PM2001

Dynamic ProperOes of PM Materials

MaterialsConcepts and RequiredFatigue Design of PM Components

Cetin Morris Sonsino

Fraunhofer-institute for Stmcturel Durability (LBF), Barbringstr 47, D-64289 Darmstadt,Germany

~STRACT

In genersd, there are several fatigue design concepts for components: normal stress, local

strain, local stress and fracture mechanics. According to the applied concept and loading

mode (axial, bending, constant and variable amplitudes, straitistress ratios or sliding ratios for

rolling contact) different data is required. Among the existing design concepts the most

appropriate one is the local stress concept under consideration of stress concentrations and

gradients. The data required are statistically supported S-N curves in the local stress system,

mean-stress and notch sensitivity, slope and scatter of the S-N curve and in case of variable

mplitude Ioadlng the kowledge of red damage sums. For rolling contact fatigue

applications the howledge of data comprising sliding effects is essential.

1 ~TRODUCTION

Fatigue design is an important aspect of structural durability which is divided into impact,

creep, wear and fatigue strength, see Fig. 1 [1].

I Struaural Durability ~

specialloads creep wear

Buckling oBulging

Overloads Impati

80

mile on some components like reverse spur gears (impact and fatigue), aircrafi turbine disks

(creep and fatigue) or transmission gears (wear, rolling contact and classical fatigue) these

particular aspects can occur simultaneously, a lot of PM applications like con-rods, synchronizer

hubs, miscellaneous gears, Fig. 2, are classical fatigue applications, on which the present paper

is focusing,

W Ex~ples offatiwelo~ed pM’P@s (co~ecting-rod, s~c~onizer hub>gem wheel)

The fatigue design of these ptis requires special material propefiies which differ extremely

from static material data. Wile static material data like ultimate tensile strength, yield

strength, elongation, impact, hardness, Young. s modulus, Poisson’s constit display a fist

material characterisation, the data for fatigue design are more complex because they must take

into account interacting parameters, see Fig. 3, like material, manufacturing, loading (axial,

bending, torsion, rolling contact, constant and variable amplitude, mean stress effects, sliding)

and geometry (notch and loading mode dependent stress concentration) [1].

81

Oncluting environment)

w-! &V, G*x andC M Wnm

~ Parameters of structural durability

Beyond these parameters also semice load-time-histories to which parts are submitted must be

well howm Fig. 4 displays measured strains on the stem of a con-rod of a gasoline engine

under fill load at 3000,5000 rpm and during the sweep up to 5000 rpm [2].

1,0n= 3000 rp

0

-1,0

0 0,10 0,20 0,30 0,40

1,0n = 3000- 50M rp

0

-1,0 F“II Io,d,P=, =lOObar

0 0,40 0,80 1,20 1,60

0.w- Timein s

~ Measored strains on the stem of a con-rod of a 6-cylinder engine

82

Fig. 5 presents measured engine torque during shiting ad strains on a synchronizer hub [3, 4].

2. gear 3. gear 4, gear0.3

5. gear 2. gear

o,2–z-% o,l —~g o—

?~ -0.1—

5 -o.2–

-0.3 1 1 I 1 1 I

-0.3 I1 1 1 1 1 1 I

8 9 10 11 12 13 74 s 15DIA6761. Tme

~ Engine torque and strain on a synchronizer hub

fiese examples show tiat service load-time histories are not always occuring with fully

reversed constit amplitudes without mean stresses @=-1) but with mostly time vtiable ones.

~is fact arises the question about the relevance of constant amplitude loading which is usually

applied for generating fatigue data. me decision despite variable arnpli~des in which cases

constant amplitude fatigue data can be applied is explained in Fig. 6:

I ---- Design based on vatiable amplitudes

if6a, (N<106)>a.E

— Oesign based on endurance limit

if6,1(N<106)>aaE

0“~

2 5,1=Q 4F ------E ---. zm~ 522 4)

A

/

SpedraL

,03 ,~4 io5 io6 i~7 /08 /09

,,. ,5,- CyclesN

U. Critefia for component desi~ b~ed on end~ance limit md v~able ~pli~de loading

83

If despite the variable smplitu& nature of loads or stresses (strains) tie tiurn value of the

spectrum (distribution of occuring amplitudes) lies below tie tecbnicd endurance tit of the

S-N curve, e.g. at 2.106 cycles, and the maximum value of the spctrurn occurs more than 106

cycles, e.g. con-rods, then the loading can be assumed ss a constant smptitudc loading with the

maximum value of the spectrum as the stress amplitude. In this me the stresses can be

assessed by using constant amplitude fatigue data [5]. However, a damage awunndation

considemtion is required only when the higher loads of the spectrum exceed the high-cycle

region of the S-N curve.

A tier question is with which bd of specimens and testing techniques the data needed for

fatigue design should be provided. The paper will give an overview of the sate of the art tig

into account the tieady used methods of structural durability dso in other sectors than powder

metilurgy, i.e. forged and wrought steels as well as durninium and magnesium, cast

dmninimn and cast magnesium. Further, it will discuss the very limited applicability of dab

obtained with unnotched specimens by some examples.

Note that in generrd S-N curves are presented in terms of strain or stress arnphtu&s and the

presence of mean-stresses is indicated by the lo~ stress or strain ratio R = Ffi~_,

Further, an endurance tit does not exist because due to the microstructure tieady under

non-corrosive laboratory conditions at ambient temperatures in the high-cycle region @>106

cycles) for fernticd steels a decrease of fatigue stiengtb by about 5°/0horn one decade to the

next one occurs. This decrease is for austcniticd steels as well as for duminiurn alloys higher.

Therefore, ordy for classification and cdctition purposes a technicrd endumnce or fatigue

tit (OW or pm at NE) can be defied as the bee point of the S-N curve. At room temperature

depending on tie strength and hardness of the matial it can lie bewecn NE = 105and 107

cycles. k case of corrosion and elevated temperatorcs the decrease of fatigue stren~ in the

high-cycle region is much higher and a hee point may not exist.

