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9Gas turbine materials selection, life

management and performance improvement

T . ÁLVAREZ TEJEDOR, Endesa Generación, Spain

Abstract: The aim of this chapter is to provide a comprehensive review of

the material technology used for high-temperature applications and their

impact on the operational life of the gas turbine. Market advantage

today relies on increasing performance and efficiency as well as reducing

life-cycle costs. The first statement is responsible for pushing present

materials and coatings to their limits with significant consequences in

terms of the durability and maintenance costs for machines that rely on

these advanced hot section designs. Gas turbine material selection will

greatly impact both gas turbine performance and life-cycle costs, in such

a way that the correct selection will make gas turbine technology

successful in the electric power generation market.

Key words: hot gas path, superalloy, thermomechanical fatigue, creep,

fracture mechanics, life management.

9.1 Introduction

The gas turbine industry must focus on several key factors that will make its

future power generation technology successful in the electric power

generation market. These factors are summarized in the list below and in

Fig. 9.1 [1]:

. competitive economic performance (i.e. higher efficiency and optimizedlife-cycle costs);

. reliable operation under a cycle duty (repeated gas turbine startups andshutdowns);

. increased dependability of current and future plants (reliability,availability, maintainability and durability, or RAM-D);

. ability to meet regulatory emissions levels and achieve high thermalefficiencies; and

330

© Woodhead Publishing Limited, 2011

. reliable fuel-switching capability and fuel flexibility.

Gas turbines will be one of the most important horizontal technologies

and will play an essential role in meeting these requirements. Gas turbine

technology is considered as horizontal due to its capacity to be widely

applied across many different types of power plant configurations, while

running with different fuels (coal gas, natural gas, hydrogen, liquid fuels,

etc.).

Gas turbine performance and life management arise as the way to achieve

competitive advantages that will enable gas turbine technology to gain the

edge over their competitors. The focus is therefore on the ‘heart’ (core) of

gas turbine technology.

The ‘hot gas path’ of a gas turbine is the core of the engine, which includes

the combustion chamber, the transition pieces and the turbine section. The

main drivers for improving hot gas path behavior are:

. Gas turbine performance – this is highly dependent on the turbine inlettemperature, which results in a greater need for the hot gas path

components to achieve high thermal efficiencies with low nitrogen oxide

(NOx) emissions.

. Gas turbine life-cycle costs – this is strongly affected by the costs of hotgas path components and maintenance, which gives rise to maintenance

practices and inspection techniques that in turn allow the improvement

of gas turbine dependability, i.e. its RAM-D.

Gas turbine material selection will greatly impact both gas turbine

performance and life-cycle costs in such a way that the correct selection will

9.1 The new competitive arena for power generation [1].

Gas turbine materials selection 331


make gas turbine technology successful in the electric power generation

market.

The primary philosophy is to build a reliable, efficient, cost-effective

machine for the intended service. This includes a materials development

program, which is expensive and time-consuming. First, new ideas and

emerging developments are screened to select the one or two with the best

potential for satisfying the material design goals. Extensive testing follows to

ensure that the materials will perform satisfactorily in heavy duty gas

turbines for tens of thousands of hours. Long-term creep testing at the

expected operating temperatures of the material is conducted to characterize

alloy performance. Additionally, laboratory evaluations typically include

items such as tensile, rupture, low- and high-cycle fatigue, thermal

mechanical fatigue, toughness, corrosion/oxidation resistance, production/

processing trials and complete physical property determination. This phase

of testing can last several years for a new nozzle or blade material. After

laboratory testing comes the actual machine-operating experience, the best

and final test of a new material to be compared and evaluated with the

current baseline material.

9.2 Superalloys

As mentioned above, the hot gas path of a gas turbine includes the

combustion chamber, the transition pieces and the turbine section. The

turbine section is constructed around several rows of blades and vanes.

The vanes in the first stage will become the hottest as they are located

closest to the combustion chamber. Then a significant performance

parameter is defined, the firing temperature [2], which is thought to be the

highest temperature reached in the Brayton cycle. It is usually defined as the

mass–flow mean total temperature at the stage 1 vane trailing edge plane.

Currently all first stage vanes are cooled to keep the temperatures within the

operating limits of the materials being used. The two types of cooling

currently employed are air and steam.

The blades and vanes in the turbine section will determine to a large

extent the ultimate efficiency of the gas turbine. These parts have to work

under extreme conditions, operating in high temperatures in an oxidizing

environment while being subjected to large thermal and mechanical stresses.

In order to increase the durability of the blades and vanes in these extreme

conditions, special metal superalloys have been developed. The high-quality

technologies used in the manufacture of the turbine blades make them the

most expensive parts of the gas turbine.

To achieve higher thermal efficiencies, higher combustion temperatures

are needed; however, higher combustion temperatures – from around

1540 8C (2800 8F) – exacerbate NOx emissions. To combat excessive NOx

Power plant life management and performance improvement332


emissions, ‘dry’ low oxides of nitrogen (NOx) and ‘ultralow’ NOxcombustors are introduced, as well as alternative methods for achieving

ultralow NOx emissions, including rich-burn, quick-quench, lean-burn and

catalytic combustors [3]. Adding further to these technological limitations,

extremely high operating temperatures – greater than 1290 8C (2350 8F) –are beyond the material tolerances of the turbine blades and vanes.

Therefore, the goal of achieving 60% efficiency while staying below

10 ppm of NOx emissions is constrained by the thermal emission reduction

and material limits of the gas turbine system. There are four main

innovations that are critical in meeting this need for high efficiency and low

emissions:

. advanced cooling systems;

. single-crystal superalloy casting;

. thermal barrier and metallic coating; and

. lean pre-mix dry low-NOx combustors.

On the other hand, to optimize the life-cycle cost of gas turbines, special

attention must be paid to the hot gas path components: typically, more than

around 70% of the total gas turbine maintenance cost corresponds to

scheduled maintenance, parts and materials. This will lead to the establish-

ment of mechanisms for risk mitigation, such as long-term service

agreements (LTSAs) [4], business interruption insurance, extended guaran-

tees and part-cost guarantees. Apart from the above considerations, it is also

necessary to take into account current operational conditions in a

deregulated electricity market. These conditions require more flexible

operations with high efficiency and low emissions for the whole power

range, high operational reliability and better maintainability.

Most heavy-duty gas turbines for operation in land-based applications

use proven technology, derived from aircraft and steam turbine applica-

tions. However, the unique requirements and special conditions for heavy-

duty gas turbines demand special materials and processes. The materials

used in stationary applications can be classified in three groups: stainless

steels (iron-based), nickel-based alloys and cobalt-based alloys.

The alloy composition has to be a compromise between mechanical

strength and the corrosion and oxidation resistance while ensuring a proper

economical lifetime. Most of the alloys applied in the turbine section have a

composition with high nickel or cobalt contents, resulting in good

mechanical properties. Eventually, the cast superalloys for the highest

temperatures are protected against oxidation and corrosion by chromium

and aluminum coatings.

The development of the increase in firing temperature and material

properties is illustrated in Fig. 9.2. In the early years of turbine

development, increases in blade alloy temperature capability accounted



for the majority of the firing temperature increase until the 1970s when

aircooling was introduced, which decoupled the firing temperature from the

blade metal temperature. Also, as the metal temperatures approached the

870 8C (1600 8F) range, oxidation and corrosion of blades became more lifelimiting than strength until the introduction of protective coatings. During

the 1980s, emphasis turned toward two major areas: improved materials

technology, to achieve greater blade alloy capability without sacrificing

alloy corrosion resistance, and advanced, highly sophisticated air-cooling

technology, to achieve the firing temperature capability required for the new

generation of gas turbines. The use of steam cooling to further increase

combined-cycle efficiencies in combustors was introduced in the mid to late

1990s.

Since 1950, turbine blade material temperature capability has advanced

by approximately 472 8C (850 8F), approximately 10 8C (20 8F) per year. Theimportance of this increase can be appreciated by noting that an increase of

56 8C (100 8F) in the turbine firing temperature can provide a correspondingincrease of 8–13% in output and a 2–4% improvement in simple-cycle

efficiency [5]. This technological development has been mainly possible

thanks to the new generation of advanced materials called superalloys.

