Heinrich J.G., Aldinger F. (Eds.) Ceramic Materials and Components for Engines

2

1

0

4

-1

-

c

C

-

-2

-3

-4

5.50

5,75

6,OO 6,25 6,50

IN4

+

tension tests

internal pressure tests

Weibull

fit

......

95

Oh

confidence interval

of

tension tests

---

95

%

confidence interval

of

internal pressure tests

figure

5:

Weibull diagrams

a)

AI2O3,

b)

MgO-Zr02

The data were transformed with equation

1

into a

theoretical 4-point bending strength

(3khm4

and com-

pared with manufacturers’ data. Of course this com-

parison should be carefully interpreted because of the

different material charges, specimen geometry and

specimen manufacturing processes. Nevertheless, the

calculated data and the manufacturers’ data (4), shown

in

table

4,

correspond very well.

table

4:

comparison of measured and manufactur-

ers data

(4)

this stud manufacturers data

500MPa

350MPa

F99.7

The maximum tolerable fiber stresses in the internal

pressure tests were much higher than in the tension

tests.

The same behavior could be observed for the

characteristic reference element strength using the

volume and the surface model. It can be concluded that

the reason is not the different stress state in the tests,

but the anisotropisms of manufacturing (hot isostatic

pressing) or mechanical processing.

For shear stress the volume and the surface model

lead to equal strength results. The Weibull modulus

(m=44) is high. The Weibull distribution function was

assumed for shear strength in order to compare com-

pression with tension data. For shear strength, the

Weibull parameters of MgO-ZQ are much higher

than for normal stress failure. The scattering of the

strength is accordifigly smaller. MgO-Zr02

(o&

=

-4)

is more sensitive

to

shear load than

A1203

(odoz>-10).

The multi-axial behavior of both ceramic materials

is characterized in the

figures 6a,b,

using the maxi-

mum fiber stresses

om

(axial tension and compression

test) and

ati

(internal pressure test).

242

-_._---

-

.---.--.-._-_-__-__-

-2

a)

-2

0

6,

IMP4

-

- - -

-

95%

confidence limits for avera e characteristic reference element strength (63,21%

-

value)

----

equivalent stress hypothesis of ieierlein

---

b)

equivalent stress hypothesis

of

Weibull-Stanley

FE-calculatuions

-

symmetry

figure 6: multi-axial diagrams a) MgO-Zr02

b)

A1203

For both materials, no multi-axial effect can be rec-

ognized in the tension-tension quadrant. The specimens

failed under the highest tensile stress. The tolerable

tangential tensile stress of MgO-ZrOz decreases with

increasing axial compression load, when the compres-

sion is higher than one third of the uniaxial compres-

sion strength. For this range a multi-axial strength

effect exits and has to be taken into account in the

calculations. This influence could not be obtained for

Al2O3

because of the limited test load.

SUB-CRITICAL

CRACK

GROWTH

The time parameter n* was determined in the ten-

sion and the compression test. The specimen made

from

A1203

failed during

4

and MgO-Zr02 during

5

tensile load steps

(figure

7

and

8).

A

time effect exits

obviously resulting from sub-critical crack growth.

In

comparison

to

instantaneous failure, an identical stress

leads to higher values of the probability of failure be-

cause of the longer load time. For compression of

ZrOz

a time effect was also detected

(figure

9),

but smaller

than for tensile stress. The specimen failed on the

6"

and

7*

load step (after

6

and

7

hours).

Thus

n*

is

quite

smaller.

figure 7: step load tests;

A1203,

m=l1,6

,

aov,=226MPa; n*=0,52

figure

8:

step load tests MgO-Zr02, m=23,8,

oOVt

407MPa; n*=0,58

243

01

-

h&anhlroum

(ihm

t

=

20

8

0

-

- -

-,

----.

