c) × (∆a/ao) Alinear relation exists between the flow stress and the lattice parameter for a single solute innickel The change in stress may also depend on the position of the solute in the periodictable For the same lattice strains, greater hardening results when the valency differencebetween the solute and the solvent is higher Differences in the modulus between the soluteand the solvent can also provide strengthening if it is argued that extra work is needed toforce a dislocation through hard or soft areas of the matrix (Fleischer, 1964) Combiningthe two parameters provides the interaction force between the solute and the dislocation

(e G = [dG/dc]/G, e¢ G = eG/[1 + |eG|]/2).

(11.1)

where a = ±16 for edge dislocations and a = 3 for the screw form If L is the distance between two solute atoms experiencing stress t c at a dislocation, then b = F/(tc L).

Precipitation-hardened nickel-based superalloys obtain most of the strength from stable

intermetallic compounds such as g′ [Ni3(Al, Ti)] and g″ [Ni3(Cb, Al, Ti)] Borides andcarbides give a lesser extent of strengthening at low temperatures, but their impact on creeprate, rupture life, and rupture strain can be considerable through their influence on the prop-erties at the grain boundary Ni3Al may be considered a superlattice form of structure, andhas a long-range order to its melting point of 2525°F Most nickel base alloys may bestrengthened by a precipitate, where titanium and columbium may substitute 60 percent of

the aluminum Single and polycrystal forms of g′ display a reversible increase in flow stressbetween −320°F and 1475°F, depending on the aluminum content Many other lattices such

as Ni3Si, Co3Ti, Ni3Ge, and Ni3Ga gain in strength over a similar temperature range (Sims,Stoloff, and Hagel, 1987)

Hardening of austenitic alloys by particles is affected by the strain energy, differences

in elastic modulii, and stacking fault energy between the particle and the matrix, creatingadditional particle–matrix interface and lattice resistance of particles with temperature.When a dislocation cuts an ordered particle, the force on the dislocation must balance theantiphase boundary energy created (Ham, 1970) For a given force the stress increases withthe size of the particle because of the increased flexibility of the dislocations as they inter-act with coarser particles Dislocation pairs interacting with the particles can occur whenone of them just shears the particle while the other is pulled forward by the boundaryremaining in all particles cut by the first dislocation This may be expected to happen atlong aging times

In the dispersion form of imparting strength to superalloys, the hardening mechanismrelies on the presence of coarse and elongated grain structures produced during processingand accumulated in service Alloys produced by Inco may possess both precipitates anddispersoids The hardening of the particles must be combined with the strengthening effects

F=Gb120 ε2 G′ −αε

of the boundaries at the grain and at the solid solution elements An extrusion press may bethe best means of obtaining coarse and elongated grains, both to consolidate the powder and

to achieve a suitable structure for the subsequent secondary recrystallization

Predicted results of g − g ′ alloys cannot be readily applied to several commercially

available materials, although calculated values for Nimonic 80 A and A-286 are widelyused Larger particle size, orientation, and dependence on strain rate in the stress–strainbehavior are the main drawbacks The microstructure of nickel base superalloys is too com-plex to permit a single mechanism to be applied in all stress and temperature ranges Little

mismatch exists between the nickel–chromium–aluminum g types of alloys, while a higher level is present in the nickel–aluminum–titanium g′ alloys (Decker, 1969), as seen in Fig 11.2.Microscopic examinations on Nimonic PE16 indicate the leading dislocation of a pair

rapidly bends between the g′ precipitates, but the trailing dislocation remains practicallystraight Evidence suggests that with little or no mismatch the volume fraction controls the

flow stress and creep resistance The volume fraction varies from 0.2 in g′-lean Nimonic

(Ni-Cr-Al)(Ni-Cr-Mo-Al-Ti)

M-252Alloy 713C

(Ni-Cr-Al-Ti)Alloy X-750Nimonic 80A

(Ni-Cr-Co-Al-Ti)Nimonic 90

80A to 0.6 in MAR-M 200 Alloys with large volume fraction are deformed by particleshear, while those with less volume fraction experience deformation from bowing ofunpaired dislocations in the face-centered cubic matrix.