The denomination of superalloys is used to those alloys generally used at

temperatures above around 540 8C (1000 8F), i.e. nickel-base, iron–nickel-base and cobalt-base corrosion-resistant alloys. The iron–nickel-base

superalloys are an extension of stainless steel technology and generally are

wrought, i.e. formed to shape or mostly to shape by hot rolling, forging, etc.

The cobalt-base and nickel-base superalloys, on the other hand, may be

9.2 Firing temperature trend with blade material improvement [5].



either wrought or cast depending on the application or the alloy

composition involved.

Superalloys consist of an austenitic face-centered-cubic (fcc) crystal

structure matrix phase, gamma (γ), plus a variety of secondary phases.Important secondary phases are gamma prime (γ ´) fcc ordered Ni3(Al, Ti)and various MC, M23C6, M6C and M7C3 (rare) carbides in nickel-base and

iron–nickel-base superalloys (Fig. 9.3). Carbides are the principal secondary

phases in cobalt-base alloys. Also, γ ´, a body-centered tetragonal (bct) phaseof ordered Ni3Nb, a hexagonal ordered Ni3Ti (η) phase and the δ-orthorhombic Ni3Nb intermetallic phase can be found in nickel-base and

iron–nickel-base superalloys.

The strengthening process in superalloys, and hence the mechanical

properties of superalloys, can be modified considerably by manipulating the

strengthening level achieved. The superalloys derive their strength from

solid-solution hardeners and secondary precipitate phases that form in the γmatrix and produce precipitation (age) hardening. The principal strengthen-

ing precipitate phase in nickel-base and iron–nickel-base superalloys is γ’(gamma prime).

Additionally, carbides may provide limited strengthening directly (e.g.

through dispersion hardening) or, more commonly, indirectly (e.g. by

stabilizing grain boundaries against movement). The δ and η phases areuseful (along with γ ´) in controlling the grain structure of wroughtsuperalloys during processing. By controlling grain structure, strength can

be significantly influenced. The extent to which the second phases contribute

directly to strengthening depends on the alloy and its processing. It should

be noted that improper distributions of carbides and precipitate phases can

be detrimental to the mechanical properties. In addition to those elements

that produce solid-solution hardening and/or promote carbide and γ ´formation, other elements (e.g. boron, zirconium, hafnium) are added to

enhance mechanical or chemical properties.

9.3 Crystal structure of gamma and gamma prime.



Superalloy microstructure, chemical composition and proper control

thereof are complex. As many as 14 elements may be added in some

superalloys. The complexity of the metallurgy is best illustrated by

Table 9.1, indicating the effect of the major alloying elements.

The Ni- and Co-based alloys, usually indicated as superalloys, are applied

because of their high strength at high temperatures. Co-based alloys are

mainly used for (stationary) vanes, whereas in general the Ni-base alloys are

used for (rotating) blades. Of course the materials selection varies per

manufacturer and per gas turbine type. Although many different alloys exist

there are a number of alloys that are widely applied by most of the

manufacturers. Table 9.2 gives the chemical composition of a number of

alloys, which at this moment are considered to be the ‘state of the art’ for the

industrial gas turbine (IGT). Although most manufacturers use identical

Table 9.1 Role of alloying elements in superalloys [6]

Effect Cobalt base Nickel base

Solid-solution strengtheners Nb, Cr, Mo, Ni, W, Ta Co, Cr, Fe, Mo, W, Ta, Refcc matrix stabilizer Ni —Carbide formMC Ti W, Ta, Ti, Mo, Nb, HfM7C3 Cr CrM23C6 Cr Cr, Mo, WM6C Mo, W Mo, W, Nb

Carbonitrides: M(CN) C, N C, NPromotes generalprecipitation of carbides — —

Forms γ´ Ni3(Al,Ti) — Al, TiRetards formation ofhexagonal — —η (Ni3Ti)

Raises solvus temperature ofγ´

Hardening precipitates and/orintermetallic phasesOxidation resistance

— Co

Al, Mo, Tib, W, Ta Al, Ti, Nb

Al, Cr Al, Cr, Y, La, CeImprove hot corrosionresistance La, Y, Th La, Th

Sulfidation resistance Cr Cr, Co, SiImproves creep properties — B, TaIncreases rupture strength B, Zr Bc

Grain-boundary refiners — B, C, Zr, HfFacilitates working Ni3Ti —Retard γ´coarsening — Re

a Not all these effects necessarily occur in a given alloy.b Hardening by precipitation of Ni3Ti also occurs if sufficient Ni is present.c If present in large amounts, borides are formed.



Table

9.2

Nominalco

mpositionofIG

Tca

stCo-base

andNi-base

superalloys[7]

Wt%

Ni

Cr

Co

Fe

Mo

WAl

Ti

Nb

Ta

Mn

VC

BOther

Buck

ets

U500

Bal

18.50

18.50

4.00

3.00

3.00

0.07

0.006

U700(Rene77)

Bal

15.00

17.00

5.30

3.35

3.35

0.07

0.020

Alloy738

Bal

16.00

8.30

0.20

1.75

2.60

3.40

3.40

0.90

1.75

0.10

0.001

MAR

M247

Bal

8.25

10.00

0.80

10.00

1.00

1.00

2.80

0.015

Hf0.15

GTG-111™

Bal

14.00

9.50

1.50

3.80

4.90

4.90

2.80

0.10

0.010

GTD-444™

Bal

9.80

7.50

1.50

6.00

3.50

3.50

0.50

4.80

0.08

0.009

Hf0.15

PW

A1483

Bal

12.80

9.00

1.90

3.80

4.00

4.00

4.00

ReneN5

Bal

7.00

7.50

1.50

5.00

6.50

0.05

0.004

Re3.0;Hf0.15;Y0.01

CMSX-4

®Bal

6.50

9.00

0.60

6.00

1.00

1.00

6.50

Re3.0;Hf0.10

PW

A1484

Bal

5.00

10.00

2.00

6.00

9.00

Re3.0;Hf0.10

Nozzles

FSX414

10.2

28.00

Bal

1.00

7.00

0.25

0.010

GTG-222™

Bal

22.50

19.00

2.30

2.00

1.20

1.20

1.00

0.10

0.008

GTG-111™

Bal

14.00

9.50

1.50

3.80

4.90

4.90

2.80

0.10

0.010

ReneN5

Bal

7.00

7.50

1.50

5.00

6.50

0.05

0.004

Re3.0;Hf0.15;Y

0.01



alloy identifications there may well be differences in alloy composition or

heat treatment, resulting from improvements by each manufacturer.

Since the design of turbomachinery is complex and efficiency is directly

related to material performance, material selection is of prime importance.

Turbine components must operate under a variety of stress, temperature

and corrosion conditions. Compressor blades operate at a relatively low

temperature but are highly stressed. The combustor operates at a relatively

high temperature and low-stress conditions. The turbine blades operate

under extreme conditions of stress, temperature and corrosion.

Advances in alloys and processing, while expensive and time-consuming,

provide significant incentives through increased power density and

improved efficiency.

9.2.1 Metallurgical behavior

The required material characteristics in gas turbine applications for high

performance and long life include limited creep, high-rupture strength,

resistance to high-temperature corrosion, good fatigue strength, low

coefficient of thermal expansion and high-thermal conductivity to reduce

thermal strains.

High-temperature corrosion plays an important role in the selection of

materials for gas turbine applications. The principal modes of high-

temperature corrosion frequently responsible for equipment problems are

oxidation, carburization, sulfidation, nitridation, halogen gas corrosion,

ash/salt deposit corrosion, molten salt corrosion and liquid metal corrosion.

Oxidation and hot corrosion (sulfidation) mechanisms are the most

important ones in this discussion and are described in the next sections.

Thus, the failure mechanism of a turbine blade is related primarily to

creep and corrosion and secondarily to thermal fatigue. Satisfying these

design criteria for turbine blades will ensure high performance, long life and

minimal maintenance. Understanding mechanical behavior and how

temperature affects the properties of the materials is an essential part for

a proper material selection and design.

All material properties change with temperature. Some do so in a simple

linear way making compensation easy, for instance the density and the

modulus. Others, however, particularly the yield strength and the rates of

oxidation and corrosion, change in more sudden ways, which if not allowed

for, can lead to disaster.