2 DESIGN CONCEPTS AND REOWD DATA

The following short survey about different design concepts [6] will explain what &d of data is

necessary for fatigue design.

2.1 Design concepts

The major concepts used in fatigue design are compiled in Fig. 7. These are the concept of

nominal stress (strain), structural stress/strain, local stress or strain and fracture mechanics [6].

As the structural stress/strain concept is usurdly used for welded joints, it will not be discussed

in the following. me fracture mechanics concept is not applied in the design of PM mass

products, but in seldom cases for the assessment of cracks.

Fratiure mechanics concept

~~m ‘m.

Fig. 7: Design concepts of structural durability

2.1.1 Nominal stress approach

Fig. 8 demonstrates tie application of this concept schematically by the example of a torque

lever of a printing machine.

M ‘,,?.

Fig. 8:

a, Desian and Loading

N: ‘F;R,= R.= 0, p.lsati”g benting

~ *=. . & , K,, = f(;,:)

Application of the nominrd stress

d Desi n cuwe a asse s t

.“aj+

-------+ ----------if :;ioe

103 lti 10$ 10$ 1o~N,

1on

concept on a torque lever of a printing machine

85

me calculation procedure requires for the part to be designed the definition of a nominal stress

(or strain) and of a notch factor. For assessing the calculated nominal stress following details

must be considered:

me S-N-curve, obtained under load control, must be available for tie selected material,

manufacturing process ad surface state (local microstructure).

me notch factor for the S-N curve and for the part as well as tie size of the specimerr.s

and part’s notch should correspond.

me loading mode (load-time history, stress ratio R = Gm~/om=, tial or bending) and

environrnenti conditions (temperature, corrosion) under which the S-N curve is obtained

shotid correspond to the loading mode and environment of the part.

Material and manufacturing scatters for deriving a design curve with required safety

@probabilityof failure) shodd be bown.

me influence of these parameters are displayed in Figs. 9 to 11: A tensile mean-stress

produced by a prcload, by assembly or by pulsating loading (R> -1) reduces the endurable

fatigue strength, Fig. 9a. me decrease of fatigue strength by increased tensile mean stiess,

described by the mean-stress sensitivity M, is for ductile materials less than for britie ones.

Fig. 9b presents the mean-stress sensitivity M in a Haigh-dia~ this requires at least two S-

N curves determined for two different stress ratios R. In case of compressive mean-stresses,

e.g. they occur on con-rods due to the ignition pressure (R<- 1), the fatigue strength is

increased. me brittle tie material, tie higher is the increase under compressive mean-stresses.

a.$-NcuM b.~

R,

\.2-.

1

P,=50%

‘-, ---.1 -.-, .;.2-.-lp. i-.-.-,

-.

20:&;~~:’’:-:<~

I , IY5 105 106 2 3

Cycles to2failure N?

2R=-2 150

~. ~ pa

110 ~ *.Q

~ 100-g

S1.7a ,,

.$

50 N=2.106P,= 50%

.50 0 50 100 MPa 150Mean stres o~

90

W Fe-1.5%C.(1120”BOmin)p = 7.1 @cm3

& f=25s-l, R=0 +“-ka-”<-- : ‘+

.,. 6761. -Q;”’”+

= I~Uence Ofme~ s~esses ad me~-s~ess sensitiviv on fati~e life

86

Fig. 10 compares tie fatigue behaviour of uunotched and notched specimens under mid

loadlng and bending. For bending the endurable fatigue strength is higher than for uial loadlng

because of the steeper stress gradients. Further, under bending the strength reduction by

notches is far less than under =ird loading.

L150

Kti=l.OMPa k= 13.9100 J/ C.E, . :----

?5-._75

,, &.G. -.

k=<9- . =:240so P,= 50%

*1W 5 105 2 5 106 2 3

‘r. k = 9.5

:-+.:”96

.-:~k = s,5 87

so;

:~2104 5 105 2 5 106 2

Cycles to failure Nj

Fe -1 .5%CU(1120”BOmin)~ = 6.8 ~cm,

R = 250 MPa, R,:,...1 R=” ‘02=200 Mpa’A5=g%

--”””,— ---, ,, —.-ground (R, s 10pm),radii and hole as sintered T-

U: S-N c~es ofFe-1.5~0 CU>P =6.8 g/ccm in the nomi~l s~ess system

me notch sensitivity is derived by the ratio of fatigue strengths for the notched and urmotched

states, Fig. 11. The higher the notch sensitivity, the higher is the decrease of the nominal

fatigue strength.

-/lv “o~ ~A IIu+ %-- -B“ 0“~~.-—nE

0,5mf.GmE%E 012

1.0 2.0 3.0 4.0 5,0k.x Stressconcentration factor K,[

W Fatigue stren~h reduction by notches– notch sensitivityIf the needed S-N curve is not available, in many cases it can be obtained by knowledge of

parameters like notch sensitivity, mean-stress effects, loading mode etc.

87

2.1.2 hcd concmts

As most components have a complex shape for which neitim a nominal stress or strain nor a

stress concentration factor can be assigned and additiody as damage is a local process, there

is no other way then to apply local concepts. ~is is not anymore a problem because in todays

design practice the fitc element method ~~ delivers the needed Iocrd strain or stresses,

which arc connected with eachother by the Young.s modtius E and the Poisson’s constant p:

~(E, +v.E*)“=1-~2

(1)

+(P. E1+E2)‘2=1–U

(2)

2.1.2.1 bcd strain concmt

me major ideas of this concept are that for the fatigue failure of a part the maximum local

strain in a critical notch is responsible and that the deformation behaviour in a notch is strain

controlled due to the support effect of the present strsi~stress gradients. As the strain in critical

areas of parts are us~y of mtitiaxid nature, for tie assessment of the strain state the

components of the strain tensor must be transferred kto an equivrdent strain according to a

ductility rekted hypothesis [7]. With the local maximum equivalent strain of the part

&termine~ the fatigue fife to crack initiation can then be assessed by assi~g this value to a

S-N curve obtained with unnotched specimens ~t = 1.0) under tily reversed @= -1) d

strain control. ~ese ideas are displayed in Fig. 12.