Alloys containing substantial volume fraction of g′ behave in the same manner as pure

g′ in that the flow stress increases with temperature The strength of the flow is moderatelyhigh at low temperature, reaches a shallow peak near 1300°F, and falls off at a slightly highertemperature than for a leaner alloy

Studies of precipitate morphology of cobalt base alloys indicate a similar behavior withnickel base alloys Flow stresses are relatively insensitive to temperature when the particlesare sheared by paired dislocation But as the particles are redissolved on aging with testtemperatures above 930°F, the flow stress drops rapidly Increased volume fraction causesthe flow stress to rise in both aged cobalt and nickel base alloys But no commercially avail-able cobalt base alloys have taken advantage of this mechanism for hardening

Primary creep in austenitic alloys has not been extensively investigated over large ranges

of temperature Creep mechanism in MAR-M 200 single crystals at 1400°F have beenreported (Leverant and Kear, 1970), with primary creep strain and rate indicating sensitivity

to orientation Creep takes place due to the motion at dislocation pairs in the super lattice inconjunction with faults at a pace controlled by the diffusion process At high strain rates thedislocations do not alter to obtain the right shearing sequence, and deformation is a conse-quence of slippage alone A constant volume fraction causes larger particles to be more ben-eficial in restricting primary creep, as the line tension precludes penetration of the particles Factors that control steady-state creep resistance in single-phase crystalline solids arediffusivity, elastic modulus, temperature, stacking fault energy, and stress Thus, a conse-quence of high modulus and low fault energy and diffusivity in solute additions is enhancedcreep strength Tungsten and molybdenum help in raising the modulus and reducing thediffusivity of austenitic superalloys In nickel base alloys the fault energy can be decreased

by cobalt In the presence of second-phase particles the activation energy for creep is higherthan for self-diffusion The difference can be minimized by including the temperaturedependence of the elastic modulus Development of a substructure during primary creepand after substantial strain hardening helps in raising the steady-state creep in MAR-M 200

at 1400°F Dislocations forming between the g and g ′ are limited from moving by the ticle size, thus leading to a low creep rate The g′ can be altered in nickel base by anneal-ing under stress, with the orientation dictated by the direction of the applied stress in platesand rods Yielding in U-700 crystals is raised when the temperature is 1400°F Nickel–aluminum–molybdenum–tantalum alloy specimens in the air-cooled and solution-treatedcondition display reduced steady-state creep rates and longer rupture life when comparedwith a standard heat treatment A prestrain undercreep condition additionally improves the

par-properties because of the formation of g′ during the primary creep

11.3 NICKEL BASE ALLOYS

Nearly half the total weight of aircraft engines comprises parts made from nickel basealloys The alloys are favored in elevated temperature regions of the power plant, in spite

of the complex physical metallurgy The tensile- and creep-rupture strength up to 5000 h

of these alloys in the 1200 to 2000°F temperature zone makes them the prime candidatesfor turbine blades Industrial gas turbines, on the other hand, require creep-rupture charac-teristics over longer periods and resistance to oxidation and corrosion at high temperatures.New air transport engines also aim at 50,000 h of operating life, while power generationturbines dedicated to intermittent peaking operation target for a 100,000-h life, and so resis-tance to low-cycle fatigue is of significance

A dozen different elements constitute the composition of nickel base alloys The ufacturing process requires control of these elements and at the same time the amount ofsilicon, phosphorus, sulfur, oxygen, and nitrogen must be limited during the meltingprocess Most nickel alloys have 10 to 20 percent chromium, up to 8 percent of aluminumand titanium, 5 to 10 percent of cobalt, and lesser quantities of boron, zirconium, carbon,molybdenum, tungsten, columbium, tantalum, and hafnium Slight quantities of selenium,thallium, tellurium, lead, and bismuth are dictated by the requirements for the part.

