30079_18c.pdf

Class 1

Class 2

Class 3

Single load path

Single load path— Multiple load path

damage arrest capability Redundant load path

Fig. 18.61 Structural arrangements. (After Ref. 74.)

2 structures, including pressurized cabins and pressure vessels, relatively large amounts of damage

may be contained by providing tear straps or stiffeners. There is usually a high probability of damage

detection for a class 2 structure because of fuel or pressure leakage, that is, "leak-before-break"

design is characteristic of class 2 structures. Class 3 structures are usually designed to provide a

specified percentage of the original strength, that is, a specified residual strength, during and subse-

quent to the failure of one element. This is often called "failsafe" type of structure. However, the

preexisting flaw concept requires that all members, including every member of a multiple load path

structure, be assumed to contain flaws. It is usual to assume a smaller initial flaw size for class 3

structures because it is appropriate to take a larger risk of operating with cracks if multiple load

paths are available.

The development of inspection procedures is an important part of any fracture control program.

Appropriate inspection procedures must be established for each structural element, and regions within

elements may be classified with respect to required NDI sensitivity. Inspection intervals are estab-

lished on the basis of crack growth information assuming a specified initial flaw size and a "detect-

able" flaw size that depends on the NDI procedure. Inspection intervals are established to ensure

that an undetected flaw will not grow to critical size before the next inspection, with a comfortable

margin of safety. The intervals are usually picked so that two inspections will occur before any crack

will reach critical size.

A good fracture-control program should encompass and interact with design, materials selection,

fabrication, inspection, and operational phases in the development of any high-performance engi-

neering system.

18.6 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 ac-

cumulated creep strain results in a deformation 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 member

actually separates into two parts. Stress rupture is a term used interchangeably 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 18.62 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 temper-

atures reach a range of approximately 35-70% of the melting point on a scale of absolute temperature.

The approximate melting temperature for several substances is shown in Table 18.2.

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

Fig. 18.62 Illustration of creep and stress rupture.

Table 18.2 Melting Temperatures 4 9

Material

°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

Creep deformation and rupture are initiated in the grain boundaries and proceed by sliding and

separation. Thus, creep rupture failures are intercrystalline, in contrast, for example, to the transcrys-

talline failure surface exhibited by room-temperature fatigue failures. Although creep is a plastic flow

phenomenon, the 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 theo-

retical 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 empirical 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 temperatures 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.

18.6.1 Prediction of Long-Term Creep Behavior

Much time and effort has been expended in attempting to device 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 obtained only by conducting long-term creep tests that duplicate

actual service loading and temperature conditions as nearly as possible. Unfortunately, designers are

unable to wait for years to obtain design data needed in creep failure analysis. Therefore, certain

useful techniques have been developed for approximating long-term creep behavior based on a series

of short-term tests. Data from creep testing may be cross 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. 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 in recent years to correlate the results of short-time

elevated-temperature tests with long-term service performance at more moderate temperatures. The

more accurate and useful of these proposals to date are the Larson-Miller theory and the

Manson-Haferd theory.

The Larson-Miller theory 7 5 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

p = (0 + 46O)(C + Iog 10 0

(18.64)

where P = Larson-Miller parameter, constant for a given material and stress level

6 = temperature, 0 F

C = constant, usually assumed to be 20

t = 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 different materials by

Larson and Miller with good success. By using (18.64) 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 18.3

should be equivalent to the operating conditions.

Table 18.3 Equivalent Conditions Based on

Larson-Miller Parameter

Operating Condition

Equivalent Test Condition

13 hours at 120O 0 F

10,000 hours at 100O 0 F

12 hours at 135O 0 F

1,000 hours at 120O 0 F

12 hours at 150O 0 F

1,000 hours at 135O 0 F

2.2 hours at 40O 0 F

1,000 hours at 30O 0 F

The Manson-Haferd 7 6 theory postulates that for a given material and stress level there exists a

unique value of a parameter P' that is related to temperature and time by the equation

O - 6 a

P' =

-2

(18.65)

Iog 10 f - Iog 10 f f l

where P' = Manson-Haferd parameter, constant for a given material and stress level

O = temperature, 0 F

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

O a , t a = material constants

In the Manson-Haferd equation values of the constants for several materials are shown in Table 18.4.

18.6.2 Creep under Uniaxial State of Stress

Many relationships have been proposed to relate stress, strain, time, and temperature 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. 18.63 for three different materials. An equation

describing this type of behavior is

8 = At*

(18.66)

where 8 = true creep strain

t = time

A, a = empirical constants

Differentiating (18.66) with respect to time gives

8 = aAt< a -»

(18.67)

or, setting a A = b and (1 — a) = n,

8 = br n

(18.68)

This equation represents a variety of different types of creep strain versus time curves, depending on

the magnitude of the exponent n. If n is zero, the behavior, characteristic of high temperatures, is

termed constant creep rate, and the creep strain is given as

Table 18.4 Constants for Manson-Haferd Equation 7 6

Material

Creep or Rupture

0 a

log-, O f a

25-20 stainless steel

Rupture

100

18-8 stainless steel

Rupture

100

S-590 alloy

Rupture

DM steel

Rupture

100

Inconel X

Rupture

100

Nimonic 80

Rupture

100

Nimonic 80

0.2 percent plastic strain

100

Nimonic 80

0.1 percent plastic strain

100

Fig. 18.63 Creep curves for three materials plotted on log-log coordinates. (From Ref. 77.)

8 = b,t + C 1

(18.69)

If n lies between O and 1, the behavior is termed parabolic creep, and the creep strain is given by

8 = b 3 t m + C 3

(18.70)

This type of creep behavior occurs at intermediate and high temperatures. The coefficient b 3 increases

exponentially with stress and temperature, and the exponent m decreases with stress and increases

with temperature. The influence of stress level a on creep rate can often be represented by the

empirical expression

8 = BCT N

(18.71)

Assuming the stress cr to be independent of time, we may integrate (18.71) to yield the creep

strain

8 = Btcr N + C

(18.72)

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