88

me materiaI data needed for this concept are strain-controlled S-N curves, Fig. 13, damage-

parsmeter/fatigu&life @-N ewes, Fig. 14, and cyclic stress-straincurves,Fig. 15, dl

obtained with wotched specimens under axial, fully reversed @=l) strain-controlled

loading. me cyclic stress-sti curve ia needed for the cdctition of tie local ek~plastic

strain and stress if the loading exc=ds tie elasticity limit and tie damage-parameter/fatigue-

life curve is used for *g mem-stress effects into accomt. If the Iocd stress is not flly

reversed @$ -l), then the damaging effect of the mean stress is considered by this parameter

by tmnsfomdng the stress amphmde into a damage eqtivdent my reversed @= -1)

amplitude, which is assessed by assigning it to the damage-pammeter/fatigue-fife curve. me

fatigue life c~es are vtid for the criterion irdtiation ofa kcticdly detectable crack with a

depth ot e.g. a = 0.5 mm.

0,1

“j0,0s

m

0,01

qcbs m a-k intitin N, (.*.5 mm)mm’,.

- s~-con~oll~ S-N c~e of Fe- 1.5CW P = 6.8 ~ccm

I2000. *

.;: ::~:b m’E-

MPa Fe-1.5c” ,m . 112wm0mh b- 4.0-7

1000- — C- C8~cm3, ~-9.1% .;. 0.W79

aoo - R. - 2U Mh c- 4.81M

600

~ 400-

!200.

100-— PM(N)= ~2.(2N~+E. df. d‘ (Nybfij

80-

60

40.

1 1

5 100 5 lo~ 5 102 5 103 5 104 5 105 5 10s 5 1070.m, Cycks * crack in~on Ni (=0.5mm)

U D~ge p-e~r - fati~e fife c~e ofFe-1.5CUt P = 6.8 ~CCUZ

89

100 ~ 1 /

/ /_~mm- 267 Mh Kw-3W,5 MW

n n,- -0375 “’W- a1W6

o/, I I

10,0 0.2 OA 0,6 0,8 1,0

Strain e %

= Monotofic and cyclic s~ess-s~ti ewes ofFe-1 .5CU, P = 6.8 ~ccrn

me Cofi-Mrmson, damage-parameter (according to [8]) and hberg-Osgood equations and

tieir constants are compiled in Figs. 13, 14 and 15 for the sintered steel Fe-1 ,5%CUwith

~6.8@ccm. These data, see Table 1, are required in todays modem fatigue life estimation

pro~es.

1. Strain contro~ed

Cofi – Maon : &,(N)= Ea,e(N)+ Ea,p(N)= + (2Mb+ E; - (2N~

Damage parmeter: P~w (N)= ~G~2 . (2N)2b+ E. a;. &;. (2N)(bK)

()

1/”

Osgood –bberg: &,=&,e+E,P=~+ ~ (monotonic: & n ; cyclic: K’, n’)

2. Load controlled

[)-Ilk

(1-l/k

Basquin: 6,(N)= C.f # , P,(N)= P,E # for N<N,

for N 2 NE: ~onstit amplitude loading K ~ 44.9; variable arnphtudeloading W = 2k – i with ii = 1 for wrou@t and i = 2 for castor porousmaterirds

3. Crack urouagation

Paris – Erdogan : da~= Co.(AK)m with AK=Au.~.Y(a,d); propagation n for AKti<AK< AK,,

Table 1: Equations for fatigue design

However, this approach does not consider effects from ~dienk, from different sizes between

part md specimen and delivers in many cases extreme conservative resdts, especially if the

highest Strainetistressed material volume in a notch of a pti is much smaller than tie volume

90

of the unnotched specimen with which the S-N curve has been obtained. How these features

are to be considered will be discussed later together with the Iocd stress concept. The attempt

to consider notch effects by introduction of a fatigue notch factor Kfrnay be helpfi [6,9, 10],

but for complex shaped parts it cannot be defined.

Further, if the locrd service strains are in the range rendetig more than 5.104 cycles, i.e. the

lod strtistress-state is more or less macroscopicdly elastic and MS is valid for the majority

of PM pm, then the local strain-cycle curve obtained with urmotched specimens @t= 1.0)

can be converted by u = E. Einto a locrd stress-cycle curve and instead of the local strain

concept dso the locrd stress concept can be applied.

2.1.2.2 Local stress concept

The local stress concept reveals following advantages:

■ A desi~ engineer thirdm more in terms of stresses than in terms of strains; he compares

cdcrdated s~esses with the titimate tensile stress or yield stress in case of static desi~,

and in case of fatigue design with the technicrd endurance limit.

. The performance of load-controlled tests which deliver the S-N curves for the noti as

well as local stiess concepts is much easier and faster than the performance of strain:

controlled tests.

For abroad application of this concept the bowledge of S-N curves obtained ordy witi

unnotched specimens, mosfly under axial and tily reversed @=-l) loading, is not sufficient

because there are no parts without notches and loadings with mean stresses@ $ -1) can occur,

too. Effects occuring in notches due to stress gradients shodd not be neglegted for an optimum

exploitation of tie materials fatigue performance. Therefore, the idea of the Iocd stress

concept, to use&b horn tests with notched specimens is very similar to the idea of the locrd

strain concept, however, it possesses the superion~ of inclutig the effects of stress gradients

and mdtitidity on fatigue stiength and life, Fig. 16.

