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Fatigue

Part 2

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6-8 Fatigue Strength : Basics

Low-cycle fatigue considers the range fromN=1 to about 1000 cycles.

In this region, the fatigue strength is only

slightly smaller than the tensile strength .

High-cycle fatigue domain extends from 103

to the endurance limit life (106 to 107 cycles).

Experience has shown that high-cycle fatigue

data are rectified by a logarithmic transform

to both stress and cycles-to-failure.

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Fatigue Strength at Different

N Define the fatigue strength at a specified number of cycles as

By combining the elastic strain relations, we can get

Define fas the fraction of tensile strength. The value offat 103 cycles isthen

To find b, substitute the endurance strength and the corresponding cyclesand solving for b as

For example, for steels when

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Fatigue Strength : General

For actual mechanical applications, the fatigue strength

calculated above is extended to a more general form as

: cycle to failure

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Endurance Limit Modifying

Factors The endurance limit of the rotating-beam specimen might differ from

the actual application due to the following differences fromlaboratory tests.

Material : composition, basis of failure, variability

Manufacturing : method, heat treatment, fretting corrosion, surface

condition, stress concentration

Environment : corrosion, temperature, stress state, relaxation times.

Design : size, shape, life, stress state, stress concentration, speed,fretting, galling

Modifying factors ofsurface condition, size, loading, temperature,and miscellaneous items are proposed by Marin to quantify thesedifferences.

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Marin Modification Factors on

Endurance Limit

where

= surface condition modification factor = size modification factor

= load modification factor

= temperature modification factor

= reliability factor

= miscellaneous-effects modification factor

= rotary-beam test specimen endurance limit

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Surface and Loading Factors

Surface Factor : the surface modification factor depends on thequality of the finish of the actual part surface and on the tensilestrength of the part material. It can be calculated as

Loading Factor : the axial and torsional loadings results in differentendurance limit than that of a standard rotating-bending test. Theload factor applies to other loading conditions as

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Size Factor

Size Factor : the size factor has been evaluated using 133 set

of data points in the literature. For axial loading, . Forbending and torsion can be expressed as

Effective dimension is introduced for non-circular cross sectionby equating the volume of the material stressed at and above95 percent of the maximum stress to the same volume in therotating-beam specimen.

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Temperature Factor

At temperatures lower thanroom temperature, brittle

fracture of a component

needs to be considered first;

at operating temperatureshigher than room

temperature, yield should be

investigated.

If only tensile-strength data

are available, polynomial

fitting to the data could

provide the temperature

Fig.2-9 : yield stress drops with

temperature

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Reliability Factor

Most endurance strength data arereported as mean values.

To account for the scatter of measurement

data, the reliability modification factor iswritten as

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Miscellaneous-Effects Factor

The miscellaneous factor intends toaccount for the reduction in endurance

limit due to all other effects, such as

residual stresses, different material

treatments, directional characteristics of

operations, and corrosion.

One should also treat the miscellaneous-

effect factor as a reminder that these must

accounted for, because actual values of

are not always available.

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Fatigue Stress

Concentration Factor

The fatigue stress concentration factorfrom the existence of irregularities or

discontinuities in materials is defined a

Let be the static stressconcentration factor, the relations

between fatigue stress concentration

and the notch sensitivity is

for bending and axial loadings

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Characterizing Fluctuating

Stresses

Fluctuating stressesoften of sinusoidalpatters due to thenature of somerotating machinery.

The peaks of the waveare more importantthan its shape.

Fluctuating stressesare described using asteady componentand an alternating

component.

F ti F il C it i f

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Fatigue Failure Criteria for

Fluctuating Stresses

Gerber

modified Goodman

Soldergerg

ASME-elliptic

Langer

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Combination of Load Modes

Fatigue problems can be categorized into- completely reversing simple loads : can be handled using S-N curve; only one type of

loading is allowed with midrange stress being zero.

- fluctuating simple loads : can be resolved using a criterion to relate midrange and

alternating stresses; again, only one type of loading is allowed.

- combinations of loading modes : a combinations of different types of loading.

apply appropriate stress concentration factors to each type ofstress

calculate equivalent von Mises stress

select a fatigue failure criteriondiscard the load factor for torsional stress, consider axial stress

only.

C bi ti f B di

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Combination of Bending,

Torsion, and Axial Stressesapply appropriate stress concentration factors to each type of stress

calculate equivalent von Mises stress

select a fatigue failure criterion

discard the load factor for torsional stress, consider axial stressonly.

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Varying, Fluctuating Stresses

Instead of a single fully reversed stresshistory block composed of n cycles,

suppose a machine part, at a critical

location is subjected to.

A fully reversed stress for cycles, for cycles, ..., or

A wiggly time line of stress exhibiting many and different peaks and

valleys.

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Cumulative Fatigue Damage

The Palmgren-Miner cycle-ratiosummation rule uses linear damage

accumulation concept as

: the number of cycles at stress level : the number of cycles to failure at stress level

: the parameter determined by experiment, in the range

with an average value near unity