5m

5y1

am

sm

?m

7s

a0

sm

ma

1mo

1-

w.1

figure

9:

step load tests MgO-Zr02 (compression),

m=44,0,

ro

=913MPa; n*=0,45

n'

n* was determined assuming a linear damage ac-

cumulation. The total risk of rupture BG is the

sum

of

the risks of rupture per load step i (equation

2):

lower value average value upper value llerature

[5]

n1

nm

nu n

For each data point the time probability of failure

was calculated and compared with the probability of

failure for instantaneous failure. n* was determined by

minimizing the sum of the square deviance between the

both probabilities of failure. To check the congruence

between calculation and experimental data n* was used

to

generate theoretical data points.

A

good congruence

can be obtained

(figure

8,

9). Transforming of n* into

the crack growth parameter

n

with the equation

L

A1203

0.52

9

22

53

21

MgO-ZrOz (tension)

0.58

22

41 74 40

MgO-Zr02 (shear)

0.45

28 98

162

nodata

m

nz-

.-

I

n*

results in a good accordance to values given by the

literature

(5)

(table

5). The conlusion is that Nadler's

model is suitable for practical work.

_____

_________~

A

multi-axial effect for time failure could be dis-

covered for compression-tension stress combinations

only. For combined tension-tension stresses the speci-

men always failed under the higher tensile stress.

and MgO-Zr02 the maximum principle stress hypothe-

sis is sufficient in the tensile stress field. Compressive

loads can be neglected as far as the compressive load is

below

1/3

of the compressive strength.

REFERENCES

Kriiger,

S.:

Ein Beitrag zur praxisgerechten Di-

mensionierung keramischer Bauteile bei me-

hrachsigen Beanspruchungen; Dissertation TU

Clausthal, Papierflieger (1 999), ISBN 3-89720-

Kriiger,

S.;

Barth, H.-J.: Entwicklung einer Priif-

maschine

fW

die keramische Werkstoffpriifung;

5.

Kongrefi fiir industrielle Mefi- und Automa-

tisierungstechnik, Hiithing-Verlag

(2000).

Nadler,

P.:

Liisung von Problemen des Proof-

Testes in der Praxis; Mechanische Eigenschaften

keramischer

Konstruktionswerkstoffe;

Hrsg.: G.

Grathwohl; DGM

Informationsgesellschaft

mbH;

Oberursel(l993); S.277-288.

FRIATEC AG, Informationsbroschiire "Erzeug-

nisse aus Oxidkeramik", Mannheim

(1

999).

Wedingen, A; Grathwohl, G: Ermiidung keramis-

cher Werkstoffe; Mechanische Eigenschaften

keramischer Werkstoffe; Hrsg.: G. Grathwohl;

DGM Informationsgesellschaft mbH; Oberursel

345-6.

(1993);

S.

149-160.

SUMMARY

For computation of ceramic components the multi-

axial strength effect is from less importance. For AI203

244

111.

Design, Modelling and Simulation

This Page Intentionally Left Blank

FATIGUE DESIGN

AND

TESTING

OF

CERAMIC INTAKE AND

EXHAUST VALVES

C.M. Sonsino

Fraunhofer-Institute for Structural Durability

(LBF)

D-64289 Darms tad t/Germany

ABSTRACT

Fatigue design of components subjected to cyclic loading

require special testing methods, component related

material data and an appropriate safety concept. The

following contribution presents a newly developed

methodology for the fatigue design and testing of highly

loaded ceramic components. This methodology is veri-

fied by laboratory and in-service testing

of

Si,N,-intake

and exhaust valves.

INTRODUCTION

While design relevant data like S-N curve, slope and

scatter, notch and mean stress sensitivity, influence of

loading mode (axial, bending, torsion),

environment

(temperature, corrosion) and defects exist since many

years for a large amount of metallic materials, fatigue

properties and design principles for ceramic materials are

almost unknown. The application of structural ceramics

for functionally important components like turbine

wheels, gudgeon pins

or

motor valves subjected

to

re-

peated loading require the knowledge of corresponding

data. In the following, basic relationships about the fa-

tigue behaviour of the structural

A1,0,-

and Si,N,-cera-

mics will be presented that were evaluated within former

investigations

(1,

2). After this, the fatigue design of

Si,N,-intake and exhaust valves will be reported.