~. Principle of the local stress concept

For the determination of the local stress-cycle curves, tie nonrind stress-cycle curves, Fig. 10,

have to be tmnsfonned into Iocd stresses. me mtimurn @rincipd) local stress in a notch is

cdtiatcd by Cl,loc = Kt. ~om, while for an unnotched specimen @t = 1.0) Iocd and

noti stresses are eqti. As in critical areas of components as well as in notches of

specimens tie local swss states are of mdtitid nature and as for the assessment a

compatibility between component and specimen is required [11], the mtititid stress must be

transformed into an equivalent shte. For sintered steels titb densities up to 7.4 @cenr the

principal stress hypothesis can be apphed [7], for higher densities the von Mses criterion can

be considered m appropriate, provided tit the direction of principal stresses remain constant

during the loading [7]. According to this, the S-N curves presenti in Fig. 10 in the noti

stress system can be transferred for the material Fe-1 .5~oCUwith p = 6.8 #ccm into the lod

swss system by using the pnnciprd stress hypothesis with the local equivalent stress, Fig. 17.

Uw = Oj)x = K, . OnOm (3)

92

b. -30

n

-.

; (Tl):t;.r .gF4.,

~~o. -;=:. ,610

k = 9.5

75 (~1)

5 P,= 50%

2.1 W 5 105 2 5 106 2 3

Cycles to failure N,

~Fe -1.5%CU(1120°BOmin) 90p = 6.8 ~cm3Rm= 250 MPa, RP0.2= 200 MPa, AS = g~o

_f=25s-l, R=0- ground (R, s 10pm),radiiand hole as sintered

-’=’=’”O

D~61~~-~’;

~ S-N curves of Fe-1 .5%~, p = 6.8 ~ccm in the local stress ayatem

h contrast to the noti syam Fig. 10, the curves of the notched specimens are now lying

above the curves for the unnotched ones. me reason ia that due to the stress gradients, locdy

higher stresses can be supported compared to the homogeneous stress distribution in smitiy

loaded unnotched specimens or hear stress distribution in unnokhed specimens under

bending.

me amount of the local supportable fatigue strength is related to tie highest stressed matiriad

volume. me sdler this volume, tie lower is the probability of crack initiating defects and ao

the higher is the supportable fatigue stiength. ma relationship for fatigue stren~ values in

Fig. 17 at N = 2.106 cycles is presented in Fig. 18. me Mgheat streaaed volume VgO is

defied as the rnsterid volume in which the _mn local stress drops along the surface,

thicbesa and depth from 100 to 90 % [12].

If the ~imurn stressed matend volume VWof the component is calculated then horn such a

relationship the local supportable atmss can be derived or the appertaining S-N curve can be

selected for the fatigue life assessment among different possibilities.

93

transformed to asQntered mu

Y

>

ground

‘;:*K

50

Fe -1,5%CU(1120°BOmin)p = 6.8 ~cm3, As = 9%

as sintered or ground

(Rzs 10pm)

g~ltial

NF=2.106~-2.8

h

Y

as sintered

R=OuaE,k= 103.vm% 4~9 bending —

&=l.o P,= 50%

T

tial&=l.o

me advantage of the local stress concept using data obtained with notched specimens will be

discussed by following design example. Fig. 19 shows the loading of an mgle lever, the atreas

distributions in the notch as well as along tie outer stiace and tie ptisating loading mode

@+). ~s requires&h obtained under pdsating loading or if not available, the consideration

of the mean-stress effect if ody dab for ~ly reversed loading @ = -1) wotid be at disposal.

me maximum local equivalent stress amplitude in the notch is ❑q = ~ 106 ma with R = O.

@or the application of the local stin concept tiis stress can be converted into a local strain

amplitude by G = ufi.)

J*J 47,5

c. ~1 eaulv a~aa=+106MPai106MPa (RO=O)

F=+500N*500N(RF=O) e ~ = + 0.076% + 0.076% (~= O)

~. htig of an an@e lever, lod strain ad stress distibutiom

94

Now, the S-N curve the closest @the present application must be selected among the available

S-N curves in the local stress sys~m for the occurring stress ratio, Fig. 17. me stress

distribution at the long bom of the angle lever and the highest stressed volume is approached

the best by the axial loaded centi nomhed specimen. me assignment of the dctiated stress

amplitude to this S-N curve, Fig. 20, ~dts a fatigue life of more than N = 2‘ 106cycles with a

probability of survivrd of P, = 50%. me good agreement between the S-N curves horn notchd

specimens and angle levm conti the demonstrated approach. k this contex~ it must be

added that not ordy the cdfition of the local equivalent strain or stress is a decisive criterion

of ~ferability, but also the use of S-N curves for the criterion fatigue life to crack initiation

e.g. 0.5 mm and not the fatigue fife for total failure. Notched specimens and components can be

still compmd with regard to crack initiatio% but not crack propagation.

If his stress is assigned to the S-N curve obtained with unnotched specimens, due to the

ne~ection of the supporting effect of stress gradients and of the sdler highest stressed

volume in the long bore, an extreme low fatigue life of N = 2‘ 104cycles resdta and leads to

the conclusion to change the dimensions or the rnaterird. (me local strain concept wodd rdso

render a similar fatigue fife.)

250 .179

MPa %

200 .143

150 .107

100 .071

90

so ,057

70

m .043

50

40 .029

D. emCycles to sack initiation Na (a = 0.5 mm)

~ Evrduation of the 10A stress on the long bore of an an~e lever

~s example underlines the superiority of the Iocd stress concept under consideration of

effects from the stress distribution @ghest stressed material volume). me example bases here

on mean values ~, = 500A)and does not discuss the safety aspect. For tis, see chapter 2.3 and

[11] in which this example is tier elaborated.

95

2.1.2.3 bcal stress cencmt for rollino contact

me local stress concept is not ordy restricted for the loading modes &d-loading, bending,

torsion with different mean stresses expressed by the load ratio ~ but it comprises also the

loading mode rotig conti~ which occurs on gear fl~, Fig. 21 [13].