Thermal conductivity and conductivity for matter flow (diffusion) change

in more complex ways. The last of these is particularly important in our

discussion, due to diffusion (the intermixing of atoms in solids and the ways

it allows creep and creep fracture) has a profound effect on mechanical

properties when temperatures are high. To understand and use diffusion we



need the idea of thermal activation, the ability of atoms to jump from one

site to another, using thermal energy as the springboard.

Mechanical properties of interest for elevated-temperature applications

include short-time elevated-temperature tensile properties, creep and stress-

rupture, low-cycle and high-cycle fatigue, thermal and thermomechanical

fatigue and creep–fatigue interaction. Thus, extensive testing is conducted to

ensure that the materials will perform satisfactorily in tens of thousands of

hours.

The influence of temperature on the strength of materials can be

demonstrated by running standard, short-time tensile tests at a series of

increasing temperatures where materials are taken to failure. Such test

conditions are often called ‘static’ or monotonic conditions, and allow for

the strain to develop with the load being applied gradually until the

specimen fails.

Typical tensile stress–strain curves for an alloy are defined at different

temperatures, from which such useful properties as the ultimate tensile

strength (UTS), yield stress (proof stress), elastic modulus, ductility and

toughness modulus can be obtained. Stresses above the elastic limit cause

permanent deformation (ductile behavior) or brittle fracture.

Gas turbine components should not fail (break) when subjected to the

ultimate load. This would mean that any amount of plastic deformation is

allowable providing that the component does not break in a brittle fracture.

Ductility and toughness (resistance to fracture) properties are required for

alloys in gas turbine components.

Ductility is an important mechanical property and commonly measured

by elongation and reduction in area (Table 9.3). It is a measure of the degree

of plastic deformation that has been sustained at fracture. A material that

experiences very little or no plastic deformation upon fracture is termed

brittle (brittle materials are considered to be those having a fracture strain of

approximately less then about 5%).

Ductility may be expressed quantitatively as either percent elongation or

percent reduction in area, i.e.

%EL ¼ lf � l0l0

� �6100 ½9:1�

or

%ROA ¼ A0 � AfA0

� �6100 ½9:2�

The area under the elastic part of the stress–strain curve is identified as the

elastic energy stored per unit volume (σy2/(2E)). Beyond the elastic limit

plastic work is done in deforming a material permanently by yield or



crushing. The increment of plastic work done for a small permanent

extension or compression dL under a force F, per unit volume V = AL0, is

dWpl ¼ F dLV

¼ FA0

dL

L0¼ s depl ½9:3�

Thus, the plastic work per unit volume at fracture, important in energy-

absorbing applications, is

Wpl ¼Z ef0

s depl ½9:4�

which is just the area under the stress–strain curve (toughness module).

Toughness requires a new material property, fracture toughness (resistance

of materials to cracking and fracture), which is developed in the next

sections. In load-limited designs, the best material selection involves a

combination of fracture toughness and Young’s modulus.

Having assessed the loads that will act upon a gas turbine component

with a defined geometry (stress analysis), the effect of the applied load

compared with the strength and the other relevant properties of the material

selected will reveal whether it is favorable for the intended service. It is

common to impose a safety factor into the design, in order that an adequate

margin of safety be established or to allow for uncertainty in material

properties, i.e. variability. The common factors used are the proof and

ultimate factor, scatter factor, casting factor, stress concentration factor,

etc.

Once we consider the ability of a given material to resist load it becomes

quite apparent that the way in which the load is applied and the conditions

under which it is applied are very important. It leads us to consider the

failure modes as well as the material’s ability to resist these failure modes. In

particular, the availability of creep-resistant materials has proved to be

extremely useful whenever components are operating at high temperatures,

9.3 Room-temperature mechanical properties (in tension) for various materials[8]

Yield strength Tensile strength

Material MPa ksi MPa ksi Ductility, %EL (in 50mm (2 in))metal alloys

Molybdenum 565 82 655 95 35Titanium 450 65 520 75 25Steel (1020) 180 26 380 55 25Nickel 138 20 480 70 40Iron 130 19 262 38 45Aluminum 35 5 90 13 40



i.e. in turbomachine casing, bolts and studs, turbine blades and nozzles,

compressor and turbine disc applications.

The phenomenon known as creep, in which progressive deformation may

occur under the application of a constant load, has been known for many

years. Creep is defined as the tendency of a solid material to slowly deform

plastically, under the influence of (elastic) stresses. Creep is a temperature-

and time-dependent phenomenon. High temperature results in a higher

mobility of dislocations by the mechanism of climb and in an increase in the

equilibrium concentration of vacancies. Grain boundaries become less well

defined at relative low temperatures (as low at 0.4Tm, where Tm is the

melting point), and there is a greater mobility of atoms at elevated

temperatures.

Then, we have to consider creep as a failure mode at running

temperatures well below the melting point of the material. The melting

point of different metals varies considerably, and their strengths at various

temperatures are different. At low temperatures all materials deform

elastically, then plastically, and are time-independent. However, at higher

temperatures, deformation is noted under constant load conditions (within

the elastic range of the material). This high-temperature, time-dependent

behavior is called creep-rupture. Figure 9.4 shows a schematic of a creep

curve with the various stages of creep.

In many respects such materials behave in a viscoelastic manner, and

when subject to a constant tensile load at elevated temperature undergo a

time-dependent increase in dimension, i.e. they creep. Fig. 9.4 shows the

generally accepted idealization of the three-stage creep process, where ε0 isan instantaneous elastic stage prior to stage I and de=dt /or _e is known as thecreep rate.

After the initial, virtually instantaneous, elastic straining (ε0), stage I

9.4 Creep-rupture schematic curve (time-dependent deformationunder constant load at constant high temperature followed by finalrupture, where all loads are below the short-time yield strength) [9].



represents a region of primary creep in which the creep resistance of a

material increases as a function of its own deformation and is characterized

as a decreasing creep rate. Stage II creep, known as secondary creep, is a

period with a nearly constant creep rate, resulting from the balance between

the competing processes of strain-hardening and recovery. Hence, second

stage creep is often referred to as steady-state creep and the average value of

the creep rate during this stage is called the minimum creep rate (Fig. 9.5).

Stage III or tertiary creep reveals itself in the form of cavities (voids) at grain

boundaries, being the behavior used to identify whether or not a creep-

loaded component is approaching end-of-life. Due to the fact that

superalloy creep stage III is developing very fast, it is almost impossible

to clearly identify the point in time of transition from stage I/II to stage III.

In actual superalloy components the formation of creep voids is hardly ever

observed and used as end-of-life criteria.

Stage III or tertiary creep occurs mainly in constant load–creep tests at

high stress and temperature when there is an effective reduction in cross-

sectional area usually produced by necking. The tertiary strain rate increases

rapidly until fracture (rupture) occurs. There are quite often metallurgical

changes associated with tertiary creep.

Andrade [10] attempted to characterize the creep curve putting forward

that creep is composed of two separated processes: (a) transient creep with

dε/dt decreasing in time and (b) a constant dε/dt viscous creep component.Andrade’s equation [10] in terms of strain is

e ¼ e0ð1þ bt 1=3ð ÞÞekt ½9:5�

where ε is the strain at time t. It should be noted that Andrade’s equation[10] does not include allowance for tertiary creep (if it exists).

Walles and Graham [11] introduced a third term into the Andrade

equation [10] to arrive at the complete equation:

e ¼ at1=3 þ btþ ct3 ½9:6�

9.5 Time-dependent deformation.



Norton [12] suggested a simplified approximate form as (the Norton creep

law)

_e ¼ Bsn ½9:7�

where B, n are material parameters and _e is the stationary strain rate.The nature of this creep depends on the material, stress, temperature and

environment. Limited creep (less than 1%) is desired for turbine blade

application design. Cast superalloys fail with only a minimum elongation.

These alloys fail in a brittle fracture even at elevated operating temperatures.

The current design for creep is very much based upon empirical materials

data. One method of plotting tensile creep data is shown in Fig. 9.6. This

format fits in well with a well-established mathematical model for creep,

namely:

C ¼ Bsn ½9:8�

where

C = creep rate in _e tensionB = stress intercept for a long-creep rate

n = slope of line on a log–log plot

σ = applied stressDesigning to cope with creep in a gas turbine where clearances are critical

means considering creep strain as a design-limiting factor. We need to know

how the strain rate or time to failure tf depends on the stress σ andtemperature T to which it is exposed. That requires creep testing.

