f f f fThe region of a fracture surface that formed during stage II propagation is characterized by two types of markings termed

beachmarksbeachmarks

and

striations.

9

Beachmarks (clamshell marks) are of macroscopic dimensions and are found in components that have experienced interruptions during stage II propagationin components that have experienced interruptions during stage II propagation.

Fracture surface of a rotating steel shaft that experiencedthat experiencedfatigue failure.

10

On the other hand, fatigue striations are microscopic in size and subject to, g p jobservation with the electron microscope (either TEM or SEM).

Transmission electron fractograph showing fatigue striations in aluminum.

11

Each striation is thought to represent the advance distance of the crack front during a single load cycle.

Striation width depends on, and increases with, increasing stress range.p , , g g

The presence of beachmarks and/or striations on a fracture surface confirms that the cause of failure was fatigue. Nevertheless, the absence of either or both does not exclude fatigue as the cause ofabsence of either or both does not exclude fatigue as the cause of failure.

12

Region of slow crack propagation

Beachmarks andBeachmarks and striationswill not appear on ppthat region over which the rapid failure occursfailure occurs.

13Region of rapid fracture

Ratchet marks and radial marks

Fracture surface

Radial marks

surface Connecting ligament

Radial marks

When cracks initiate at the surface of a component on two closelyp yspaced planes, the cracks grow and eventually join to form a ratchet mark.

Radial marks, on the other hand, radiate from the fracture origin and are visible to the unaided eye or at low magnification.

14

y g

(Source: A F Liu(Source: A.F. Liu,Mechanics and Mechanisms of Fracture: An Introduction, ASM International, 2005, pp. 130)

Schematic of marks on surfaces of fatigue fractures produced in smooth and notched components with round cross sections under various loading conditions at high and low nominal stressloading conditions at high and low nominal stress.

15

Crack Propagation Rate

Even though measures may be taken to minimize the possibility of

p g

fatigue failure, cracks and crack nucleation sites will always exist in structural components. Under the influence of cyclic stresses, cracks will inevitably form and grow; this process if unabated can ultimately lead toinevitably form and grow; this process, if unabated, can ultimately lead to failure.

The intent of the present discussion is to develop a criterion whereby fatigue life may be predicted on the basis of material and stress state parameters.

16

E i t l t h i il bl f it i k l th d iExperimental techniques are available for monitoring crack length during the cyclic stressing. Data are recorded and plotted as crack length avs. number of cycles N .vs. number of cycles N .

17

The stage II crack growth rate is a function of not only stress level and crack size but also material variables. This rate may be expressed in terms of the stress intensity factor K and takes the form:

d mKAdNda

Paris-Erdoğan LawdN

A mdepend on environment frequency and the stress ratio

and are constants for the particular material, which will alsodepend on environment, frequency, and the stress ratio.

18

K is the stress intensity factor range at the crack tip, i.e.

minmax KKK

or from fracture mechanics:

aYaYK minmax

dNdaThe typical fatigue crack growth rate behavior of materials is representedschematically as the logarithm of crack growth rate vs thedNda

Kschematically as the logarithm of crack growth ratelogarithm of the stress intensity factor range

vs. the

.

19

ale)

(log

sca

mKAdNda

, da/

dN

dN

wth

rate

ack

grow

Region I Region II Region III

tigue

cra

Non-propagating

Unstable crack growth

Linear relationship between

da

Fat

fatigue cracksdNdaK loglog and

20Stress intensity factor range, K (log scale)

The curve is essentially linear in Region II.

mKAdNda

dN

mKAdNda

loglog

dN

gg

AKmda logloglog

AKm

dNlogloglog

21

Design Against FatigueOne of the goals of failure analysis is to be able to predict fatigue life for some component, given its service constraints and laboratory test data.

fN , due to stage II, by integration of the Paris-Erdogan equation.We are now able to develop an analytical expression for

mKAdadN

cf a

m

N

f KAdadNNIntegrating; a

mf KA00

ca daN

amf

aYAN

0

ca

ammmmf aY

daA

N0

22

1

22

a0

Design Example 1Design Example 1

A relatively large sheet of steel is to be exposed to cyclic tensiley g p y

respectively Prior to testing it has been determined that the length of

andMPa 001 MPa 05and compressive stresses of magnitudes ,

respectively. Prior to testing, it has been determined that the length of

the largest surface crack is . Estimate the fatigue life of thismm 02.

mMPa 25 and thesheet if its plane strain fracture toughness is

03 andin the Paris Erdoğan equation areandvalues of Am

ain MPa andfor in m.

03.

, respectively,121001 .

andin the Paris-Erdoğan equation areandvalues of Am

23

SolutionFirst we need to find the upper limit of the integral for the Paris-Erdoğan

ti A i t f 100 MP i th f t t hequation. Assuming a stress of 100 MPa in the fracture toughness equation,

m0201MP100

mMPa 251122

.

YKa Ic

c 1MPa100

Yc

ca

mmmmf aYda

AN 22

1

ca

a

da

aYA0

1

a aYA

0

233323

24

a

f aYA

Nc

21 213323

aYA

112

0

caaYA

112

03323

0201

00201

110010012

332312

cycles 10495

0200020110010016

332312

....

25