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An Introduction to the concepts

BITSPilaniPilani Campus

MATERIALS SCIENCE AND ENGINEERING

Creep

Creep may be defined as a time-dependent

deformation at elevated temperature and

constant stress

Occurs when material supports a load for very long

period of time, and continues to deform until a

sudden fracture or usefulness is impairedsudden fracture or usefulness is impaired

Is only considered when metals and ceramics are

used for structural members or mechanical parts

are subjected to high temperatures

Other materials (such as polymers & composites)

are also affected by creep without influence of

temperature

*3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUE

Creep

Stress and/or temperature significantly affects the

rate of creep of a material

Creep strength represents the highest initial stress

the material can withstand during given time

Mechanical Performance of Materials

the material can withstand during given time

without causing specified creep strain

Simple method to determine creep strength

Test several specimens simultaneously

At constant temperature, but

Each specimen subjected to different axial stress

*3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUE

Creep

Simple method to determine creep strength

Measure time taken to produce allowable strain or

rupture strain for each specimen

Plot stress vs. strain

Mechanical Performance of Materials

Plot stress vs. strain

Creep strength inversely proportional to

temperature and applied stresses

*3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUECreep

Schematic creep curve for a constant load; a plot of the change

in length verses time. The weight or load on the specimen is

held constant for the duration of the test.

*3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUECreep

Creep deformation occurs by grain-boundary

sliding. That is, adjacent grains or crystals move

as a unit relative to each other

*3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUECreep

There are four portions of the curve

that are of interest:

An initial steep rate that is at least partly of

elastic origin, from point "0" to point "A" in

Figure.

This is followed by a region in which the

elongation or deformation rate decreases with

time, the so-called transient or primary creep,

from region "A" to "B". The portion from point from region "A" to "B". The portion from point

"0" to point "B" occurs fairly quickly.

The next portion of the creep curve is the area of engineering interest,

where the creep rate is almost constant. The portion from "B" to "C" is

nearly linear and predictable.

The fourth portion of the creep curve, beyond the constant-creep-rate or

linear region, shows a rapidly increasing creep rate which culminates in

failure. Even under constant-load test conditions, the effective stress may

actually increase due to the damage that forms within the microstructure.

Fatigue

Fatigue is the lowering of strength or the failure of a

material due to repetitive stress, which may be above

or below the yield strength.

Mechanical Performance of Materials

Many engineering materials such as those used in

cars, planes, turbine engines, machinery, shoes, etc

are subjected constantly to repetitive stresses in the

form of tension, compression, bending, vibration,

thermal expansion and contraction or other stresses.

FATIGUE

Fracture surface which usually exhibits:

Smooth areas -correspond to the gradual crack growth stage, and

Rough areas-correspond to the catastrophic fracture stage.

The smooth parts of the fracture surface usually The smooth parts of the fracture surface usually exhibit beach marks which occurs as a result of changes in the magnitude of the fluctuating fatigue load.

9

Fatigue Failures Are Often Easy To Identify

10

*3.7 FAILURE OF MATERIALS DUE TO CREEP & FATIGUEMethod to Determine Fatigue

Fatigue behavior of materials is usually described by

means of the S-N diagram which gives the number

of cycles to failure, N as a function of the max

applied alternating stress.

Subject series of

specimens to specified

Fatigue

specimens to specified

stress and cycle to failure

Plot stress (S) against

number of cycles-to-

failure N

(S-N diagram) on

logarithmic scale

DESIGNING AGAINST FATIGUE

S-N curve is a graphical representation of the maximum

applied stress versus the number of stress cycles N before

the fatigue failure on a semi-log graph. For ferrous metals

like steel the curve becomes asymptotic at 106 cycles.

The completely reversed stress which a material can

withstand 106 cycles without failure is called ENDURANCE

12

withstand 106 cycles without failure is called ENDURANCE

LIMIT of the material.

For non ferrous materials, the curve slopes gradually even

after 106 cycles. These materials do not have a limiting

value of endurance in true sense. In these cases endurance

limit is expressed as a function of number of cycles.

Fatigue

Fatigue Limit:

For some materials such as BCC steels and Ti alloys, the S-N

curves become horizontal when the stress amplitude is

decreased to a certain level.

This stress level is called the Fatigue Limit, or Endurance

Limit, which is typically ~35-60% of the tensile strength

for steels.for steels.

In some materials, including steels, the endurance limit is

approximately half (50%) the tensile strength, given by:

5.0strength tensile

limit endurance ratio Endurance =

The S-N curves for a tool steel and an aluminum alloy showing the number of cycles to

failure

DESIGNING AGAINST FATIGUE

In the majority cases, the reported fatigue strength or endurance limits of the materials are based on the test of carefully prepared small samples under laboratory condition.

