Kutz M. Handbook of materials selection

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5 FATIGUE 739

the local stress–strain approach

1,33

may be used to compute the number of cycles

required to initiate a crack, the corresponding length of this initiated crack is

not deﬁned speciﬁcally. No consensus has yet been reached regarding the length

of this initiated crack. A size of between 0.25 and 5.0 mm has been suggested,

as cracks of this size normally exist at fracture in the small laboratory specimens

used to generate the strain versus cycles to failure data required for the local

stress–strain approach. An alternative approach would involve the assumption

of a preexisting material or manufacturing defect such that N

⬇ 0. For example,

such an assumption is often made during the analysis of welded joints.

nondestructive techniques are employed, a reasonable assumption for the size of

this initial defect would be the largest ﬂaw that could avoid detection.

Crack growth rates determined from constant-amplitude cyclic loading tests

are approximately the same as for random loading tests in which the maximum

stress is held constant but mean and range of stress vary randomly. However, in

random loading tests where the maximum stress is also allowed to vary, the

sequence of loading cycles may have a marked effect on crack growth rate, with

the overall crack growth being signiﬁcantly higher for random loading spectra.

Many investigations have shown a signiﬁcant delay in crack propagation fol-

lowing intermittent application of high stresses. That is, fatigue damage and

crack extension are dependent on preceding cyclic load history. This dependence

of crack extension on preceding history and the effects upon future damage

increments are referred to as interaction effects. Most of the interaction studies

conducted have dealt with retardation of crack growth as a result of the appli-

cation of occasional tensile overload cycles. Retardation may be characterized

as a period of reduced crack growth rate following the application of a peak

load or loads higher and in the same direction as those peaks that follow.

The modeling of interaction effects requires consideration of crack-tip plas-

ticity and its subsequent inﬂuence. In metals of all types, cracks will remain

closed or partially closed for a portion of the applied cyclic load as a conse-

quence of plastically deformed material left in the wake of the growing crack.

Under cyclic loading, crack growth will occur during the loading portion of the

cycle. Given that a plastic zone exists at the crack tip prior to crack extension,

as the material at the crack tip separates, the newly formed crack surfaces will

exhibit a layer of plastically deformed material along the newly formed crack

faces. Subsequent unloading will compress this plastically deformed material,

closing the crack while the applied stress remains tensile. This phenomenon is

known as plasticity-induced fatigue crack closure and was ﬁrst discussed by

Elber.

Upon reloading during the following cycle, crack growth will not con-

tinue unless the applied load is sufﬁciently large such that the compressive

stresses acting along the crack surfaces are overcome and the crack is fully

opened. This load is known as the crack opening load and has been demonstrated

to be a key parameter in determining fatigue crack growth rates under both

constant amplitude and spectrum loading. Further information regarding crack

closure may be found in Refs. 1, 4, 16, 26, and 31.

Discussion to this point has been limited to the growth of through-thickness

cracks under mode I loading. While mode I loading is often dominant, under

the most general circumstances the applied cyclic loads will generate stress

intensity factor ranges

⌬K

, ⌬K

, and ⌬K

III

at the crack tip, and mixed-mode

fatigue crack growth must be considered. Modeling methodologies for mixed-

740 FAILURE MODES

mode fatigue crack growth are discussed in Refs. 34 and 35. In addition, fatigue

cracks in machine elements and structures are often not through-thickness cracks

but rather surface cracks that extend partially through the thickness. Such surface

cracks are often semielliptical in shape and the analysis of these cracks is con-

siderably more complicated. Information regarding surface cracks may be found

in Refs. 4 and 29.

Research has suggested that when fatigue cracks are small, crack growth rates

are larger than would be predicted using Eq. (15) for a given

⌬K.

Small-crack

behavior is often important, as a signiﬁcant portion of the fatigue life may be

spent in the small-crack regime. The fatigue crack propagation life N

will also

be inﬂuenced by the presence of residual stresses such as might exist as a con-

sequence of welding, heat treatment, carburizing, grinding, or shot-peening.

Compressive residual stresses are beneﬁcial, decreasing the rate of fatigue crack

growth and increasing propagation life. While approximate methodologies exist

for incorporating the effects of residual stress within fatigue crack growth pre-

dictions,

residual stress distributions are often difﬁcult to characterize.

Reasonable design estimates for the fatigue crack propagation life may be

obtained using Eq. (17). However, the many uncertainties typically associated

with fatigue life predictions emphasize the essential requirement to conduct full-

scale fatigue tests to provide acceptable reliability.