FATIGUE BEHAVIOUR OF CERAMICS

Scatter and

slope

of

S-N

curves

The normalized evaluation of

350

fatigue tests carried

out with almost unnotched and notched specimens under

filly reversed

(R

=

omin/ompx

=

-1) and pulsating

(R

=

0)

four-point-bending at room temperature,

800

and 1200"

C

resulted in a uniform

S-N

curve (1,

2)

with following

characteristics

(3),

Fig.

1:

The slope of the S-N curve k

=

AlgN/Algo,

=

85

(inverse

Basquin

exponent) is

extremely flat and all results are covered within the

probability of survival

P,

=

10 and 90

%

by a scatter of

stress amplitudes

T,,

=

1

:

[oa(lO%)

:

0a(90%)]

=

1

:

1.40.

This scatter is also found for cast aluminium

or

nodular iron as well as aluminium and steel welds. The

particular stress-amplitudes of the different test series

were normalized with regard to the appertaining particu-

lar fatigue strength at

2.5

. lo6

cycles with

P,

=

50

%.

Fig.

1

Uniform S-N curve for different

A1,0,-

and

Si,N,-ceramics

The facts of the very flat inclination of the S-N curve and

the determined scatter band are also confirmed by other

until now statistically not evaluated results

(4,

5,

6)

which fit fairly well into the derived uniform S-N curve.

Fig. 2 shows the evaluation of results obtained for a

high-strength Si,N,-ceramic developed for turbo-charger

turbine wheels and combustion engine valves

(5).

The

fatigue strength of this material can be well covered by

the uniform

S-N

curve. When 1000"

C

is exceeded the

softening of the glas phase decreases the fatigue strength.

Fig.

2

Fatigue behaviour of a Si,N,-ceramic

Up to 1000"

C

the static and fatigue strengths of struc-

tural ceramics like AI,O, and Si,N, are not affected by

temperature.

The very flat slope of the S-N curve and the very high

life scatter (not stress scatter) are related to the ,,non

247

forgiving" brittleness of ceramics

.

This requires a well

controlled manufacturing process with not exceeded al-

lowable defect sizes. The determined uniform slope and

scatter will remain for any ceramic, but the level of the

fatigue strength will depend on the particular material

quality. This knowledge facilitates the statistical evalua-

tion even of few tests by covering them with the uniform

slope and scatter band.

The influence of the defect size on fatigue strength can

be estimated by a threshold-stress intensity derived for a

given endurable stress amplitude

oal,

defect depth a1

and width cl and loading mode dependent geometry fac-

tor

Y(al, c1)

:

AK~,,

=2.oS1

-,/~-Y(a,,c,).

For another defect geometry the fatigue strength is then

Because of the very flat S-N curves the fatigue strength

of ceramic materials cannot be separated into low-,

finite-

or

high-cycle fatigue ranges. Ceramics are also not

suitable for a design against variable amplitude loading

which allows among others occasional exceedences of

the fatigue limit.

The fact that for ceramics even a fatigue limit in the

classical sense does not exist is not a major problem

because for a required fatigue life, e.g.

2

.

lo9

cycles for

valves, the decrease of fatigue strength is very small due

to

the shallow inclination of the S-N curve.

All

these characteristics suggest that for the fatigue

design of ceramic components the allowable design

stresses must lie below the scatter band in order to ex-

clude failures. The distance of allowable stresses from

endurable stresses with

P,

=

50

%,

i.e. safety margin, is

for a given scatter only a question of required probability

of failure

Pf,

see section

3.

Fracture mechanics

The extreme low inclination of the SN-curves is also

supported by fracture mechanical investigations on

Si,N,-ceramics

(7):

Compared to conventional metallic

materials the difference between threshold and critical

stress intensities is very small. The threshold level

AKh

corresponds to the endurable high-cycle fatigue strength

and the critical stress intensity

AKc

to the ultimate tensile

strength. The ratio between

A&

and

AK,

is comparable

to the ratio between ultimate tensile strength and

endurable high-cycle fatigue strength. When

AKh

is

exceeded, SipN, reveals due to its brittleness a very high

crack propagation rate, Fig.

3.