Such values cannot be directly used for design purposes because the behavior of a component or structure under fatigue loading does depend not only on the fatigue or endurance limit of the material used in making it, but also an several other factors including :endurance limit of the material used in making it, but also an several other factors including :

Size and shape of the component or structure

Type of loading and state of stress

Stress concentration

Surface finish

Operating temperature

Service environment

Method of fabrication 15

Endurance-limit modifying factorsse = kakbkckdkekfkgkhse

Where se = endurance limit of component

se = endurance limit experimental

ka = surface finish factor (machined parts have different finish)

kb = size factor (larger parts greater probability of finding defects)

DESIGNING AGAINST FATIGUE

defects)

kc = reliability / statistical scatter factor (accounts for random variation)

kd = operating T factor (accounts for diff. in working T & room T)

ke = loading factor (differences in loading types)

kf = stress concentration factor

kg = service environment factor (action of hostile environment)

kh = manufacturing processes factor (influence of fabrication parameters)

16

DESIGNING AGAINST FATIGUE

ka = Surface finish factor

17

DESIGNING AGAINST FATIGUE

kb = Size factor

Large engineering parts have lower fatigue

strength than smaller test specimen

Greater is the probability of finding metallurgical

flaws that can cause crack initiation

Following values can be taken as rough guidelines :

kb = 1.0 for component diameters less than 10

mm

kb = 0.9 for diameters in the range 10 to 50 mm

kb = 1 [( D 0.03)/15], where D is diameter

expressed in inches, for sizes 50 to 225 mm.

18

DESIGNING AGAINST FATIGUE

kc = Reliability factor

Accounts for random variation in fatigue

strength.

The following value can be taken as

guidelinesguidelines

kc = 0.900 for 90% reliability

kc = 0.814 for 99 % reliability

kc = 0.752 for 99.9 % reliability

19

DESIGNING AGAINST FATIGUE

kd = Operating temperature factor

Accounts for the difference between the test

temperature and operating temperature of the

component

For carbon and alloy steels, fatigue strength not

affected by operating temperature 45 to affected by operating temperature 45 to

4500C kd = 1

At higher operating temperature

kd = 1 5800( T 450 ) for T between 450 and

550oC, or

kd = 1 3200( T 840 ) for T between 840 and

1020oF20

DESIGNING AGAINST FATIGUE

ke = Loading factor

Different type of loading, give

different stress distribution

ke = 1 for application ke = 1 for application

involving bending

ke = 0.9 for axial loading

ke = 0.58 for torsional loading

21

DESIGNING AGAINST FATIGUE

kf = Fatigue stress concentration factor

Accounts for the stress concentration

which may arise when change in cross-

section

kf = endurance limit of notch-free partkf = endurance limit of notch-free part

endurance limit of notched part

Low strength, ductile steels are less

sensitive to notch than high-strength

steels

22

DESIGNING AGAINST FATIGUE

kg = Service environment factor

Accounts for the reduced fatigue strength

due to the action of a hostile environment.

23

DESIGNING AGAINST FATIGUE

kh = Manufacturing process factor

Accounts for the influence of fabrication

parameter

Heat treatment, cold working, residual

stresses and protective coating on the stresses and protective coating on the

fatigue material.

It is difficult to quantify, but important to

be included.

24

Fatigue Failures

Types of stresses for fatigue tests include,

axial (tension compression)

flexural (bending)

torsional (twisting)

From these tests the following data are generated.

+

By convention, tensile stresses are positive and compression stresses are

negative.

max

min

minmaxr

minmaxa

minmaxm

Ratio, Stress

Range, Stress

2 Amplitude, Stress

2 Stress,Mean

=

=

=

+=

R

Fatigue Failures

Examples of stress

cycles where a) shows

the stress in

compression and

tension, b) shows

a

tension, b) shows

theres greater tensile

stress than

compressive stress

and in c) all of the

stress is tensile.

b

c

Fatigue Failures

As the mean stress, m, increases, the stress amplitude, a,must decrease in order for the material to withstand the

applied stress. This condition is summarized by the

Goodman relationship:

= mfsa 1 Amplitude, Stress

Where fs is the desired fatigue strength for zero mean stress and TS is the tensile strength of the material.

TS

fsa

Fatigue FailuresCrack Growth Rate

To estimate whether a crack will grow, the stress intensity

factor (K), which characterizes the crack geometry and the stress amplitude can be used.

Below a threshold K a crack doesnt grow.

For somewhat higher stress intensities, the cracks grow

slowly.slowly.

For still higher stress-intensities a crack grows at a rate

given by:

Where C and n are empirical constants that depend

on the material.

When DK is high, the cracks grow in a rapid and

unstable manner until fracture occurs.

( )nKCdN

da=

Fatigue Failures

Fatigue Failures

if we integrate between the initial size of a crack and the

crack size required for fracture to occur, we find that the

number of cycles to failure is given by

( )nKCdN

da=

From the steady state crack growth relationship of

number of cycles to failure is given by

where C and n are empirical constants that depend on the

material.

[ ]2/

2/)2(2/)2(

)2(

)()(2nnn

n

i

n

c

Cfn

aaN

=