The creep test is simple to comprehend since it requires the application of

a steady load to a specimen held at constant temperature and the

measurement of the strain of the specimen at intervals of time, i.e. the

extension is measured as a function of time. Metals have creep curves with

the general shape shown in the Fig. 9.4. Creep requires the use of four

parameters for its description: time, temperature, stress and strain. Creep

tests can be carried out for periods of 2000 to 10 000 h (or more), and be so

arranged that strains of less than 0.5% occur in this time.

The initial elastic and the primary creep strains occur quickly and can be

treated in much the same way as elastic deflection is allowed for in a

structure. Thereafter, the strain increases steadily with time in what is called

the secondary creep or the steady-state creep regime. Plotting the log of the

steady-state creep rate, _e, against the log of the stress, σ, at constant time T,as in Fig. 9.7, shows that

_e ¼ Bsn ½9:9�

where n, the creep exponent, usually lies between 3 and 8 and for that reason



this behavior is called power-law creep. At low σ there is a tail with slope n= 1 (the part of the curve labeled ‘diffusional flow’).

As creep continues, damage accumulates. It takes the form of voids or

internal cracks that slowly expand and link, eating away the cross-section

and causing the stress to rise. This makes the creep rate accelerate, as shown

in the tertiary stage of the creep curve of Fig. 9.4. Since ε is proportional toσn with n = 5, the creep rate goes up even faster than the stress: an increasein stress of 10% gives an increase in the creep rate of 60%.

Materials can deform by dislocation plasticity or, if the temperature is

high enough, by diffusional flow or power-law creep. If the stress and

temperature are too low for any of these, the deformation is elastic. This

shows the range of stress and temperature in which we expect to find each

sort of deformation and the strain rate that any combination of them

produces (the contours). Diagrams like these (Fig. 9.8) are available for

many metals and are a useful summary of creep behavior, helpful in

selecting a material for high-temperature applications.

Where selecting materials for creep resistance we must therefore consider

diffusional flow, which is important when grains are small and when the

component is subject to high temperatures at low loads. The way to avoid

9.6 Time to rupture (tr) as a function of the steady-state creep rate (e�ss)

for single crystals tested in tension at several temperatures [13].



diffusional flow is to choose a material with a high melting temperature and

a large grain size, so that diffusion distances are long. Single crystals are best

of all; they have no grain boundaries to act as sinks and sources for

vacancies, so diffusional creep is suppressed completely. This is the rationale

behind the wide use of single-crystal turbine blades in jet and industrial

engines.

That still leaves power-law creep. Materials that best resist power-law

creep are those with high melting points, since diffusion and thus creep rates

scale as T/Tm, and with a microstructure that maximizes obstruction to

9.7 The stress and temperature dependence of the creep rate [14].

9.8 A deformation mechanismmap, showing the regime in which eachmechanism operates [14].



dislocation motion through alloying to give a solid solution and precipitate

particles. Current creep-resistant materials of superalloys are remarkably

successful in this.

The prediction of rupture times at various combinations of stress and

temperature usually involves some measure of extrapolation from short-

term creep tests to long component lifetimes. One method of extrapolation,

from short to longer times, is to formulate an equation that describes the

creep strain in terms of stress and temperature. This involves the use of

relationships knows as time–temperature parameters. The most popular is

known as the Larson–Miller parameter. This parameter can be used for long

life extrapolation or for assessing cumulative creep damage.

Thus, stress-rupture data are often presented in a Larson–Miller curve,

which indicates the performance of an alloy in a complete and compact

graphical style. While widely used to describe an alloy’s stress-rupture

characteristics over a wide temperature, life and stress range, it is also useful

in comparing the elevated temperature capabilities of many alloys. The

Larson–Miller parameter is

PLM ¼ T 20þ log tð Þ610�3 ½9:10�

where

PLM = Larson–Miller parameter.

T = temperature (8R)t = rupture time (h)

The Larson–Miller parameters are plotted in Fig. 9.9 for the specified

turbine blade alloys.

Larson and Miller [16] first proposed their method for creep data, i.e. the

life expressed at t would be that which reached a particular strain, say 0.1%.

However, this technique has been extended to cover rupture strength, in

which case t would be the life to reach fracture. There is some doubt as to

whether rupture strength can be considered in the same way as creep

strength. It is true that rupture is the terminus at the creep curve, but the

point of rupture is dictated by the ductility of the material. In general, the

creep ductility is determined by the superposition of strains accumulated in

void formation and growth phases separately (Ashby et al. [17]), and is

affected by rupture time, which depends on applied stress as well as the

steady-state creep rate of alloy. In other words, the decrease in ductility can

be tied to quick void formation behavior, causing brittle fracture, while an

increase in ductility may be regarded as the result of delayed void formation

and the change in the fracture mechanism from intergranular to

transgranular, which are very effective in changing crack growth character-

istics of steel leading to ductile behavior.

In many cases, all three stages of creep shown in Fig. 9.3 are not present.



At high temperatures or stresses, very little primary creep is seen, while in

the case of cast superalloys failure occurs with just a small extension. This

amount of extension is ductility. In a time–creep curve there are two

elongations of interest. One elongation is from the plastic strain rate and the

second elongation is the total elongation or the elongation at fracture.

Ductility is erratic in its behavior and is not always repeatable, even under

laboratory conditions. Ductility of a metal is affected by the grain size, the

specimen shape and the techniques used for manufacturing. A brittle

fracture is intergranular with little or no elongation. A ductile fracture is

transgranular and typical of normal ductile tensile fracture. Turbine blade

alloys tend to indicate low ductility at operating temperatures. As a result,

an alloy with low ductility will be sensitive for surface notches and then

cracks may develop rapidly from these notches by fatigue or impact loads.

As discussed, another important mechanical term in our discussion is

toughness, defined as a measure of the ability of a material to absorb energy

up to fracture. To determine toughness, we have to consider the specimen

geometry as well as the manner of load applications. For dynamic loading

(high strain rate) conditions and when a notch (or point of stress

concentration) is present, notch toughness is assessed by using an impact

test. Furthermore, fracture toughness is a property indicative of a material’s

resistance to fracture when a crack is present. For the static (low strain rate)

situation, toughness may be obtained from the result of a tensile stress–

strain test. It is the area under the σ–ε curve up to the point of fracture. Theunits for toughness are energy per unit volume.

In practice, however, and in particular for the case of rotating machinery,

9.9 Larson–Miller parameter for various types of blades [15].



the applied loads are seldom constant (static or monotonic condition) and

usually fluctuate, either about some mean stress or with complete reversal in

sign. This leads to fluctuations in the stresses and strains existing within the

components. If these fluctuating stresses are large enough, even though the

maximum applied stress may be considerably less than the static strength of

the material, failure may occur when the stress is repeated often enough. The

connection between the cyclic loading and failure is known as fatigue.

Fatigue is defined as the progressive, localized and permanent structural

damage that occurs when a material is subjected to cyclic or fluctuating

strains at nominal stresses that have maximum values less than (and often

much less than) the static yield strength of the material.

There are different stages of fatigue damage in an engineering component

where defects may nucleate in an initially undamaged section and propagate

in a stable manner until catastrophic fracture ensues. For this most general

situation, the progression of fatigue damage can be broadly classified into

the following stages:

. Substructural and microstructural changes that cause nucleation ofpermanent damage.

. The creation of microscopic cracks.

. The growth and coalescence of microscopic flaws to form ‘dominant’cracks, which may eventually lead to catastrophic failure. (From a

practical standpoint, this stage of fatigue generally constitutes the

demarkation between crack initiation and propagation.)

. Stable propagation of the dominant macrocrack.

. Structural instability or complete fracture.

The conditions for the nucleation of microdefects and the rate of advance of

the dominant fatigue crack are strongly influenced by a wide range of

mechanical, microstructural and environmental factors. The principal

differences among different design philosophies often rest on how the

crack initiation and the crack propagation stages of fatigue are quantita-

tively treated.

It is important to note here that a major obstacle to the development of

life prediction models for fatigue lies in the choice of a definition for crack

initiation. The total fatigue life is defined as the sum of the number of cycles

to initiate a fatigue crack and the number of cycles to propagate it

subcritically to some final crack size.