6 CREEP AND STRESS RUPTURE

Creep in its simplest form is the progressive accumulation of plastic strain in a

specimen or machine part under stress at elevated temperature over a period of

time. Creep failure occurs when the accumulated creep strain results in a defor-

mation of the machine part that exceeds the design limits. Creep rupture is an

extension of the creep process to the limiting condition where the stressed mem-

ber actually separates into two parts. Stress rupture is a term used interchange-

ably by many with creep rupture; however, others reserve the term stress rupture

for the rupture termination of a creep process in which steady-state creep is

never reached, and use the term creep rupture for the rupture termination of a

creep process in which a period of steady-state creep has persisted. Figure 26

illustrates these differences. The interaction of creep and stress rupture with

cyclic stressing and the fatigue process has not yet been clearly understood but

is of great importance in many modern high-performance engineering systems.

Creep strains of engineering signiﬁcance are not usually encountered until

the operating temperatures reach a range of approximately 35–70% of the melt-

ing point on a scale of absolute temperature. The approximate melting temper-

ature for several substances is shown in Table 2.

Not only is excessive deformation due to creep an important consideration,

but other consequences of the creep process may also be important. These might

include creep rupture, thermal relaxation, dynamic creep under cyclic loads or

cyclic temperatures, creep and rupture under multiaxial states of stress, cumu-

lative creep effects, and effects of combined creep and fatigue.

Creep deformation and rupture are initiated in the grain boundaries and pro-

ceed by sliding and separation. Thus, creep rupture failures are intercrystalline,

in contrast, for example, to the transcrystalline failure surface exhibited by room

temperature fatigue failures. Although creep is a plastic ﬂow phenomenon, the

6 CREEP AND STRESS RUPTURE 741

Fig. 26 Illustration of creep and stress rupture.

Table 2 Melting Temperatures

Material ⬚F ⬚C

Hafnium carbide 7030 3887

Graphite (sublimes) 6330 3500

Tungsten 6100 3370

Tungsten carbide 5190 2867

Magnesia 5070 2800

Molybdenum 4740 2620

Boron 4170 2300

Titanium 3260 1795

Platinum 3180 1750

Silica 3140 1728

Chromium 3000 1650

Iron 2800 1540

Stainless steels 2640 1450

Steel 2550 1400

Aluminum alloys 1220 660

Magnesium alloys 1200 650

Lead alloys 605 320

742 FAILURE MODES

intercrystalline failure path gives a rupture surface that has the appearance of

brittle fracture. Creep rupture typically occurs without necking and without

warning. Current state-of-the-art knowledge does not permit a reliable prediction

of creep or stress rupture properties on a theoretical basis. Furthermore, there

seems to be little or no correlation between the creep properties of a material

and its room temperature mechanical properties. Therefore, test data and empir-

ical methods of extending these data are relied on heavily for prediction of creep

behavior under anticipated service conditions.

Metallurgical stability under long-time exposure to elevated temperatures is

mandatory for good creep-resistant alloys. Prolonged time at elevated tempera-

tures acts as a tempering process, and any improvement in properties originally

gained by quenching may be lost. Resistance to oxidation and other corrosive

media are also usually important attributes for a good creep-resistant alloy.

Larger grain size may also be advantageous since this reduces the length of

grain boundary, where much of the creep process resides.

6.1 Prediction of Long-Term Creep Behavior

Much time and effort has been expended in attempting to develop good short-

time creep tests for accurate and reliable prediction of long-term creep and stress

rupture behavior. It appears, however, that really reliable creep data can be ob-

tained only by conducting long-term creep tests that duplicate actual service

loading and temperature conditions as nearly as possible. Unfortunately, design-

ers are unable to wait for years to obtain design data needed in creep failure

analysis. Therefore, certain useful techniques have been developed for approx-

imating long-term creep behavior based on a series of short-term tests. Data

from creep testing may be plotted in a variety of different ways. The basic

variables involved are stress, strain, time, temperature, and, perhaps, strain rate.

