SHM by khaja

7/29/2019 SHM by khaja

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FATIGUE

• Fatigue is the progressive and localized

structural damage that occurs when a material

is subjected to cyclic loading.

• The nominal maximum stress values are less

than the ultimate tensile stress limit, and may

be below the yield stress limit of the material.



ANALYSIS OF FATIGUE

• Stress life approach

• Strain life approach

•

Fracture mechanics approach

In this presentation we shall see about Stress life

approach.



STRESS LIFE APPROACH

• This nominal stress (S-N) method was the first

approach developed to try to understand this

failure process

• The nominal stress approach is best suited to

that area of the fatigue process known

as high-cycle fatigue



Stress Cycles

Typical Fatigue Stress Cycles,

(a) Fully Reversed (b) Offset, (c) Random



The S-N Curve

• In high-cycle fatigue situations, materials

performance is commonly characterized by

an S-N curve, also known as a Wohler curve

• Most determinations of fatigue properties

have been made in completely reversed

bending (i.e., R = –1), by means of the so-

called rotating bend test



• The stress level at the surface of the specimen is

calculated using the elastic beam equation,

S= Mc/I

S- the nominal stress acting normal to the cross-

section

M- the bending moment

c - the distance of the surface from the neutral axis

I - the moment of inertia



• S-N data are nearly always presented in the

form of a log-log plot of alternating stress

amplitude versus cycles to failure, with the

actual Wöhler line representing the mean of

the data



Limits of the S-N Curve

• The S-N approach is applicable to situations

where cyclic loading is essentially elastic

• This means that the S-N curve should be

confined on the life axis to numbers greater

than about 10,000 cycles in order to ensure no

significant plasticity is occurring.



The Influence of Mean Stress

• Most basic fatigue data are collected in thelaboratory by means of testing procedureswhich employ fully reversed loading

• Most realistic service situations involvenonzero mean stresses

• Fatigue data collected from a series of tests

designed to investigate different combinationsof stress amplitude and mean stress arecharacterized by Haigh diagram



HAIGH’s diagram

• Notice that the influence of mean stress is

different for compressive and tensile meanstress values for a given number of cycles to

failure



EMPERICAL RELATIONS

• Several empirical relationships which relate

alternating stress amplitude to mean stress

have been developed

• Of all the proposed relationships, two have

been most widely accepted

1. Goodman :

2. Gerber :



Factors Influencing Fatigue Life

• Component size

• The type of loading

•

The effect of notches• The effect of surface finish

• The effect of surface treatment



RAINFLOW CYCLE COUNTING

• The signal measured, in general, a random

stress S(t) is not only made up of a peak alone

between two passages by zero, but also

several peaks appear, which makes difficultthe determination of the number of cycles

absorbed by the structure





• The counting of peaks makes it possible toconstitute a histogram of the peaks of therandom stress which can then be transformed

into a stress spectrum giving the number of events for lower than a given stress value.

• The stress spectrum is thus a representationof the statistical distribution of thecharacteristic amplitudes of the random stressas a function of time



Rules of the flow

• The origin of the random stress is placed on

the axis at the abscissa of the largest peak of

the random stress

If the fall starts from a peak :

a) The drop will stop if it meets an opposing

peak larger than that of departure.

b) it will also stop if it meets the path traversed

by another drop previously determined



c) The drop can fall on another roof and tocontinue to slip according to rules a and b



If the fall begins from a valley:

d) the fall will stop if the drop meets a valley

deeper than that of departure



e) the fall will stop if it crosses the path of a drop

coming from a preceding valley



f) the drop can fall on another roof and continue

according to rules d and e.

• The horizontal length of each rainflow defines

a range which can be regarded as equivalent

to a half-cycle of a constant amplitude load



• Lets explain it with an example.



• First, the stress S(t) is transformed to aprocess of peaks and valleys. Then the timeaxis is rotated so that it points downward.

• At both peaks and valleys, water sources areconsidered. Water flows downward accordingto the rules

•

Let X denotes range under consideration; Y,previous range adjacent to X; and S startingpoint in the history





Details of the cycle counting are as follows:

• S=A; Y=|A-B| ; X=|B-C|; X>Y. Y contains S, that

is, point A. Count |A-B| as one-half cycle and

discard point A; S=B

• Y=|B-C|; X=|C-D|; X>Y. Y contains S, that is,

point B. Count |B-C| as one half-cycle and

discard point B; S=C

• Y=|C-D|; X=|D-E|; X<Y



• Y=|D-E|; X=|E-F|; X<Y

• Y=|E-F|; X=|F-G|; X>Y. Count |E-F| as one

cycle and discard points E and F.• Y=|C-D|; X=|D-G|; X>Y. Y contains S, that is,

point C. Count |C-D| as one-half cycle and

discard point C. S=D.



• Y=|C-D|; X=|D-G|; X>Y. Y contains S, that is,

point C. Count |C-D| as one-half cycle and

discard point C. S=D.• Y=|D-G|; X=|G-H|; X<Y.

• Y=|G-H|; X=|H-I|; X<Y



• Count |D-G| as one-half cycle, |G-H| as one-

half cycle, and |H-I| as one-half cycle

• End of counting.

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SHM by khaja