man-The major phases present in nickel base superalloys are the g and g′ matrices, carbides,

grain boundary g′, and borides Chemically dynamic structures appear at high temperatureswith the phases interacting and reacting continuously, so the definition of chemical equa-tions of state with activation energies is not easily made Nickel by itself does not possess

high elastic modulus or low diffusivity, but the g matrix proves beneficial at high

temper-atures and time periods Some of the alloys may be subject to 90 percent of the meltingtemperature, and can function for 80,000 h at lower temperatures These endurance char-acteristics may be attributed to high levels of phase stability, formation of Cr2O3protectivescales, and additional Al2O3rich scales at higher temperatures for outstanding resistance tooxidation Figure 11.3 provides some phase diagrams at around 2000°F, with the nickelcorner placed at the opposite apex

Hardening of nickel base superalloys can be related to the atomic diameter of the mental constituents as measured by expansion of the lattice Aluminum is good for bothprecipitation and solid solution strengthening, with effects persisting at high temperatures

ele-up to 60 percent of melt temperature Other elements also contribute to the strength in ing extents, with the slower diffusing molybdenum and tungsten proving to be the mostpotent hardeners (Sims, 1970)

Cr

Co Fe

Co Co

CoMo

MoMo

Ni-Co-Cr-Mo

A high nickel content matrix favors precipitation of the γ ′ phase, with nickel and

alu-minum dominating Since this is a unique intermetallic phase, g′ provides considerablestrengthening by the interaction of dislocation from applied force at increased tempera-

tures An added advantage accrues from the inherent ductility of g′, preventing it from

being a source of fracture and contrasting with the brittle s phase The process of

substitu-tion and partisubstitu-tion of the elements with nickel and aluminum is represented in the schematicternary section of Fig 11.4 at 2100°F for many alloys

Aluminum is replaced by titanium, columbium, tantalum, and hafnium, as indicated bythe phase running diagonally from Ni3Al to Ni3X Molybdenum, chromium, and iron arenoted to replace both nickel and aluminum positions

Carbides play a complex role, appearing in the form of grain boundaries in nickel alloys.Detrimental effects on ductility may be overcome by reducing the carbon content in certaingrain boundaries, but this can severely reduce creep life as illustrated in Nimonic 80A with0.3 percent carbon (Fell, Mitchell, and Wakeman, 1969) Carbides generally form in super-alloys during freezing, and are a major source of carbon for the alloy during heat treat andoperation

Grain size and its relation to the thickness of a component play a big role in the strength

of an alloy Rupture life and creep resistance vary proportionately with the ratio of ness and size of the grain in wrought and cast alloys When large grains occur in thin sec-tions, the consequence may be reduced creep-rupture resistance Since larger grains lowertensile strength but have good rupture strength, fine grains must then be balanced withlarger ones to obtain the right combination of the characteristics Creep properties can also

thick-be improved by small additions of boron and zirconium, increasing life 13 times, tion 7 times, and nearly doubling stress at rupture Magnesium helps during forging oper-ations of wrought alloys by tying up sulfur

elonga-An addition of hafnium of most creep resistant alloys for turbine airfoils has been mined to facilitate production by the investment casting method The intricately shapedcomponents with internal cooling passages are susceptible to predominantly intergranularfailures Provision to accommodate localized plastic strain without compromising creepresistance in the grain is obtained from hafnium in the form of a more acceptable boundary

deter-at the grain Hafnium has good carbide-forming capability and can strengthen g′, but lems arising from its high reactivity must be controlled during melting from the ingot andduring component manufacturing

FIGURE 11.4 Ni Al solid-solution field for different alloys (Sims, 1970).

6 Wt 6.86 At 5 5.76 4 4.64 3 3.50 2 2.35 Titanium content %

1 1.18 0 0 50

Ni

Al

750 800 850 900 950

°C 1000

1050 1100 1150 59% Ni 22% Cr 19% Co

78% Ni 22% Cr γ

γ + γ′

Aluminum content, at %

Ternary alloy content, at %

Cb Ti

Fe Co

Mo Cr V

Ni3Al

Heat treatment of nickel-base alloys requires knowledge of the constitution, phase bility, and properties Solutioning temperature of wrought alloys is between 1950 and

sta-2250°F Formation of certain carbides during solutioning in alloys such as Rene 41 canreduce other subsequent carbide reactions Most strengthening processes call for a series of

ages Linkage between heat treatment, g′ formation, and strengthening must be consideredfor specific materials Murphy, Sims, and Heckman (1967) illustrate the case of wroughtU-500 rupture bars treated according to the following schedule:

Primary solution 2050°F for 2 h, air-cooled

Secondary solution 1975°F for 2 h, air-cooled

Primary age 1700°F for 24 h, air-cooled

Secondary age 1400°F for 16 h, air-cooled

Inspection of the microstructure reveals formation of g′ in the primary and secondarysolutions, with air-cooling causing finer particles that dissolved in the subsequent phase

Aging causes the g′ to grow again The final age results in a combination of moderate sile strength and rupture life required for longer lasting turbine airfoils

ten-Cast alloys may be heat treated to a simpler cycle After cooling in the mold, aging maytake place for 12 h at 1400°F More complex alloys may require more extensive heat-treating steps The freezing pattern of cast alloys is often visible after service because of thecarbides in the boundaries and concentrations of refractory elements

Controlled solidification of turbine airfoils was initially achieved with MAR-M 200.The process of directional solidification causes grains of lower elastic modulus to grow lon-gitudinally The combination of eliminated grain boundaries in the transverse direction andthe lower elastic modulus improves the thermal fatigue life by 300 to 500 percent over con-ventionally cast equiaxed alloys, such as Rene 80 and MAR-M 247 By adding 2 percenthafnium to MAR-M 200, the directionally solidified grain boundaries become more duc-tile, preventing cracks at the grain boundary Elimination of all grain boundaries also elim-inates the need for ductilizers/strengtheners such as boron, zirconium, and hafnium Sincethese elements considerably reduce the melting point of the alloy, this permits an extra100–200°F higher heat treatment of the single crystals The higher solutioning temperature

causes greater usage of g′ and an improvement in the strength capability of single crystalalloys over directionally solidified and conventionally cast materials

11.4 COBALT BASE ALLOYS

The g′-strengthened nickel alloys generally surpass the capabilities of cobalt alloysbecause of the lack of adequate hardening mechanisms In the cast and wrought formscobalt-based alloys are used for turbochargers and gas turbines because of their highermelting temperatures and superior resistance to corrosion and thermal fatigue The chemi-cal composition of cobalt alloys follows on the same lines as the stainless steel Chromium

is a key element, constituting 20 to 30 percent by weight, and is responsible for providingoxidation and hot corrosion resistance Since carbide strengthening is a primary hardeningmechanism, the presence of carbon is crucial for casting alloys requiring high creep-rupture strength In the range of 0.3 to 0.6 percent by weight of carbon, the tensile and rup-ture strength increase nonlinearly, but ductility decreases noticeably Carbides are alsoresponsible for controlling the grain size during processing and heat treatment

Most of the commercially available cobalt alloys are melted in air or argon because ofthe absence of aluminum and titanium These reactive elements necessitate the use ofexpensive vacuum melting procedures Silicon and manganese are added to control levels

of sulfur and to improve fluidity of the alloy melt during casting Addition of 5 percent byweight of aluminum for wrought and cast cobalt alloys obtains improved oxidation and hotcorrosion resistance, as seen in cobalt–chromium–aluminum–yttrium coatings Titanium isadded in wrought alloys CM-7 to develop a uniform and coherent precipitate High tensilestrength is obtained to about 1300°F

Cobalt alloys with high temperature capabilities posses a complex chemical andcrystallographic composition, as is true also of nickel and iron alloys Consisting of anaustenitic matrix and a variety of precipitated phases such as carbides and intermetalliccompounds in the geometrically and topologically closely packed family of structures, thealloys cannot be defined as stable at the operating temperatures encountered in gas turbinesbecause of the high levels of dynamic stress, time, and interactions between the surface andthe environment Transformation of phase from the mobility of partial dislocations alongthe closely packed planes, referred as martensitic, and its effects on the mechanical prop-erties of cobalt alloys is not extensively documented