Only a small exceedance

of the threshold level leads under cyclic loading to a total

failure.

I

R=Q.J

4

.3;

P

m

10'

lVI

4

U

aJ

c

*

h

C

a

m

Q

a

Y

U

.-

2

10'0

-

+

4

m

2

h

"

10"

-

7

-

I

\AK~

i

0.5

0.1

0

-

Material:

Si,

N,

#

Rb=gOOMPa

I

8

#

0

@"

0

@

&

LQdlrg:

.

Compact

tension,

T=RT

f=

25s.'

rn

0

I

0

m:

Gilbert

et

al

Stress

intensity

AK,

(MPa

mfi)

Fig.

3

Crack propagation in Si,N,-ceramics

Mean-stress and notch sensitivity

Tensile mean stresses, which may occur e.g. by a pre-

loading, residual stresses, a centrifugal force

or

thermal

stress transients diminish the fatigue strength signifi-

cantly.

For

ceramics under pulsating loading

(R

=

0)

only

about half of the amount of the endurable stress ampli-

tude for fully-reversed loading

(R

=

-1)

was

found (1

,

2),

Fig.

4.

For ductile steels the decrease by pulsating load is

only about

15

%.

While ceramics ,,dislike" tensile mean

stresses they ,,like" compressive mean stresses due to the

defect (crack)-closure. Therefore, in presence of com-

pressive mean stresses the endurable stresses will be

much higher than the fatigue strength under fully-re-

versed loading as indicated in Fig.

4.

The knowledge of

the relationship between mean stresses and stress ampli-

tudes

is

necessary for transforming of amplitudes super-

posed to different mean stresses to amplitudes with a

constant R-value, e.g. R

=

0.

As it can be seen from Fig.

4

the fatigue strength of the

almost unnotched state is reduced fully by the theoretical

stress concentration.

248

\

-Z(P,-)

0

K.

=

108

K.

*

190

P..

50%

N

.

ZSd

T

i

8W.C

5.20 5.61 6.00 6.36 6.71 7.03

\I/

Hmlarrl:

Alp,

~

SG

Looding:

Plan.

bending

Fig. 4 Mean stress-amplitude-diagram and mean-stress

sensitivity

In Fig.

5

the comparison of the theoretical notch factors

Ktb

and fatigue notch factors

Kfi

reveal that they are

within a scatter of

-

+

10

%

equal.

2.0

.?

r

1.0

SG.

SG:

SG.

TV

963.

TV

1063.

wm

sg1.

9005

sg1.

07

I

PVA

I.

HP.

Rl.

R=

-1. 0

8OO.C.

R

z

-1,

0

RT. R.

-1

RT. R. -I

8OO.C.

R

-

-1

8W.C.

R.

-1

RT.

R.4

800.C.

RI-l

RT.

Ri-I

RT

8OO.C

RT

8OO.C

+

R*-1

0

R.0

10

15

20

Th.Oi.11COI

nolch

faclw

K.

Fig.

5

Relation between theoretical and fatigue notch

factors for Al2O3- and Si3N4-ceramics

This indicates missing stress-gradient dependent volume

effects. This maximum notch sensitivity can also be ob-

served for brittle metallic materials. Although the rnaxi-

mum stressed volume of the notched specimens is

smaller than the volume of the unnotched specimens, the

local endurable stresses in the notch are not significantly

higher than the endurable stresses of the unnotched state

for a given fatigue life. Hence, volume effects known

from static loading do not occur under cyclic loading

or

are at least of minor importance. This fact facilitates the

evaluation of local stresses, in the sence that stress gradi-

ents and volume effects are not to be considered under

cyclic loading.

SAFETY

CONCEPT

In design, service dependent occuring stresses must lie

below the allowable stresses which are derived from en-

durable stresses with

P,

=

50%:

oc,dl

=

0s

(50%)/j,.

The safety margin

ja

depends on the stress scatter T, and

the required theoretical probability of failure (3). Under

the assumption of a logarithmical Gaussian distribution

jo

=

=,

where the standard deviation of the stress

amplitudes

s

=

[lg(l/T,)]

/

2.56 and

z

is the normalized

safety factor which depends on the failure probability

Pf,

see Table

1.

