Chap 1 Stress-Life

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Chap 1 Stress-Life

1.1 Introduction

1.2 S-N Diagram

1.3 Mean Stress Effects

1.4 Modifying Factors

1.5 Important Concepts



1.1 Introduction

S-N approach used to understand and quantifymetal fatigue.

applied stress is primarily within the elasticrange of material and the cycles to failure arelong.

The S-N method doesn’

t work well in low-cycle applications.



1.2 S-N Diagram

Disadvantage：treats all strains as elastic.

Se（endurance limit）：a stress level below which

the material has an infinite life.



Most nonferrous alloys have no endurance limit.

8105



Se/Su=fatigue ratio

Over 200Ksi carbide inclusions formed



A power relationship estimate the S-N curve forsteel： bc N S 10

63085.0101062.1

N for N SS u



1.3 Mean Stress Effects

Δσ=σmax-σmin= stressrange

σa=(σmax-σmin)/2= stress

amplitude σm=(σmax+σmin)/2= mean

stress

R= σmin / σmax= stressratio

A= σa / σm = amplituderatio

a

m

max

min



The result of a fatigue test are plotted on aHaigh diagram.



Mean stress equations

Soderberg:

Goodman:

Gerber:

Morrow:

1

y

m

e

a

SS

1u

m

e

a

SS

1)(2

u

m

e

a

SS

1

f

m

e

a

S

Infinite life



Compressive mean

stresses are verybenefincial.

compressive meanstress has no effect fornotched components.



1.4 Modifying Factors The variables include：

1、Size

2、Type of loading

3、Surface finish

4、Surface treatments

5、Environment

Se=Se’ CsizeCloadCsurf.fin.......

(Se’ by R.R.Moore test)



1.4.1 Size effects

Correlated with the thinlayer of surface material.

Less pronounced size

effect for axial loadingthan for bending ortorsion.

In English units

ind if

ind inif d sizeC

3.0

103.0

0.1

869.0{ 097.0

d



1.4.2 Loading Effects

The ratio of endurance limits found using axialand rotating bending test.

using torsion and rotating bending test.

(0.577 using von Mises failure criterion)

)(70.0)( bendingSaxialS ee

)(577.0)( bendingStorsion ee



1.4.3 Surface Finish



1.4.4 Surface Treatment

Residualstress

yield



Presetting(prestressing) ：

1、Initial overload is favorable for the same

direction.

2、Don’t use in fully reversed loading.



Plating：Se Alleviate the residual tensile stress：

Nitride,Shot peen,bake,anneal.

The extra corrosion resistance offered by plating.



Thermal：

Hot rolling and forging

Carburizing,nitriding,and induction hardeningproduce residual compressive surface stresses.

Surface decarburization.

Produce residual tensile stresses.

Se



Mechanical： Cold rolling

Shot peening

Cold rolling：

Se



Shot peening：

advantage：used on oddly shaped parts

disadvantage：leave a rough dimpled surface

Fatigue ratio=0.5



Temperature：

Se for steels increase at low temperature,butreduction in fracture toughness.

At high temperature, Se for steels disapper dueto the mobilizing of dislocations.

At temperature beyond ½ of melting point,creepbecomes important.

High temperature can cause annealing,whichremove residual compressive stress.



1.4.6 Environment

Corrosion-fatigue

Higher strength steels have no advantage



1.5 Important concepts

Increase Se :1、Carburization

2、Nitriding3、Shot peening

3、Cold rolling

4、Flame

5、Induction hardening

Reduce Se :

1、Decarburization(hot rolling)

2、Cr or Ni plating3、Severe grinding

4、Rough surface finish

5、Large section size

6、 Tensile mean stress

Chap 1 Stress-Life

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