Classical approaches to fatigue design involve the characterization of

total fatigue life to failure in terms of the cyclic stress range (the S–N curve

approach) or the (plastic or total) strain range. In these methods, the

number of stress or strain cycles necessary to induce fatigue failure in

initially uncracked (and nominally smooth-surfaced) laboratory specimens

is estimated under controlled amplitudes of cyclic stresses or strains. The



resulting fatigue life incorporates the number of fatigue cycles to initiate a

dominant crack (which can be as high as some 90% of the total fatigue life)

and to propagate this dominant flaw until catastrophic failure occurs.

Various techniques are available to account for the effects of mean stress,

stress concentrations, environments, multiaxial stresses and variable

amplitude stress fluctuations in the prediction of total fatigue life using

the classical approaches. Since the crack initiation life constitutes a major

component of the total fatigue life in smooth specimens, the classical stress-

based and strain-based methods represent, in many cases, design against

fatigue crack initiation.

Under high-cycle, low-stress fatigue situations, the material deforms

primarily elastically. The failure time or the number of cycles to failure

under such high-cycle fatigue has traditionally been characterized in terms

of the stress range. However, the stresses associated with low-cycle fatigue

are generally high enough to cause appreciable plastic deformation prior to

failure. Under these circumstances, the fatigue life is characterized in terms

of the strain range.

The fracture mechanics approach to fatigue design, on the other hand,

invokes a ‘defect-tolerant’ philosophy. The basic premise here is that all

engineering components are inherently flawed. The size of a pre-existing

flaw is generally determined from non-destructive flaw detection techniques

(such as visual, dye-penetrant or X-ray techniques or the ultrasonic,

magnetic or acoustic emission methods) [18].

The useful fatigue life is then defined as the number of fatigue cycles or

time to propagate the dominant crack from this initial size to some critical

dimension. The choice of the critical size for the fatigue crack may be based

on the fracture toughness of the material, the limit load for the particular

structural part, the allowable strain or the permissible change in the

compliance of the component. The prediction of crack propagation life

using the defect-tolerant approach involves empirical crack growth laws

based on fracture mechanics. Various methods are available to incorporate

the effects of mean stresses, stress concentrations, environments, variable

amplitude loading spectra and multiaxial stresses in the estimation of useful

crack growth life.

In the safe-life approach to fatigue design, the typical cyclic load spectra,

which are imposed on a structural component in service, are first

determined. On the basis of this information, the components are analyzed

or tested in the laboratory under load conditions that are typical of service

spectra, and a useful fatigue life is estimated for the component. The

estimated fatigue life, suitably modified with a factor of safety (or an

ignorance factor), then provides a prediction of ‘safe life’ for the component.

At the end of the expected safe operation life, the component is

automatically retired from service, even if no failure has occurred during



service (and the component has considerable residual fatigue life). This

procedure invariably has to account for several unknowns and by selecting a

large margin of safety, a safe operating life can be guaranteed, although

such a conservative approach may not be desirable from the viewpoints of

economy and performance. On the other hand, if fatigue cracks are

nucleated in the component during service, the component may well fail

catastrophically. As noted by Gurney in 1968 [19], the safe-life approach

depends on achieving a specified life without the development of a fatigue

crack so that the emphasis is on the prevention of crack initiation [18].

The fail-safe concept, by contrast, is based on the argument that, even if

an individual member of a large structure fails, there should be sufficient

structural integrity in the remaining parts to enable the structure to operate

safely until the crack is detected. The fail-safe approach mandates periodic

inspection along with the die requirement that the crack-detection

techniques be capable of identifying flaws to enable prompt repairs or

replacements.

Whatever philosophy is employed in design, it is often preferable and even

required in some safety-critical situations, e.g. aircraft and nuclear

industries, that the critical components of a structure be inspected

periodically. This step eliminates dangerous consequences arising from

false estimates and errors in the design stage, especially with the safe-life

approach.

The three basic types of fatigue properties are [20]:

. stress-life (S–N) (design philosophy: safe-life, infinite-life),

. strain-life (ε–N) (design philosophy: safe-life, finite-life),

. fracture mechanic crack growth (da/dN�ΔK) (design philosophy:damage tolerance),

and each property plays a role in the context of a fatigue design philosophy

as previously discussed.

The safe-life, infinite-life philosophy is the oldest of the approaches to

fatigue. Much of the technology in application of this approach is based on

ferrous metals, especially steels. Steels are predominant as a structural

material, but steels also display a fatigue limit or endurance limit at a high

number of cycles (typically > 106) under benign environmental conditions.

This limit is the highest stress level that the material can withstand for an

infinite number of load cycles without failure. The infinite-life asymptotic

behavior of steel fatigue life thus provides a useful and beneficial result of S–

N testing. However, most other materials do not exhibit this infinite-life

response (see Fig. 9.10).

The stress at which a material fails by fatigue after a certain number of

cycles is known as the ‘fatigue strength’. For materials such as non-ferrous

metals, it is usual to define the design stress as that which occurs at some



arbitrary number of cycles. For such materials it is common practice to set

an arbitrary value for the fatigue strength (endurance limit) at, say, 107

cycles. Stress is the controlling quantity in this method (S–N data

presentation). The most typical formats for the data are plots of the log

number of cycles to failure (sample separation) versus either stress

amplitude (Sa), maximum stress (Smax) or perhaps stress range (ΔS).In any fatigue analysis (Fig. 9.11) for a particular component it is

necessary to take account of the factors that influence fatigue behavior.

Some of these factors are the type and nature of loading, size of component,

surface finish and directional properties, stress or strain concentrations,

mean stress or strain, environmental effects, etc.

Mean stress influences are also very important, and each design approach

must consider them. The reversed cycles employed when deriving an S–N

curve would not produce the same amount of damage as a cyclic stress

superimposed upon a mean stress. Therefore carrying out a series of tests

involves various combinations of ± σr and σm in such a way that a numberof methods of plotting such data are found.

The expressions that define the three lines shown in Fig. 9.12 are as

follows:

Goodman [22]:

srse

þ smsult

¼ 1 ½9:11�

Soderberg [23]:

srse

þ smsy

¼ 1 ½9:12�

9.10 S–N diagram trends [21].



Gerberg [24]:

srse

þ smsult

� �2¼ 1 ½9:13�

Almost any variation in the environmental conditions will affect the fatigue

life of a component. In particular, the effects of temperature and corrosive

materials are most pronounced.

The combined action of repeated loading and a corrosive environment is

usually known as corrosion fatigue. The combined effect of cyclic stress and

9.11 Allowance for factors that affect fatigue [21].

9.12 Effect of mean stress on alternating stress amplitude [21].



corrosion usually (but not always) reduces the fatigue life of a component.

Although we can appreciate that corrosion on its own can produce pitting of

the surface and that this could in turn provide a notch from which fatigue

can propagate, the combined effect of cyclic stress and corrosion is much

more than this. It is found that the chemical attack greatly accelerates the

rate at which fatigue cracks propagate. Some materials that have a definite

fatigue (endurance) limit, when tested in air, are found to have either a lower

or no such limit when tested in a corrosive atmosphere.

The effects of corrosion fatigue can be reduced in a number of ways.

However, in general the best approach is to emphasize the corrosion-

resisting properties of the material rather than the mechanical fatigue

properties. Protection of the metal from contact with the corrosive medium

by means of metallic coatings has been found to be successful providing that

the coating does not become ruptured by the cyclic strain, which will be

discussed in the next section.

Strain life is the general approach employed for a continuum response in

the safe-life, finite-life regime. It is primarily intended to address the low-

cycle fatigue area (e.g. from approximately 102 to 106 cycles). The ε–Nmethod can also be used to characterize the ‘long-life’ fatigue behavior of

materials that do not show a fatigue limit.

From a properties standpoint, the representations of strain-life data are

similar to those for stress-life data. However, because plastic strain is a

required condition for fatigue, strain-controlled testing offers advantages in

the characterization of fatigue crack initiation (prior to subsequent crack

growth and final failure). The S–N method is based on just one failure

criterion, the total separation of the test coupon. In contrast, any of the

following may be used as the failure criterion in strain-controlled fatigue

testing: separation, modulus ratio, microcracking (initiation) or percentage

of maximum load drop. This flexibility can provide better characterization

of fatigue behavior [20].

The S–N and ε–N techniques are usually appropriate for situations wherea component or structure can be considered a continuum (i.e. those meeting

the ‘no cracks’ assumption). In the case of a crack-like discontinuity, the S–

N and ε–N techniques offer little or a quantitative basis for assessment offatigue life.