/

~: Equiwdent stresses on gear flh under Hefisn pressnre

me Hemisn pressure is nothing else than a pressure and geometry dependent stress which

causes a fatigue damage at or below the stiaee. me mtitiaxid stress state is transformed into

an uniaxial one by the von Mises criterion because of the compressive nature of the stress state.

~s damage is dso dependent on the grade of sliding between the contact partners. me

-um sfiding which can occur on gear flti is -24~o and diminishes the fatigue strength

in contrast to a loading without sliding (OYO),Fig. 22.

96

MPa1750-

1500 .

1250.

1000.

~(F-.O%NI-O,5%MOW.5%C,

quentied and timpe~d

P7.1 ~cm’

~Th=l 250”U40 rein, 90%N#l 0%H2

T,m = 800”UOmin

Tw . Oiwo”c~ =200”w0 minT

750 J baling: n= 1420pm, f=71 s’EnvimmentGeati oilSAE80(MIL<2105 = GL 4)Failuremde Ptings

Tmfia= 80”C

5001@ i 4 L $lbs 2 4 & $lb6 2 4 6 ~~bl 2 4 k ~lbs

.-Rolling ~cles N

~ RoUing contact fatigue cme6 for different 61idingmtios

k tie ro~ing contact fatigue re8earch different propos~ about testing modes and specimens

etist. However, the closest one to gear applications i6 the test principle accounting to ~

(~ab~ FrietichsMen), Fig. 23, which enables a good comparative -g of

different materirds snd treatments.

a. Test Dtinriole

Contact sutiace

..-

~ ticiple of rowig contact fatigue test rig

b. Specimen

Contact sutiace

However, tie transferabihty of ro~ing contact fatigue dak from specimens to gears is not yet

satisfacto~ [14], Fig. 24.

97

2000MPa

1750

1500

1250

1000

750

500 I I I I I I I Ilb i

I I I I I I I I I4 k 41b5 i i k ~1~6 i 4 6 $lb7 i 4 6 $1~8

M.n!! Rolhng ~cles N

~ Comparison of rol~ig contact behsviour of specimens and gesrs

me difference between the S-N curve of the specimens and of the gears are not yet

exptible. me research with regard to the transfersbitity of rolling contact data obtained with

specimens to gears is ongoing tie parameters to be considered are compfled in Fig. 25.

a. Lmdna of RCF -Soecimens b. ~ c. Loadina of Gears

Geome~. Material Co”tid ~u~amo Sutiace *te0 Equivalent atres

I >

0 Residual fire-s0 Entiron ment. Lwdo Stidng

W p-~e~ forme-ferabiliv ofrol~~g oon~t fatiwe~~forbe desisn ofgem

2.2 Fracture mechanics conceut

h most cases the operation of parts with cracks and crack propagation is not accepted because

of psychological but dso legal reasons and crack propagation data do not rdlow a direct and

simple assessment of fatigue fife compared to the allocation of a stress smphtnde to a S-N

curve. ~erefore, this concept found in the design of PM parts ordy a very restricted

application especially for the assessment of defects. @owever, fracture mechanics is a very

essentird and indispensable tool witi regard to anicrosticti design and assessment of

98

resistance to crack initiation.) In the following, for reasons of completeness in the discussion of

the different design concepts ordy the basic data for the application of linear-elastic fracture

mechanics will be presented by an exaple of a con-rod which revealed cracks in the small eye

due to manufacturing [15]. Elasto-plastic fracture mechanics and the behaviour of small cracks

(a< 0.5 mm) [6, 9] will not be discussed here.

~.

10-2

m

cycle 5‘

2’

z 10-3

m>m 5’amLc 2’0.~ 104GmQp 5Q

2um 2G

10-5

5

2

10-6

Material: / ~1 ‘Fe–1.5 Cu -0.6 C

//

~~ / -Slfll = 1120 °/30min ;quenched and tempered ~;p = 7.1 g/cm3 ,.

I

. .

F .. ....T.l/..

“““’”’’:,.,.; $ = C(AK)m

. P, in YO: 9 / , , .- .

TIO

R> ~.05 .......

;

AKth ,; ,

\ ~,.

r [ 1

2102 5 103 2

N,mm325’ ’03

DIA 6769e Stress - intensity AK

~ Fracture mechanics data for a sintered steel

h Fig. 26 basic crack propagation data obtained under three point bending of single edge

specimens are compiled. Fig. 27 shows the shear crack which occurred due to the interaction

between local powder flow and shear stresses during the pressing of the con-rod. For

preliminary prototype tests in fired engines it had to be assessed if this defect would lead to a

99

premature failure of the rods and so prevent the analysis of the fatigue behaviour of other

critical areas of the component. me acceptance of these con-rods depended only on the proof

fiat the shear cracks would not propagate under the maximum engine load, i.e. the stress-

intensity at the crack tip

AK= Au~Y(a/d)<AKti (4)

must be lower than the threshold stress intensivi~. For the crack length of ~ = 2.5 nun and

the tensile local stress range of Ao = 39 ma a crack opening stress intensity of W = 131

N/rnrn3’2results which is much lower than the threshold value, Fig. 26. During tie engine test

runs no failure occurred.

~

+.

crack alongthe sm.,, e“d

+

~ Con-rod with shear cracks due to manufacturing

2.3 Safetv considerations

Based on experience and assuming a logarithmic Gaussian distribution, it is possible to

calctiate the probability of failure – by coupling the various scatters - and to derive a

statistically founded safety margin ja, which is a tiction of the standard deviation of the

loading (sB),the standard deviation of the strength values around a mean value (s0), and the

stidard deviation of the mean value fluctuations (sM).It can be calculated according to the

following equation

100

j. = 10“uO(pt)withs = ~- (5)

where w is a relative aafev margin dependent on the probability of failure Pf, s. Table 2. ~s

means that when the mhum service loading is hewn and under guaranteed production

conditions, -y no component fails.