Any two of these basic variables may be selected as plotting coordinates, with

the remaining variables treated as parametric constants for a given curve. Three

commonly used methods for extrapolating short-time creep data to long-term

applications are the abridged method, the mechanical acceleration method, and

the thermal acceleration method. In the abridged method of creep testing the

tests are conducted at several different stress levels and at the contemplated

operating temperature. The data are plotted as creep strain versus time for a

family of stress levels, all run at constant temperature. The curves are plotted

out to the laboratory test duration and then extrapolated to the required design

life. In the mechanical acceleration method of creep testing, the stress levels

used in the laboratory tests are signiﬁcantly higher than the contemplated design

stress levels, so the limiting design strains are reached in a much shorter time

than in actual service. The data taken in the mechanical acceleration method are

plotted as stress level versus time for a family of constant strain curves all run

at a constant temperature. The thermal acceleration method involves laboratory

testing at temperatures much higher than the actual service temperature expected.

The data are plotted as stress versus time for a family of constant temperatures

where the creep strain produced is constant for the whole plot.

It is important to recognize that such extrapolations are not able to predict

the potential of failure by creep rupture prior to reaching the creep design life.

6 CREEP AND STRESS RUPTURE 743

Table 3 Equivalent Conditions Based on

Larson–Miller Parameter

Operating Condition Equivalent Test Condition

10,000 h at 1000⬚F 13 h at 1200⬚F

1,000 h at 1200

⬚F 12 h at 1350⬚F

1,000 h at 1350

⬚F 12 h at 1500⬚F

1,000 h at 300

⬚F 2.2 h at 400⬚F

In any testing method it should be noted that creep testing guidelines usually

dictate that test periods of less than 1% of the expected life are not deemed to

give signiﬁcant results. Tests extending to at least 10% of the expected life are

preferred where feasible.

Several different theories have been proposed to correlate the results of short-

time elevated-temperature tests with long-term service performance at more

moderate temperatures. One of the more accurate and useful of these proposals

is the Larson–Miller theory.

The Larson–Miller theory

postulates that for each combination of material

and stress level there exists a unique value of a parameter P that is related to

temperature and time by the equation

⫽ (

␪

⫹ 460)(C ⫹ log t) (19)

where P ⫽ Larson–Miller parameter, constant for a given material and stress

level

␪

⫽ temperature, ⬚F

⫽ constant, usually assumed to be 20

⫽ time in hours to rupture or to reach a speciﬁed value of creep strain

This equation was investigated for both creep and rupture for some 28 dif-

ferent materials by Larson and Miller with good success. By using (19) it is a

simple matter to ﬁnd a short-term combination of temperature and time that is

equivalent to any desired long-term service requirement. For example, for any

given material at a speciﬁed stress level the test conditions listed in Table 3

should be equivalent to the operating conditions.

6.2 Creep under a Uniaxial State of Stress

Many relationships have been proposed to relate stress, strain, time, and tem-

perature in the creep process. If one investigates experimental creep strain versus

time data, it will be observed that the data are close to linear for a wide variety

of materials when plotted on log strain versus log time coordinates. Such a plot

is shown, for example, in Fig. 27 for three different materials. An equation

describing this type of behavior is

␦

⫽ At (20)

744 FAILURE MODES

Fig. 27 Creep curves for three materials. (From Ref. 40.)

where

␦

⫽ true creep strain

⫽ time

A, a

⫽ empirical constants

Differentiating (20) with respect to time gives

⫺

␦

⫽ bt (21)

or, setting aA

⫽ b and 1 ⫺ a ⫽ n,

⫺

␦

⫽ bt (22)

This equation represents a variety of different types of creep strain versus time

6 CREEP AND STRESS RUPTURE 745

curves, depending on the magnitude of the exponent n.Ifn is zero, the behavior,

characteristic of high temperatures, is termed constant creep rate, and the creep

strain is given as

␦

⫽ bt⫹ C (23)

If n lies between 0 and 1, the behavior is termed parabolic creep, and the creep

strain is given by

␦

⫽ bt ⫹ C (24)

This type of creep behavior occurs at intermediate and high temperatures. The

coefﬁcient b

increases exponentially with stress and temperature, and the ex-

ponent m decreases with stress and increases with temperature. The inﬂuence of

stress level

␴

on creep rate can often be represented by the empirical expression

␦

⫽ b

␴

(25)

Assuming the stress

␴

to be independent of time, we may integrate (25) to

yield the creep strain

␦

⫽ Bt

␴

⫹ C⬘ (26)

If the constant C

⬘ is small compared with Bt

␴

, as it often is, the result is called

the log-log stress–time creep law, given as

␴

⫽ Bt

␴

(27)

As long as the instantaneous deformation on load application and the stage I

transient creep are small compared to stage II steady-state creep, Eq. (27) is

useful as a design tool.

