Files 2 Lectures LEC 25 CH 07

7/30/2019 Files 2 Lectures LEC 25 CH 07

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Dr. A. Aziz Bazoune Chapter 7: Fatigue Failure Resulting from Variable Loading

ME 307 Machine Design IME 307 Machine Design I

Dr. A. Aziz Bazoune

King Fahd University of PetroleumKing Fahd University of Petroleum& Minerals& Minerals

Mechanical EngineeringMechanical EngineeringDepartmentDepartment


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CH-07 LEC 25 Slide 2


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7-11 Characterizing Fluctuating Stresses7-11 Characterizing Fluctuating Stresses

Fluctuating stresses in machinery often take the form ofsinusoidal

pattern because of the nature of the nature of some rotating machinery.

Other patterns some quite irregular do occur.


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7-11 Characterizing Fluctuating Stresses7-11 Characterizing Fluctuating Stresses

In periodic patterns exhibiting a single maximum and single minimum offorce, the shape of the wave is not important.

The peaks on both sides (maximum, minimum) are important.

Fmax and Fmin in a cycle can be used to characterize the force pattern.

A steady component and an alternating component can be constructed as

follows:


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Stress RangeStress Range

Mean (MidrangeMean (Midrange

Stress)Stress)

Stress AmplitudeStress Amplitude

(Alternating Stress)(Alternating Stress)

Stress RatioStress Ratio

Stress AmplitudeStress Amplitude

(R>0 )

(R =0)

(R =-1)


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Any varying stress with a nonzero meanis considered a fluctuating stress.


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The steady, or static, stress is not the

same as the midrange stress.

The steady stress may have any value

between minand min. The steady stress exists because of a

fixed load or preload applied to a part.

The steady load is independent of the

varying portion of the load.


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A helical compression spring is always loaded into a space shorter

than the free length of the spring.

The stress created by this initial compression is called the steady,

or static, component of the stress.


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Equations (7-39) use symbols a and m as the stress components at the

location of scrutiny.

In the absence of a notch, aandm are equal to the nominal stresses

aoandmoinduced by loadsFa andFm , respectively.

With a notch they are a = Kfaoand m = Kfmo, respectively.


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When the steady stress component is high enough to induce localized

notch yielding, the designer has problem.

The first-cycle local yielding produces plastic strain and strain-

strengthening.

This is occurring at the location where fatigue crack nucleation and

growth are most likely.

30 hME 307 M hi D i I


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Residual Stress MethodResidual Stress Method

All stresses (both mean and alternating) are multiplied by the fatigue

stress concentration factor Kf , and correction is made for yielding and

resultant residual stresses if the calculated peak stress exceeds the material

yield strength.

Nominal Mean Stress MethodNominal Mean Stress Method

In this method, stress concentration factor is applied only to alternating

stress.

Reduction in mean stress from not multiplying it by Kf , might be about

the same as the reduction in mean stress achieved with the residual stress

method by taking yielding and residual stress into account.

Possible ways of quantifying the problem:

ME 307 M hi D i IME 307 M hi D i I


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7-12 Fatigue Failure Criteria for Fluctuating Stress7-12 Fatigue Failure Criteria for Fluctuating Stress

After having defined the various components of stress associated with a

part subjected to fluctuating stresses, we want to vary both the midrange

stress and the stress amplitude or alternating component, to learn about

the FATIGUE RESISTANCE of parts when subjected to such situations.

Many machine elements involve fluctuating stresses about a non-zero

mean.

The influence of non-zero mean stress is estimated by using one of several

empirical relationships that determine failure at a given life when both

alternating and mean stresses are nonzero.

ME 307 M hi D i IME 307 M hi D ig I


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It has midrange stress plotted along the

abscissa and all other components of

stress plotted on the ordinate, with

tension in the positive direction.

The endurance limit, fatigue strength,

or finite-life strength whichever

applies, is plotted on the ordinate above

and below the origin.

The midrange line is a 45o line from the

origin to the tensile strength of the

part.


Modified GoodmanModified Goodman

DiagramDiagram

Figure 7-24

Modified Goodman diagram showing all the strengths

and the limiting values of all the stress components for

a particular midrange stress



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Plot of Fatigue Failures for Midrange Stresses in bothPlot of Fatigue Failures for Midrange Stresses in both

Tensile and Compressive Regions.Tensile and Compressive Regions.

Figure 7-25Plot of fatigue failuresfor midrange stresses

in both tensile and

compressive regions.

Normalizing the data

by using the ratio of

steady strengthcomponents to tensile

strength Sm/Sut,

steady strength

component to

compressive strength

Sm/Suc, and strength

amplitude componentto endurance limit

Sa/Se enables a plot

of experimental

results for a variety of

steels.



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Master Fatigue Diagram.Master Fatigue Diagram.

Figure 7-26

Master fatiguediagram for

AISI 4340 steelwith Sut = 158

Sy = 147 kpsi.

The stresscomponent atA are

min = 20,

max = 120,

m = 70,

o = 50

all in kpsi

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Files 2 Lectures LEC 25 CH 07