Assuming that the -urn service loading is known, e.g. sB= O,md with so = 0.04 and sM=

0.02, a safety margin j. of about 1.6 for a probability of failure Pf= 10-5is obtained by which J

the mean endurance ~tit established in tests @probabilityof survival P,= 50Yo)must be

divided by the safety margin to obtain the allowable endurance limit a@. h Fig. 28 the

endurance tit of O@ = 115 ma is reduced to the Wowable vahse of am = 72 ma. As in

the finite life region, the scatter of the stress is smaller, the appropriate safety margin is

consequently lower, e.g. ja = 1.4 for 105cycles. The derivation of allowable stresses with tis

safety margin presupposes a certain production reliability and howledge of the *USU

loading which occurs in actuad service. If tie aforementioned scatters are partidy tiown,

the safety margin must be increased as a restit of which tie &sign curves must be lowered to

sanrdlerallowable stresses, e.g. by a factor of 2 or possible even more.

250MPa

P,[%]:1o--- Testresults

2oo-.

6Notch surface

P,= 105as- sintered

g 150-.——aE Design curvem3p 100-G

To= o,(90%) Io, (1OYO)~ 90-

.5 80- SO= 0.39 Ig (l/T. )

‘: 70- SM= stindard dev. manufa~uring

~ 60 -SF = Standard dev. Ioa&ng uaE, .I1.(pel0-3 = 72

~Material: Fe-1 .5°hCu

50 - p = 6,8- 6.9 @cm’ (1120°CB0 rein)

Loading: axial, R = O, f = 25 S-l40 I I I I I I I I

5 I 04 2 5 105 2 5 106 2DIA ~ Cycles to crack initiation NW (a = 0.5 mm)

W Derivation of a ~siw me

101

1 Cdctiatory probability of failure Pf and nodized safety factor M for Gaussianlogaritiic distribution

Pf ,..1 ~o.z ,.-3 lo~ ~o-s lo~

-w 1.28 2.33 3.09 3.72 4.27 4.75

2 Dterminstion of statistically based safety factor j.

19je=-uo-=-uosSc : Standard deviation of endurable swss around its mean value

~P,.so%with S. = 0.3g 19(l/T.)sM: Stiw &tiation of the me~ value of stiess, if it ~tigoes a scatigsB: Standard deviation of load ifmsxim ~ loti is ~s~e~ th~ sB= O

3 Mowable stress for a required cdctitory probability of ftilure0,1 = UP,=50M/ jd

Table 2. Determination of allowable stiesses—.

It becomes obvious that the rnstend scatter

To =1: [u(P, = 10%) : U(P5 = 90%)] (6)

iBanother parameter necessary for desi~ which requires seved fatigue tests and their

statistical evaluation [16]. Besides this, dso the howledge of manufacturing scatters and at

last not least the scatter of service loading is require~ too. h the Gaussian s~tistics the

standard deviation is related to the scatter

()S=*19 + (7)

3 V~LE -LI~E LOAD~G

At the end of the introduction it was distin@shed between vsriabIe mplitude loadings below

and above the tcchnicd endurance limit, Fig. 6. As long as the variable amplitu&s do not

exceed the technical endurance limit and the occursnce of the maximum value of the spectrum

is more the 106cycles, this can be treated as a constant amplitude Joading in the high-cycle

sre~ for the fatigue strength assessment the howledge of the technical endurance ~it is

sticient.

102

In this context dso the importance of tie slope k (inverse Basquin exponent) of the S-N curve

must be mentioned. The slope does not depend only on stress concentration and loading mode, ~

but dso on the material. Materials with shallow inclination of the Woehler-curve Nigh k-

vahres), e.g. hard metals, ceramics, are not suitable for exceedmces of the technical endnmnce

limit, because of the big risk of failure. The slope k is an indication whether a material can

digest dso cyclic loads above the technical endurance limit without failure.

But in practice there are also a lot of parts for which a limited exceedance of the high-cycle

area of the WoeMer-cnrve is allowed for realizing light-weight design parts [1], e.g. steering

components. The knowledge of the fatigue behaviour of especially high-strength PM’ steels

under such spectrum loading can open broad applications in future. Therefore, rdso a short

insight into the cumulative fatigue performance of PM materials will be presented here.

Fig. 29 presents the behaviour of a Fe-1 .5%CU alloy under a Gaussian spectrum [17], i.e.

distribution of the stress amplitudes is Gaussian. The sequence length of the spectrum is

SL= 5 105cycles, which is repeated until failure occurs. On the stress axis the results are

presented by the maximum value of the spectrum. The comparison of the constant amplitude

fatigue curve (Woehler-curve) and of the variable amplitide fatigue curve (Gassner-curve)

obtained Mder fully reversed bending shows that in the high cycle area a significrmt exceeding

of the constant amplitude high-cycle fatigue is possible. This sort of exceedance is also

observed for spectrum loading under rolling contact [13], Fig. 30. The sequence length of the

repeated Gaussian-like spectrum is SL= 5 105cycles.

,,,

; :i:~””’”-~////)v‘ j:~:l..::~::]:: *.:.~l10:>.*~~-–i------------....T ... .... . ....6—.. . .

I ‘1 ----] K. ........ ... ..... .-..5=52::.’

0“Woehler curve I I I=- ““~la Gassner curve ~ [ “-.

=--””t--l-”-t””-”t--l”””--t-2m -- ‘----- --- -6------------- ~= 10.6, --

/150 -lj- Mw-l---l---

~lW Matetiak Fe-1.5%CU90

“’~::$~:l-\----p = 7.1 @cm3 (, , *~.~~~mln) --–- ---- .- --...—. -

80 Loading: Bending, R, R=-1, f=l 5s!,!, ,, ,,, !, ,., l-------- K.= 1.49

70 ii’;”;’ ‘:”103 10, 105 106 IF 10, 1(

D,. ,7s,. Cycles to rupture N,, fir

Woehler- and Gassner-curves of a Fe-1 .5%CU alloy under fully reversed bending

103

3000, .