If it is necessary to consider all stages of the creep process, the creep strain

expression becomes much more complex. The most general expression for the

creep process is

␴

⫺

qt n p

␦

⫽⫹k

␴

⫹ k (1 ⫺ e )

␴

⫹ kt

␴

(28)

12 3

where

␦

⫽ total creep strain

␴

/E ⫽ initial elastic strain

␴

⫽ initial plastic strain

(1 ⫺ e

⫺

)

␴

⫽ anelastic strain

␴

⫽ viscous strain

␴

⫽ stress

⫽ modulus of elasticity

⫽ reciprocal of strain-hardening exponent

⫽ reciprocal of strength coefﬁcient

746 FAILURE MODES

q ⫽ reciprocal of Kelvin retardation time

⫽ anelastic coefﬁcient

⫽ empirical exponent

⫽ viscous coefﬁcient

⫽ empirical exponent

⫽ time

To utilize this empirical nonlinear expression in a design environment requires

speciﬁc knowledge of the constants and exponents that characterize the material

and temperature of the application. In all cases it must be recognized that stress

rupture may intervene to terminate the creep process, and the prediction of this

occurrence is difﬁcult.

7 FRETTING AND WEAR

Fretting and wear share many common characteristics but, at the same time, are

distinctly different in several ways. Basically, fretting action has, for many years,

been deﬁned as a combined mechanical and chemical action in which contacting

surfaces of two solid bodies are pressed together by a normal force and are

caused to execute oscillatory sliding relative motion, wherein the magnitude of

normal force is great enough and the amplitude of the oscillatory sliding motion

is small enough to signiﬁcantly restrict the ﬂow of fretting debris away from the

originating site.

More recent deﬁnitions of fretting action have been broadened

to include cases in which contacting surfaces periodically separate and then

reengage, as well as cases in which the ﬂuctuating friction-induced surface trac-

tions produce stress ﬁelds that may ultimately result in failure. The complexities

of fretting action have been discussed by numerous investigators, who have

postulated the combination of many mechanical, chemical, thermal, and other

phenomena that interact to produce fretting. Among the postulated phenomena

are plastic deformation caused by surface asperities plowing through each other,

welding and tearing of contacting asperities, shear and rupture of asperities,

friction-generated subsurface shearing stresses, dislodging of particles and

corrosion products at the surfaces, chemical reactions, debris accumulation

and entrapment, abrasive action, microcrack initiation, and surface delamina-

tion.

43–58

Damage to machine parts due to fretting action may be manifested as cor-

rosive surface damage due to fretting corrosion, loss of proper ﬁt or change in

dimensions due to fretting wear, or accelerated fatigue failure due to fretting

fatigue. Typical sites of fretting damage include interference ﬁts; bolted, keyed,

splined, and riveted joints; points of contact between wires in wire ropes and

ﬂexible shafts; friction clamps; small-amplitude-of-oscillation bearings of all

kinds; contacting surfaces between the leaves of leaf springs; and all other places

where the conditions of fretting persist. Thus, the efﬁciency and reliability of

the design and operation of a wide range of mechanical systems are related to

the fretting phenomenon.

Wear may be deﬁned as the undesired cumulative change in dimensions

caused by the gradual removal of discrete particles from contacting surfaces in

motion, due predominantly to mechanical action. It should be further recognized

that corrosion often interacts with the wear process to change the character of

7 FRETTING AND WEAR 747

the surfaces of wear particles through reaction with the environment. Wear is,

in fact, not a single process but a number of different processes that may take

place by themselves or in combination. It is generally accepted that there are at

least ﬁve major subcategories of wear (see p. 120 of Ref. 59, see also Ref. 60),

including adhesive wear, abrasive wear, corrosive wear, surface fatigue wear,

and deformation wear. In addition, the categories of fretting wear and impact

wear

55,61,62

have been recognized by wear specialists. Erosion and cavitation are

sometimes considered to be categories of wear as well. Each of these types of

wear proceeds by a distinctly different physical process and must be separately

considered, although the various subcategories may combine their inﬂuence ei-

ther by shifting from one mode to another during different eras in the operational

lifetime of a machine or by simultaneous activity of two or more different wear

modes.