Once a crack has formed in a component, even static loads producing

average tensile stresses well below the material’s nominal strength may

produce fracture, particularly in relatively brittle materials. The reason lies

in the formation of high-stress concentrations at the leading edge of the

crack. ‘Fracture mechanics’ investigations have shown that the fracture

toughness of a material at a given temperature is proportional to a stress

level and to the square root of a crack dimension. The fracture toughness

can thus be expressed by a single parameter, the critical stress intensity



factor K, which has units of MPa m0.5 (or MN/m1.5) and which can be

determined experimentally by producing a crack from cyclic tests and then

loading it statically until it fractures. Fracture mechanics methodology

offers considerable promise for improved understanding of propagation of

fatigue cracks and problem resolution in designing to prevent failures by

fatigue.

The characterization and quantification of the stress field at the crack tip

in terms of stress intensity in linear elastic fracture mechanics allow us to

recognize the singularity of stress at the tip and provides a controlling

quantity and measurable material property. A more accurate calculation of

this critical crack size can be obtained by elastic–plastic fracture mechanic

calculations. This is, however, a much more complicated calculation

technique, where accurate material properties (KIC) are needed. The use

of stress intensity as a controlling quantity for crack extension under cyclic

loading thus enhances the engineering analysis of the fatigue process.

Initiation of fatigue cracks in structural and equipment components

occurs in regions of stress concentrations, such as notches, as a result of

stress fluctuation. The material element at the tip of a notch in a cyclically

loaded component is subjected to the maximum stress range, Δσmax.Consequently, this material element is most susceptible to fatigue damage

and is, in general, the origin of fatigue crack initiation.

It can be shown that, for sharp notches, the maximum-stress range on this

element can be related to the stress intensity factor range, ΔKI, as follows:

Dsmax ¼ 2ffiffiffix

p DKIffiffiffir

p ¼ Ds ktð Þ ½9:14�

where ρ is the notch-tip radius, Δσ is the range of applied nominal stress andkt is the stress concentration factor.

The data show (Fig. 9.13) that DKI=ffiffiffir

pand, therefore, Δσmax is the

primary parameter that governs fatigue crack initiation behavior in regions

of stress concentration for a given steel tested in a benign environment. The

data also indicate the existence of a fatigue crack initiation threshold,

DKI=ffiffiffiffiffiffirth

p, below which fatigue cracks would not initiate at the roots of the

tested notches. For instance, the value of this threshold is characteristic of

the steel and increases with increasing yield or tensile strength of the steel.

The data show that the fatigue crack initiation life of a component subjected

to a given nominal-stress range increases with increasing strength.

Due to the inevitability of cracks (or imperfections) in engineering

structures, fatigue crack propagation is important from a designing point of

view. This approach attempts to determine the safe load or safe inherent

fault dimension that will preclude failure. The fatigue crack propagation

behavior of metals is primarily controlled by the stress intensity factor range



ΔK, which can be divided into three regions, as shown in Fig. 9.14. Thebehavior in region 1 exhibits a fatigue crack propagation threshold, ΔKth,which corresponds to the stress intensity factor range, below which cracks

do not propagate under cyclic-stress fluctuations.

The fatigue crack propagation threshold for steels is primarily a function

of the stress ratio and is essentially independent of chemical or mechanical

properties. In 1963, Paris and Erdogan [25] published an analysis with

considerable fatigue crack growth rate data and demonstrated that a

correlation exists between da/dN and the cyclic stress intensity parameter,

ΔK. They argued that ΔK characterizes the magnitude of the fatigue stressesin the crack-tip region; hence, it should characterize the crack growth rate.

The data for intermediate fatigue crack growth rate values can be

represented by a simple mathematical relationship, commonly known as

the Paris equation. This region (Fig. 9.14) represents the fatigue crack

propagation behavior above ΔKth (region 2), which can be represented bythe power-law relationship:

da

dN¼ C DKð Þn ½9:15�

where a is the crack length, N is the number of cycles, and C and n are

constants. Thus, the fatigue crack growth rate behavior expressed as da/dN

versus ΔK can be regarded as a fundamental material property analogous tothe yield and ultimate tensile strengths and plane strain fracture toughness,

KIC.

9.13 Fatigue crack initiation behavior of various steels at a stress ratioof +0.1 [20].



The acceleration of fatigue crack growth rates that determines the

transition from region 2 to region 3 appears to be caused by the

superposition of a brittle or a ductile-tearing mechanism on to the

mechanism of cyclic subcritical crack extension, which leaves fatigue

striations on the fracture surface. These mechanisms occur when the strain

at the tip of the crack reaches a critical value. Thus, the fatigue-rate

transition from region 2 to region 3 depends on the maximum stress

intensity factor, on the stress ratio and on the fracture properties of the

material.

Low-cycle fatigue (LCF) conditions are frequently created where the

repeated stresses are of thermal origin, which is denominated thermo-

mechanical fatigue (TMF). TMF is a structural failure mode in many high-

temperature components. Thermal fatigue loading is induced by tempera-

ture gradients during transient heating or cooling from one high

temperature of operation to another. Thermal fatigue loading can also

occur when heating and cooling are present simultaneously and thermal

gradients are maintained during steady-state operation. Internally air-

cooled high-temperature turbine blades are very representative examples.

Thermal gradients produce differential expansion as the hottest material

wants to expand more than the cooler, but is constrained from doing so by

the cooler and stronger material. The constraint is perceived by the hottest

material as a compressive thermal strain that is no different in its effect on

the material than would be a mechanically induced strain of equal

magnitude. Similarly, the coldest material is forced by the hottest to expand

9.14 Schematic illustration of the variation of the fatigue-crack-growthrate, da/dN, with alternating stress intensity, ΔK, in steels, showingregions of primary crack growth mechanisms [20].



more than normal. The thermally induced strain in the colder material is

tensile.

The analysis of thermal fatigue (Fig. 9.15) is essentially a problem in heat

transfer and properties such as modulus of elasticity, coefficient of thermal

expansion and thermal conductivity (see Fig. 9.14). The most important

metallurgical factors are ductility and toughness. Highly ductile materials

tend to be more resistant to thermal fatigue. They also seem more resistant

to crack initiation and propagation.

As a result of observations of environmental effects, these play a major

role in high-temperature fatigue crack growth of superalloys. The presence

of sulfur has a significant impact, which provokes profound changes in the

material strength. It is also meaningful to remark on the effect of oxygen

and the combined effect of oxygen and carbon on the base material.

Exposure in air at high temperatures (greater than about 900 8C, or 1650 8F)could lead to profound embrittlement at intermediate temperatures (700 to

800 8C, or 1290 to 1470 8F).With nickel-base superalloys, it has been found that surface cracks related

to environmental attack may develop at strains as low as 0.5%. Since these

cracks result in severe loss in fatigue life, this is an appropriate failure

criterion rather than rupture life. Gas turbine blades may therefore be

designed on the basis of time to 0.5% creep with a suitable safety factor on

stress.

We can conclude that in order to develop an improved design

methodology for machines and equipment operating at high temperatures,

9.15 Comparison of the average thermal fatigue lives of conventionallycast, DS cast and SX-cast nickel-base superalloys [13].



several key concepts and their synergism must be considered. Particularly, it

must include [26]:

. Plastic instability at elevated temperatures, which leads to tertiary creep.

. Deformation mechanisms and strain components associated with creepprocesses.

. Stress and temperature dependence.

. Fracture at elevated temperatures.

. Environmental effects.

. Cycle stress and strain range.

As discussed, the nature of the design process requires serious consideration

of the relationships between predicted machine conditions, such as stress,

strain and temperature, and the capability of the component materials to

withstand those conditions.

Engineers will utilize the most appropriate analytical methods and the

most precise mechanical and thermal boundary conditions in the design

efforts. They will then modify the analytical results by factors of safety,

correlations or experience to arrive at the specific for stress and temperature

for assessing component life. This value is understood to be a reasonably

close and conservative approximation. It is of particular significance that

this value is specific, and it becomes the standard against which the design

and materials are measured to judge acceptability [2].