MPa

20w

1000 Mateti k W .5 C r 0 i ded,p= 7.l@ (1 Omin)c- ,.CS

h both cases the observed excetice of the high-cycle constant ampfitudc fatigue s~ngth

can be used in design for a significant weight reduction by allowing higher stresses through

reduction of cross sections.

me position of Gassner--es compsred to the WoeMer-curves can be seldom prcdicte~

b-use restits of cunndative fatigue cdctiations acmrding @ the clsssicd Ptigren-her

de with the damage sum of D = 1.0 are genetiy unreliable [1, 13 to 19]. ~erefore, for the

assessment of fatigue fife under variable amplitudes tests with service spectra is recommended

witi regard to Ii@t-weight design with PM’materids. From the comptison between

experimentrdly determined WocMcr- and Gsssner-curves real damage sums Dd can be

derived and used for more realistic fatigue hvings, Fig. 31.

Wtilwr aweCumulatbefrqwnw

Dd=+.k_,

\dtibmon[vm) dw k Wrier wweA.

p-1 \

-------—--

n---- ----

A.- —-- —- —-_-- __--- _->m->m

.m= 1: *mI, ~umi”[um N4

m. 2 &ad tiwerd mwdh

,i Qcles M i

0. ●m

~ Cdctiation of fatigue fife and red damage sums

lU

In Fig. 32 the Iod stress spectrum ofa svckontier-hub for 300000 ~ service life which

was derived from service measurements in a gear-box [3, 41 is comparedwith the designcurve

for the critical notch under consideration ofdl effects tim rnatcrid, stress gradients and

highest stressed volume.

~ R=-1 I1,‘e. Warm compatied PM’QwI

g 3.~ p = 7.3 ~cm3a

~

2m%

$ ,,

I ,,w

%.—~ O.s~ Design spetirum for 300.000 km at the highe~

sre%ed area of the ~chronizer hubn-,. ,

101 5 102 5 lb ilb” 5 ,&5 5 166 5 1;7

Cycles NR..-

Comparison of local stress spectrum with allowable stresses

Damage accunudation cdcdation for the assessment of tie fatigue life on basis of the red

damage sum of DA = 0.05 found for PM’steels [17] shows that the synchroni=r hub will

exceed the mission requirement of 300000 h without any failure. Consequently, a load

increase by about 300A,or a wei@t reduction horn presently 359 g to about 320 g can be still

allowed without geopartig the necessary structi durabihty.

4 RECOmNDA~ON FOR TESTS AND DATA AND CONCLUSIONS

The different design concepts defie the specimens, loading and testing modes rmd tie data for

the fatigue design, as compiled in Tables 1 snd 3:

If the local strti conceptis to be applied than data obtained under tily reversed strain

control with unnotched specimens is required. me we& pointi of this concept are the

hypothetical, not material related consideration of mean-stress effects by a damage

parameter and the neglecting of stistrcss gradients and the maximum stressed volume.

The Iocd stress concept with data from unnotched specimens determined from tests

under flly reversed load control considers the effects of stress gradients, volume only if

105

●

o

0

&ta comprising the notch sensitivity is available from tests witi notched spwimens.

Mat@ rchted mean stress effects are tien into account if the mean-stress sensitivity M

is available from tests under different stress ratios R.

Teats with notched speckens dehver data which arc the closest to reality, because parts

without notches do not efist. However, the data in the no-al atreas aystern can be ody

use~ if for the component which must be assessed dso a noti stress can be defied.

Otherwise, data obtained in the noti system can be transferred into the local stress

system which Wows the best comprising consideration of the moat important parameters

which determine fatigue strength and fife.

Centrrd notched specimens are suitable for the assessment of borea (ofl borca of con-rods,

long bores of different levers), double-edge notched specimens for the assesamcnt of fillet

notches on hubs or gear roots. This specimen with different radii and consequently

different loading mode dependent notch fwtors is recommended in the 1S0 3928 [20].

For gear flti desi~ dso the local stress concept is apphed by dctcrminin g rotig

contact dati with roll specimens, Fig. 23.

At last not least in seldom cases the assessment of crack can require the application of

frac~re mechatics. For obtaining the appertaining data tie-point-bending specimens,

Table 3, is suggested.

Ratio DataSuecimen \ Notch factor I Loading mode

l~~a,:

=’ &=l.o I tial— .—.—.—.—.1! ,, strain controlled

I I

a! load controlled

+

load contro~ed

I

k,o,,, N,, To,MRF= 0,-1, -2

slidingS=O%, -24 k, P,~, NE,TO

0/0

&=o CO,m, AKti, K,,

I 1 1 1 1

Table 3: Mati of fatigue specimens, loading modes, test pamrnetcrs and data

106

Table 3 displayed ticady the miscellaneous parameters with regard to the loading mode (tid

or bending), specimen types (unnotche~ notche~ ro~s, fiture mechanics), application

dependent stress and sliding ratios. In powder metilurgy this complexi~ is further increased

by material (cloys) and manufacturing (density, sintetig conditions, post sintering treaments)

conditions as well as environmental effects [21]. For a vsrie~ of PM’materids fatigue data for

most of these concepts have been *ady compfled in a data bti [22], which needs an

updating. However, the huge time consumption to generate design data requires following

restrictions and recommendations for obtaining service relevant properties in a reasonable

time:

●

●

✠

e

●

tiysis of service load conditions (mechanical loads and environment).

Specimen manufacturing with equivalent rnatend and surface states as the designated

parts.

For not surface touching loading mid load controlled tests with urmotched ~ = 1.0) and

notched ~ = 2.5, &b= 1.8) double-edge specimens under R = -1 and Oand under service

environment.