7.1 Fretting Phenomena

Although fretting fatigue, fretting wear, and fretting corrosion phenomena are

potential failure modes in a wide variety of mechanical systems, and much

research effort has been devoted to the understanding of the fretting process,

there are very few quantitative design data available, and no generally applicable

design procedure has been established for predicting failure under fretting con-

ditions. However, even though the fretting phenomenon is not fully understood,

and a good general model for prediction of fretting fatigue or fretting wear has

not yet been developed, signiﬁcant progress has been made in establishing an

understanding of fretting and the variables of importance in the fretting process.

It has been suggested that there may be more than 50 variables that play some

role in the fretting process.

Of these, however, there are probably only 8 that

are of major importance:

1. The magnitude of relative motion between the fretting surfaces

2. The magnitude and distribution of pressure between the surfaces at the

fretting interface

3. The state of stress, including magnitude, direction, and variation with

respect to time in the region of the fretting surfaces

4. The number of fretting cycles accumulated

5. he material, and surface condition, from which each of the fretting mem-

bers is fabricated

6. Cyclic frequency of relative motion between the two members being fret-

ted

7. Temperature in the region of the two surfaces being fretted

8. Atmospheric environment surrounding the surfaces being fretted

These variables interact so that a quantitative prediction of the inﬂuence of

any given variable is very dependent on all the other variables in any speciﬁc

application or test. Also, the combination of variables that produce a very serious

consequence in terms of fretting fatigue damage may be quite different from the

combinations of variables that produce serious fretting wear damage. No general

techniques yet exist for quantitatively predicting the inﬂuence of the important

748 FAILURE MODES

variables of fretting fatigue and fretting wear damage, although many special

cases have been investigated. However, it has been observed that certain trends

usually exist when the variables just listed are changed. For example, fretting

damage tends to increase with increasing contact pressure until a nominal pres-

sure of a few thousand pounds per square inch is reached, and further increases

in pressure seem to have relatively little direct effect. The state of stress is

important, especially in fretting fatigue. Fretting damage accumulates with in-

creasing numbers of cycles at widely different rates, depending on speciﬁc op-

erating conditions. Fretting damage is strongly inﬂuenced by the material

properties of the fretting pair-surface hardness, roughness, and ﬁnish. No clear

trends have been established regarding frequency effects on fretting damage, and

although both temperature and atmospheric environment are important inﬂuenc-

ing factors, their inﬂuences have not been clearly established. A clear presen-

tation relative to these various parameters is given in Ref. 55.

Fretting fatigue is fatigue damage directly attributable to fretting action. It

has been suggested that premature fatigue nuclei may be generated by fretting

through either abrasive pit-digging action, asperity-contact microcrack initia-

tion,

friction-generated cyclic stresses that lead to the formation of micro-

cracks,

or subsurface cyclic shear stresses that lead to surface delamination in

the fretting zone.

Under the abrasive pit-digging hypothesis, it is conjectured

that tiny grooves or elongated pits are produced at the fretting interface by the

asperities and abrasive debris particles moving under the inﬂuence of oscillatory

relative motion. A pattern of tiny grooves would be produced in the fretted

region with their longitudinal axes all approximately parallel and in the direction

of fretting motion, as shown schematically in Fig. 28.

The asperity-contact microcrack initiation mechanism is postulated to proceed

due to the contact force between the tip of an asperity on one surface and another

asperity on the mating surface as the surfaces move back and forth. If the initial

contact does not shear one or the other asperity from its base, the repeated

contacts at the tips of the asperities give rise to cyclic or fatigue stresses in the

region at the base of each asperity. It has been estimated

that under such

conditions the region at the base of each asperity is subjected to large local

stresses that probably lead to the nucleation of fatigue microcracks at these sites.

As shown schematically in Fig. 29, it would be expected that the asperity-contact

mechanism would produce an array of microcracks whose longitudinal axes

would be generally perpendicular to the direction of fretting motion.

The friction-generated cyclic stress fretting hypothesis

is based on the ob-

servation that when one member is pressed against the other and caused to

undergo fretting motion, the tractive friction force induces a compressive tan-

gential stress component in a volume of material that lies ahead of the fretting

motion, and a tensile tangential stress component in a volume of material that

lies behind the fretting motion, as shown in Fig. 30a. When the fretting direction

is reversed, the tensile and compressive regions change places. Thus, the volume

of material adjacent to the contact zone is subjected to a cyclic stress that is

postulated to generate a ﬁeld of microcracks at these sites. Furthermore, the

geometrical stress concentration associated with the clamped joint may contrib-

ute to microcrack generation at these sites.

As shown in Fig. 30c, it would be

expected that the friction-generated microcrack mechanism would produce an