On the other hand, engineers have to consider the variability of materials

properties. If many tests are run at a specific temperature, a scattering of the

property about some mean value is noted. It should also be noted that there

is a finite probability (generally greater then 5%) that values for the

measured property can fall outside the scatterband of actual data. This

characteristic of material properties requires the engineer to determine just

what value of the property will be used to judge the acceptability of the

design [27].

The nature of superalloys is that they resist the creep-rupture process

better than other materials, have very good higher temperature short-time

strength (yield, ultimate), very good fatigue properties (including fatigue

crack propagation resistance) and combine these mechanical properties with

good to exceptional oxidation resistance. Consequently, superalloys are the

obvious choice when structures are to operate at higher temperatures.

Generally, the temperature range of superalloy operation is broken up into

the intermediate range of about 540 8C (1000 8F) to 760 8C (1400 8F) and thehigh-temperature range that occurs above about 816 8C (1500 8F).



9.2.2 Creep–fatigue interaction

The modes of cracking have frequently exhibited creep-like fractures

intermixed with cycle-dependent fatigue-type cracking – hence the

descriptive name, creep–fatigue interaction. Creep–fatigue interaction is a

special phenomenon that can have a detrimental effect on the performance

of metal parts or components operating at elevated temperatures. When

temperatures are high enough, time-dependent creep strains as well as cyclic

(i.e. fatigue) strains can be present and the interpretation of the effect that

one has on the other becomes extremely important. For example, it has been

found that creep strains can seriously reduce fatigue life and/or that fatigue

strains can seriously reduce creep life [13]. Creep–fatigue interaction testing

and modeling have been intense activities due to seemingly premature

failures of components in structural equipment operating at elevated

temperatures, including gas turbine engines.

The interaction between thermally activated time-dependent processes

such as creep and mechanical fatigue mechanisms severely complicates life

prediction at elevated temperatures. Factors such as frequency, wave shape

and creep/relaxation, which are of small consequence at room temperature,

take on a significant importance at high temperatures. Hold times at a given

stress or strain (e.g. a gas turbine component at constant load) often figure

strongly in high-temperature load histories. Under constant stress condi-

tions creep or crack extension may occur, which naturally results in a change

in deformation. Under constant strain conditions relaxation may occur,

which results in a reduction of the applied stress.

Manson early associated the time-dependent fatigue lifetime with

intergranular cracking and reasoned that this damage mechanism was

intimately associated with time-dependent inelastic strain (i.e. creep or

relaxation) whereas time-independent plasticity was accompanied by

transgranular cracking. Manson also conducted cyclic creep tests between

fixed strain limits and found that the lifetime did not correlate with

monotonic time to rupture in a creep test (i.e. t in the creep-rupture test).

This led to tests of four simple uniaxial cycle types involving creep and

plasticity in the increasing and decreasing halves of the strain cycle.

Manson partitioned these strains into four inelastic strain ranges (Fig.

9.16) that may be used as basic building blocks for any conceivable

hysteresis loop:

Δεpp = tensile plasticity reversed by compressive plasticityΔεcp = tensile creep reversed by compressive plasticityΔεpc = tensile plasticity reversed by compressive creepΔεcc = tensile creep reversed by compressive creep



Manson generalized this concept into a procedure for evaluating any strain–

time–temperature cycle, which he named strain-range partitioning (SRP)

[28], which will be discussed in section 9.6.2 on the strain-range partitioning

model.

Creep–fatigue interaction testing is conducted at an isothermal tempera-

ture, sufficiently high that thermally activated, diffusion-controlled creep

deformation mechanisms can operate under stress as a function of both time

and temperature. The addition of creep to a cycle of normal fatigue loading

will invariably reduce the cyclic life, although the clock time to failure may

remain constant or actually increase. Conversely, the superposition of

fatigue cycling and conventional monotonic creep will also alter the rate of

creeping and the time to rupture.

The strain-range partitioning technique referred to earlier has been used

in the analyses of several high-temperature LCF situations including

combustion liners.

9.16 Partitioning of the strain range into different component strains.



9.2.3 Oxidation and hot corrosion

The evolution of conventional superalloys has been dictated by balancing

requirements of strength, hot corrosion resistance, oxidation resistance,

freedom from deleterious sigma phase and forgeability. As explained, the

first requirement is mainly fulfilled thanks to the Ni3 (Al, Ti) phase.

However, increasing the volume fraction of this phase required the

reduction of chromium and the addition of cobalt. The loss of Cr resulted

in both a loss of solid solution strength and oxidation resistance, which were

compensated for by the addition of molybdenum and aluminum respec-

tively.

The use of Ni-base superalloys as turbine blades in an actual end-use

atmosphere produces deterioration of material properties. This deteriora-

tion can result from erosion, corrosion or oxidation. Erosion results from

hard particles impinging on the turbine blade and removing material from

the blade surface. The particles may enter through the turbine inlet or can be

loosened scale deposits from within the combustor. Metal oxidation occurs

when oxygen atoms react with metal atoms to form oxide scales. The higher

the temperature, the more rapidly this process takes place, creating the

potential for failure of the component if too much of the substrate material

is consumed in the formation of these oxides.

At higher temperatures > 899 8C (> 1650 8F), a relatively rapid oxidationattack of some materials can occur unless there is a barrier to oxygen

diffusion on the metal surface. Additionally, oxygen may also penetrate

along grain boundaries at high temperatures, causing a rapid decrease of

material strength. Aluminum oxide (Al2O3) provides such a barrier.

Aluminum oxide will form on the surface of a superalloy at high

temperatures if the superalloy’s aluminum content is sufficiently high.

Thus, the alloy forms its own protective barrier in the early stages of

oxidation by the creation of a dense, adherent aluminum oxide scale.

Hot corrosion is a rapid form of attack that is generally associated with

alkali metal contaminants, such as sodium and potassium, reacting with

sulfur in the fuel to form molten sulfates. Hot corrosion is an accelerated

oxidation of alloys caused by the deposition of Na2SO4. Hot corrosion

results from the ingestion of salts in the engine and sulfur from the

combustion of fuel. The presence of only a few parts per million (ppm) of

such contaminants in the fuel, or equivalent in the air, is sufficient to cause

this corrosion. Sodium can be introduced in a number of ways, such as salt

water in liquid fuel, through the turbine air inlet at sites near salt water or

other contaminated areas, or as contaminants in water/steam injections. As

well as alkali metals such as sodium and potassium, other chemical elements

can influence or cause corrosion on hot gas components. Notable in this

connection are vanadium, primarily found in crude and residual oils, and



lead. Corrosion causes deterioration of blade materials and reduces

component life.

There are now two distinct forms of hot corrosion recognized by the

industry (Fig. 9.17), although the end result is the same. These two types are

high-temperature (type I) occurring at 816–927 8C (1500–1700 8F) and low-temperature (type II) hot corrosion occurring at 593–760 8C (1100–1400 8F),both requiring a higher chromium to aluminum ratio and substitution of

molybdenum by other refractory elements such as W, Ta and Nb.

High-temperature hot corrosion has been known since the 1950s. It is an

extremely rapid form of oxidation that takes place in the presence of sodium

sulfate (Na2SO4). Sodium sulfate is generated in the combustion process as a

result of the reaction between sodium, sulfur and oxygen. Sulfur is present

as a natural contaminant in the fuel.

Low-temperature hot corrosion was recognized as a separate mechanism

of corrosion attack in the mid 1970s. This attack can be very aggressive if

the conditions are right. It takes place at significant partial pressure of SO2.

It is caused by low melting eutectic compounds resulting from the

combination of sodium sulfate and some of the alloy constituents such as

nickel and cobalt.

9.17 Schematic illustration of the variation in corrosion rate withtemperature [29].



The lines of defense against both types of corrosion are similar. First,

reduce the contaminants. Second, use materials that are as corrosion-

resistant as possible. Third, apply coatings to improve the corrosion

resistance of the component alloy.

A high-nickel alloy is used for increased strength at elevated temperatures

and a chromium content in excess of 20% is desired for corrosion

resistance. An optimum composition to satisfy the interaction of stress,

temperature and corrosion has not yet been developed. Thus, many high-

strength superalloys in use today cannot form sufficient protective scales

because the compositional requirements for achieving other properties, such

as high strength and metallurgical stability, do not allow for the

optimization of oxidation/corrosion resistance in the superalloy itself.

Therefore, most of today’s superalloys must receive their oxidation

protection from specially engineered coatings.