For surface boun&d loading ro~ig contact fatigue tests under tibologicd service

conditions and a sliding of S = -24°/0.

Verification with prototypes before mass production.

Best transfer of data to components is achiev~ when tie used &ta contain dl local features of

the critical areas of the part to be desiWeL i.e. rnaterid and surface state, stresdstrain state and

stress/strain distributions as we~ as ske.

5 REFERENCES

[ 1 ] Sonsino, C.M.:Fatigue Design and Testing of Componentsk La fatica ad dto nurnero & cicli @@ cycle fatigue): Problerni aperti e nuoveMetodologie. Politecnico die Milano, 10.-11.3.1998, Ed. ks~on kt., Mihoand MTS Systems, Torino (1998), pp. 19-62

[2] Gembus, K.; ROSCL.; Rupp, A.; Grubisic, V.:Stress tiysis on a Connecting RodFraunhofer-ktitut for Strut@ Durability @BF), DmtadtReport No. 7063 (1992), not published

107

[ 3 ] Rupp, A.; Sonsino, C.M.; Radereau, D.:Service had and Stress Distribution for PM Gem ComponentsS~ Paper No. 2000-01-0404SAE ht. Congress and Etibition, Detioi~ Michigsn, March 6-9,2000

[ 4 ] Sonsino, C.M.; RadereaU D.; MorisseL C.; Lipp, K.; Rupp, A. ::Determination of Service Loads of a Gcm-Box for htroduction ofNew Components by Warm Compactionh Proceedings of tie 2000 Powder Metrdlurgy World Congress and ExhibitionKyoto, Japan, Part 2, pp. 1602-1605

[ 5 ] Sonsino, C.M.; Bather-Hoecbs4 M.:Methodology for the Safe and Economical Fatigue Design of Componentsin ABSETC Btig Systems under Variable Arnplitide LoadingsSAE Paper No. 990366SAE ht. Con~ess and Exhibition, Detroit Michigm, March 14, 1999

[ 6 ] Seeger, T.:-dagen ~ Betriebsfesti@eitsnschweiseStibau Handbuch, Stahlbau-Verlagsgesellschafi mbH, K6k (1996)

[ 7 ] Sonsino, C.M.; Grubisic, V.:Mtitiaxid Fatigue Behaviour of Sintered Steels rnrder Combined k- and@t-of-Phase Bending and TorsionZeitschrifi fier Werhtoficu Vol. 18 (1987) No. 5, pp. 148-157

[ 8 ] Smith, KN.; WatsoU P.; Topper, T.H.:A Stress-Strain Function for tie Fatigue of MetisJournrd of Matirds, NSA, Vol. 5 (1970) No. 4, pp. 767-778

[ 9 ] Radaj, D.:Ermtidungsfesti@eitSpringer-Verlag, Berlin – Heidelberg (1995)

[10] Radaj, D.; Sonsino, C.M.:Fatigue Assessment of Welded Joints by bcd ApproachesAbington Wblisbing, Cambridge (1998)

[11] Esper, F.; Sonsino, C.M.:Fatigue Design for PM ComponentsEuropean Powder Metiurgy Association @PW), Shewsbury (1994)

[12] Sonsino, C.M.:ZU Bewertung &s Schwingfesti#eitsverMtcns von Bauteilen rnit Hilfe~rtlicher BeanspmchungerrKonstion 45 (1993) No. 1, pp. 25-33

[13] Sonsino, C.M.; Lipp, K.:Rohg Contact Fatigue Propertiesof Selected PM-Matcri* of Gem-Box ApplicationsSAE Paper No. 990333

108

SAE kt.Congress and Exhibition, Detroit, Michigan, March 1 – 4, 1999

[14] Lipp, K; Sonsino, C.M.:Einsati hochfester umweltfreundlicher Sinterstile fi hochbelastcte BauteileForschungskuratoriurn Maschincnbau Forschungshefi 252, Fmnkfurt (2000)

[15] Sonsino, C.M.; Lipp, K.:Fatigue Design of Sintered Con-RodsFraunhofer-Institute for Structural Durability @BF), DsrmstadtR~ort No. FB-190 (1990)

[16] Sonsino, C.M.:Metiods to Determine Relevant Material Properties for the Fatigue Designof Powder MeMlurgy PartsPowder Me~llurgy ht 16 (1984) No. 1, pp. 34-38; 16 (1984) No. 2, pp. 73-77

[17] Buxbamn, O.;’Sonsino, C.M.:Fatigue S&n@ of Sintered Steels un&r Variable Amplitide Loadingk Horimns of Powder Metilurgy. PM’86, DfiseldorfEd. W.A. Kaysser und W.J. Hupprnann. Verlag Schmi~ Freiburg (1986), pp. 487490

[18] Fatemi, A.; Yang, L.:Curmdative Fatigue Damage and Life Prediction Theories: A Surveyof the State of the M for Homogeneous Materialsht. J. Fatigue 20 (1998) No. 1, pp. 9-34

[19] Etiiti, K.-G.; Kottc, KL.:Damage Accumtiation-Limitations and Perspectives for Fatigne Life Assessmenth@/www.materidsweek.o@proceetigtiindex.htmMaterials Week 2000, Munich 25.-28.9.2000

[20] kb~tiOdStidsrd1S03928Sintered Meti Materirds, Excluding Hardrnetis – Fatigue Test Pieceskt. Org. for Standar&tioU Geneva (1999)

[21] Sonsino, CM.:Fatigue Behaviour of Sintered ~terids and Components under Operatiod Serviceti 1998 Powder Metilurgy World Congress Education PrograrnrneEdited by J.M. To~ba and F. Velssco, Granada (Spain), October 1998, pp. 185-216

[22] Sonsino, C.M.; Bender, A.; Fsati, R.:Data Bank on Fatigue Properties of Sintered Steels @ATA-FWS)Frsunhofer-Mtitute for Structi Durability &BF), D~stadt (1994)

lW