fatigue in mechanical design

8/11/2019 Fatigue in mechanical design

1/22

Fatigue

MIET Engineering College

Compiled by S Renold Elsen


2/22

Introduction

Since many of the machine parts axles, shafts,

crankshafts, connecting rods, springs,

pinion teeth are subjected to variable or alter

nating loads (also known as fluctuating or fatig

ue loads).

Therefore we shall discuss, the variable or

alternating stresses in this course.


3/22


4/22


5/22

Stresses developed in a rotating shaft

subjected to a bending load.

As the specimen rotates, the bending stress at

the upper fibres varies from maximum

compressive to maximum tensile while the

bending stress at the lower fibres varies from

maximum tensile to maximum compressive.


6/22


7/22

Endurance Limit

It is defined as maximum value of the

completely reversed bending stress which a

polished standard specimen can withstand

without failure, for infinite number of cycles

(usually 107 cycles).


8/22

Alternating stresses

The stresses which vary from a minimum

value to a maximum value of the opposite

nature.


9/22

Fluctuating stresses

The stresses which vary from a minimum

value to a maximum value of the same nature,

(i.e. tensile or compressive).


10/22

Repeated stresses

The stresses which vary from zero to a certain

maximum value.


11/22

Mean Stress

Stress amplitude

Together,s

mands

acharacterize fluctuating stress

2'

minmax ss

s

m

2

minmax' ss

s

a


12/22

Effect of Loading on Endurance Limit

(Load Factor)

Kb =Load correction factor for the reversed orrotating bending load.

Its value is usually taken as unity.

Ka =Load correction factor for thereversed axialload.

Its value may be taken as 0.8.

Ks =Load correction factor for the reversed

torsional or shear load.Its value may be taken as 0.55 for ductilematerials and 0.8 for brittle materials.


13/22

Effect of Surface Finish on Endurance

Limit (Surface Finish Factor)

When the surface finish factor is known, then the

endurance limit for the material of the machine

member may be obtained by multiplying the

endurance limit and the surface finish factor.The value of surface finish factor is unity for a

mirror polished material.

The endurance limit for mirror polished materialis maximum and it goes on reducing due to

surface condition.


14/22

Effect of Size on Endurance Limit

(Size Factor)

A little consideration will show that if the size of thestandard specimen is increased, then the endurancelimit of the material will decrease.

This is due to the fact that a longer specimen will

have more defects than a smaller one.Notes:

1. The value of size factor is taken as unity for the standardspecimen having nominal diameter of 7.657 mm.

2. When the nominal diameter of the specimen is more than7.657 mm but less than 50 mm, the value of size factormay be taken as 0.85.

3. When the nominal diameter of the specimen is more than50 mm, then the value of size factor may be taken as 0.75


15/22

Effect of Miscellaneous Factors on

Endurance Limit

Other factors such as

reliability factor (Kr),

temperature factor (Kt),

impact factor (Ki) etc.

has effect on the endurance limit of a material.

In solving problems, if the value of any of the

above factors is not known, it may be taken as unity.


16/22

Fatigue Stress Concentration Factor

When a machine member is subjected to

cyclic or fatigue loading, the value of fatigue

stress concentration factor shall be applied

instead of theoretical stress concentrationfactor.


17/22

Factor of Safety for Fatigue Loading

When a component is subjected to fatigueloading, the endurance limit is the criterion forfaliure.

For steel, e=0.8 to 0.9 y

e=Endurance limit stress for completelyreversed stress cycle, and

y=Yield point stress.


18/22

Notch Sensitivity

In cyclic loading, the effect of the notch or the fillet isusually less than predicted by the use of the theoreticalfactors.

The difference depends upon the stress gradient in the

region of the stress concentration and on the hardnessof the material.

It may be defined as the degree to which thetheoretical effect of stress concentration is actuallyreached.

The stress gradient depends mainly on the radius ofthe notch, hole or fillet and on the grain size of thematerial.


19/22

Combined Steady and Variable Stress

The failure points from fatigue tests made withdifferent steels and combinations of mean and variablestresses are plotted in Fig. 6.15 as functions of variablestress (v) and mean stress (m). The most significant

observation is that, in general, the failure point is littlerelated to the mean stress when it is compressive but isvery much a function of the mean stress when it istensile. In practice, this means that fatigue failures arerare when the mean stress is compressive (or

negative). Therefore, the greater emphasis must be given to the

combination of a variable stress and a steady (or mean)tensile stress.


20/22

Solving of combined stresses


21/22

1. Gerber method,

2. Goodman method, and

3. Soderberg method.


22/22

Gerber Method for

Combination of Stresses

fatigue in mechanical design

Documents