9.2.4 Properties of superalloys

Superalloys were initially developed for use in aircraft piston engine

turbosuperchargers, and their development over the last 60 years has been

paced by the demands of advancing gas turbine engine technology. The

design for high-temperature applications requires specific material char-

acteristics based on the main failures modes affecting its intended function.

For gas turbine applications, the performance characteristics are limited by

the operating conditions that can be tolerated by the material used.

Superalloys possess a remarkable ability to maintain their properties at high

temperature and this will be briefly discussed.

As defined, the basis of superalloys are iron, cobalt and nickel, i.e.

transition metals located in a similar area of the periodic table of the

elements in the 8th group of the periodic system of the elements. Table 9.4

shows the physical properties of the superalloy base elements.

It can be seen that pure iron has a density of 7.87 g/cm3 (0.284 lb/in3),

while pure nickel and cobalt have densities of about 8.9 g/cm3 (0.322 lb/ in3).

The superalloys are created usually by adding significant levels of the alloy

elements chromium, aluminum and titanium, plus appropriate refractory

metal elements such as tungsten and molybdenum to the base metal.

Densities of superalloys are a function of the amounts of these elements in

the final compositions. Aluminum, titanium and chromium reduce super-

alloy density whereas the refractory elements such as tungsten, rhenium and

tantalum increase it. Table 9.5 gives the density, melting range and physical

properties of some nickel-base and cobalt-base superalloys [31].

The main properties of superalloys are that they exhibit some combina-

tion of high strength at temperature; resistance to environmental attack

(including nitridation, carbonization, oxidation and sulfidation); excellent



Table

9.4

Somephysica

lpropertiesofsu

peralloybase

elements

[30]

Meltingpoint

Density

Expansionco

efficienta

Therm

alco

nductivitya

Crystalstructure

8F8C

lb/in3

g/cm

38F6

10�6

8C610�6

Btu/ft2/h/8F/in

cal/cm

2/s/8C/cm

Co

hcp

2723

1493

0.32

8.9

7.0

12.4

464

0.215

Ni

fcc

2647

1452

0.32

8.9

7.4

13.3

610

0.165

Fe

bcc

2798

1535

0.28

7.87

6.7

11.7

493

0.175

aAtroom

temperature.

Table

9.5

Physica

lpropertiesofca

stnicke

l-base

andco

balt-base

alloys[15]

Specificheat

Therm

alco

nductivity

At5388C

At10938C

Meanco

efficientoftherm

al

At218C

(708F)

(10008F)

(20008F)

At938C

(2008F)

At5388C

(10008F)

At10938C

(20008F)

expansion(10�6/K)a

Density

(g/cm

3)

Meltingrange

J/kgK

Btu/lb8F

J/kgK

Btu/lb8F

J/kgK

Btu/lb8F

W/m

KBtu

in/h

ft2-8F

W/m

KBtu

in/h

ft2-8F

W/m

KBtu

in/h

ft2-8F

At938C

(2008F)

At5388C

(10008F)

At10938C

(20008F)

Alloy

8C8F

Nicke

lbase

IN-713C

7.91

1260–

2300–

420

0.10

565

0.135

710

0.17

10.9

76

17.0

118

26.4

183

10.6

13.5

17.1

1290

2350

IN-713LC

8.00

1290–

2350–

440

0.105

565

0.135

710

0.17

10.7

74

16.7

116

25.3

176

10.1

15.8

18.9

1320

2410

Cobaltbase

FSX-414

8.3

——

——

——

——

——

——

——

——

—Haynes1002

8.75

1305–

2380–

420

0.10

530

0.126

645

0.154

11.0

76

21.8

151

32.1

222

12.2

14.4

—1420

2590

aFrom

room

temperature

toindicatedtemperature.

bLiquidustemperature.



creep resistance, stress-rupture strength toughness and metallurgical

stability; useful thermal expansion characteristics and resistance to thermal

fatigue and corrosion. The influence of temperature on the strength has been

discussed and can be demonstrated by running standard, short time tests at

a series of increasing temperatures. This leads to the conclusion that the

melting temperature of the material is a critical parameter for high-

temperature behavior. Thus the first required characteristic is the ability to

withstand loading at an operating temperature close to its melting point. If

the operating temperature is denoted Top and the meeting point Tm, a

criterion defined based upon the homologous temperature defined as Top/

Tm is important in material selection, which should be greater than about

0.6.

The melting temperatures of the base superalloy elements are nickel at

1452 8C (2647 8F), cobalt at 1493 8C (2723 8F) and iron at 1535 8C (2798 8F).When metals are alloyed, there is no longer a single melting point for a

composition. Instead, alloys melt over a range of temperatures. The lowest

melting temperature (incipient melting temperature) and melting ranges of

superalloys are functions of the composition and prior processing. Just as

the base metal is higher melting, so generally are incipient melting

temperatures higher for cobalt-base superalloys than for nickel-base or

iron–nickel-base superalloys. Nickel-base superalloys may show incipient

melting at temperatures as low as 1204 8C (2200 8F). However, advancednickel-base single-crystal superalloys having limited amounts of melting

point depressants tend to have incipient melting temperatures equal to or in

excess of those of cobalt-base superalloys [31].

Other physical properties such as electrical conductivity, thermal

conductivity and thermal expansion of superalloys tend to be low (relative

to other metal systems). These properties are influenced by the nature of the

base metals (transition elements) and the presence of refractory-metal

additions.

A second characteristic is a substantial resistance to mechanical

degradation over extended periods of time. As discussed, time-dependent

deformation and fracture of structural materials at elevated temperatures

are among the most challenging engineering problems. In order to develop

an improved design methodology for machines and equipment operating at

high temperatures, key aspects to be considered are plastic instability at

elevated temperatures and deformation mechanisms and strain components

associated with creep processes.

The superalloys have low ductility compared to iron-based steels; the

ductilities of cobalt-base superalloys are generally less than those of iron–

nickel-base and nickel-base superalloys. Short-time tensile ductilities as

determined by elongation at failure generally range from as low as 10 pct to



as high as around 70 pct, but γ ´ hardened alloys are in the lower end, usuallybetween about 10 and 40 pct [31].

Creep-rupture ductilities are generally lower than tensile ductilities. At the

760 8C (1400 8F) tensile ductility minimum area, creep-rupture ductilities ofcastings have gone below 1.5 pct; however, most current high-strength

polycrystalline (PC) equiaxed cast alloys have rupture ductilities in excess of

2.0 pct. Single-crystal directionally solidified (SCDS) superalloy ductilities

will vary with orientation of the single crystal relative to the testing direction

[31].

Superalloys typically have dynamic moduli of elasticity in the vicinity of

207 GPa (306106 psi), although moduli of specific PC equiaxed alloys canvary from 172 to 241 GPa (25 to 356106 psi) at room temperaturedepending on the alloy system. Processing that leads to directional grain or

crystal orientation can result in moduli of about 124 to 310 GPa (about 18

to 456106 psi) depending on the relation of grain or crystal orientation tothe testing direction [31].

Short-time tensile yield properties of γ ´-hardened alloys range fromaround 550MPa (80 ksi) to 1380MPa (200 ksi) at room temperature. Actual

values depend on the composition and processing (cast versus wrought).

Ultimate strengths range from around 690MPa (100 ksi) to 1520MPa (230

ksi) at room temperature, with γ ´-hardened alloys in the high end of therange [31].

Superalloys tend to show an increase of yield strength from room

temperature up to about 760 8C (1400 8F) and drop off thereafter. This is incontrast to ordinary alloys that tend to continuously decrease in short-time

strength as temperatures increase. Ultimate tensile strengths generally do

not show this trend. Concurrently, tensile ductility tends to decrease, with a

minimum at around 649 8C (1200 8F).The highest tensile properties are found in the finer grain size wrought or

powder metallurgy superalloys used in applications at the upper end of the

intermediate temperature regime, perhaps to about 760 8C (1400 8F). Thehighest creep-rupture properties invariably are found in the coarser grain

cast superalloys used in the high-temperature regime. Rupture strengths are

a function of the time at which they are to be recorded. The 1000 h rupture

stress capability is obviously lower than the 100 h capability.

Creep-rupture strengths for 100 h failure at 982 8C (1800 8F) may rangefrom 45MPa (6.5 ksi) for an older γ ´ hardened wro

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