The level of stacking faults, a function of composition, temperature, and applied stress

or consequent deformation, is of interest within the phase transformation temperature rangewhere the mechanical properties are strongly influenced Strengthening is derived from theinteraction of dislocations within the faults, especially when second phase particulate occurduring service exposure But ductility is likely to be minimized in the temperature transi-tion range Addition of nickel alleviates the potential phase instability associated with tem-perature cycling, and raises the stacking fault energy to reduce partial dislocations Thermomechanical processing controls the microstructure of cobalt base alloys, in con-junction with their chemical composition and crystallographic phases Wrought alloys havethe simplest structure because the content of carbide is limited As an example, thermome-chanical processing of thin (0.015 in) sheets can improve the low strain creep strength of HS-

188 by developing a strong recrystallized texture ( Klarstrom, 1980) The processingcomprises 80 percent final cold work, followed by annealing at 2250°F for 10 min Theimprovement is derived from a combination of better formations at the subboundary and theprecipitation of carbides in the dislocations during creep (Sims, Stoloff, and Hagel, 1987) Strengthened wrought alloys like L-605 and HS-188 possess better creep rupture char-acteristics when compared with Hastelloy X and INCO-617 by about 100°F The materialsalso permit easy machining and welding operations Investment cast carbide strengthenedcobalt alloys form a special class because of their superior tensile and rupture strength Thestress rupture parameter curve is mostly flat as a function of temperature (Fig 11.5).Strengthening is achieved by balancing the hardening of refractory elements in the solidsolution and the precipitation of carbide, the two playing a role for high temperature creeprupture and for fatigue strength Aging heat treats combined with typical solution treat-ments are not beneficial in altering the strength-to-ductility ratio in high-carbon alloys Thetrend in recent developments has been to balance the formation of carbides with more sta-ble precipitates to get the least amount of primary and eutectic precipitation

Strengthening of cobalt alloys with the dispersion of oxygen arises from the stability ofthe materials at high temperatures Addition of fine particles of inert and thermodynami-cally stable ThO2or Y2O3provide excellent creep rupture strength to temperatures nearingthe melting point of the base

Evaluation of fracture behavior of cast and heat-treated MM-509 indicates that fractureinitiates in the large carbide particles and eutectic concentrations with the onset of plasticdeformation (Woodford and McMahon, 1970) Crack propagation is controlled by aging at

1500°F for 24 h from the consequent improvement in hardness and strength of the matrix.Distribution and spacing of the carbide at the grain boundaries is a significant factor forfracture toughness in cast cobalt alloys

Cast cobalt alloys display a level of immunity from embrittlement at elevated tures Oxidation of a number of nickel alloys around 1800°F for 100 h affects their ductility,

mostly due to the accelerated diffusion of oxygen through the boundaries at the grain

MM-509 and FSX-430 cobalt alloys experience little loss in rupture life from exposure to air.This indicates that the materials are mostly prone to embrittlement from thermal effects

11.5 NICKEL–IRON ALLOYS

The nickel-iron class of superalloys is marked by a composition of around 25–60 percent

of nickel and 15–60 percent of iron Among the more extensively used nickel-iron alloys,

a few deserve special mention: A286 has a high iron content; Incoloy 901, Inconel 718,and Incoloy 706 are rich in nickel; and Incoloy 903 is a low-expansion iron-rich alloy Thematerials find usage in the manufacture of blades, disks, shafts, and casings for steam andgas turbines, and are developed from austenitic iron-based stainless steels to obtain highstrength characteristics at elevated temperatures Limitations during the melting and forg-ing processes can be overcome with the vacuum induction method to permit retention ofreactive elements such as titanium and aluminum (Sims, Stoloff, and Hagel, 1987) Some common traits with respect to the chemical composition of the alloys include anaustenitic matrix based on nickel and iron, addition of alloying elements to partition theaustenite for strengthening, ordered intermetallics, carbides and borides for strengtheningprecipitates, and modification of grain boundaries The nickel-rich (exceeding 40 percent)group possesses good mechanical properties up to 1200°F, and find wide usage because of

FIGURE 11.5 Mechanical properties of cobalt and nickel-base alloys (Sims, Stoloff, and Hagel, 1987).