In fatigue design with ceramic materials

Pf

-

values smaller than are used. For a scatter T,

=

1

:

1.40 and a required theoretical value

Pf

=

10'

j,

is

1.98.

As long as the the ratio

j*

between endurable and

occuring service stresses, i.e. safety, is higher than

j,

a

failure can be excluded.

I'

I

Tab.

1

Failure probability

Pf

and normalized safety

factor

-z

(Pf)

DESIGN EXAMPLE

FOR

S~~NJ-INTAKE AND

EXHAUST VALVES

The increased efforts of investigating the use

of

ceramic

valves, Fig. 6, bases on following advantages compared

to steel valves:

Weight reduction by about 60

'YO.

Improvement of valve dynamics and valve train effi-

ciency by about 20

%.

Smoothing of engine torque behaviour by changing

the cam profile and increasing the valve acceleration

as well as the volumetric effeciency.

Saving of fuel consumption by 3 to

4

%

and

reduction of CO-emission by 20

%.

Enaine

WD~:

2.0

t

gasoline,

16

valves,

p

=

7

MPa,

n

= 6

800

rpm

Fig.

6

Valve train middle section with Si,N,-valves

In the following, the design and evaluation methodology

applied

to ceramic valves within a collaborative work

with Adam Ope1

AG

and DairnlerChrysler

AG

will be

reported

(8,

9). The methodology was verified by fatigue

testing of valves, laboratory test runs with six engines

and field tests with five vehicles. All engines were gaso-

line heled and each equipped with 16 valves. The valves

249

manufacturered were gas pressure sintered (tensile

bending strength

1200

MPa) and ground

(R,

<

2

pm).

During the quality control all valves with defect sizes a

>

40 pm detectable by x-rays and computer tomography

were excluded from the investigations.

Table

2

compares basic properties of the Si3Ncceramic

used for the production of valves and of the substituted

valve steel.

Properties Si,N+ (GPSN*)

X45CrSi93

(AISI

W3)

I I

Densitiy

p

Youne's modulus

E

I290

-

310

GPa

I

I90

GPa

13.24

-

3.25

g/ccm

I

7.70

g/ccm

.,

Poisson constant

p

Bending

0.27

0.30

20

"C:

20

"C:

1100-1300

MPa

880-1030

MPa

Weibull modulus

m

1000

OC:

800

OC:

850-950

MPa

70

MPa

I5

-

22

1.9.1

04K-'

20-1000

"C:

20-700

"C:

20

"C:

20

WlmK

Thermal elongation

coefficient

a

20

"C:

21

WlmK

Specific thermal

capacity

h

1000

"C:

Hardness

HVlO

Fracture toughness K,c

I

I3

W/mK

I

Thermo-shock

I

.

~~

1200

-

1400

8-10

MPa mln

R

.=

R,

4-P)

I

Io6O

I-

parameter

*)

GPSN

=

Gas

pressure sintered silicon nitride

Tab.

2

Material data of the ceramic Si3N4 and valve

steel X45CrSi93 (AISI HNV3)

Loading states and local stresses

During one revolution of the camshaft a valve is sub-

jected not only to the combustion pressure from fuel

ignition but also to cyclic loadings from valve closing

and opening and all of them are superposed to thermal

stress transients which determine the mean stress level,

Fig.

7.

Fig.

7

Thermal stress and superposed cyclic stresses

at a specific point in a valve

The

mean stress remains constant when the stationary

temperature state is reached.

For

evaluating a valve, the

stress states are calculated by

FE

for different locations,

Fig.

8,

i.e. valve seat, transition to the shaft, shaft and

fillets for the attachment of the valve spring. Multiaxial

stress are evaluated by the principle stress hypothesis

valid for brittle materials.

e4

e9

e7

el0

Fig.

8

Analyzed points of a ceramic valve

While the highest stresses in the starting stage, at the

maximum thermal stress and the stationary stage occur

about

2

.

lo9

cycles, the maximum stresses due to cold

start-stop cycles may occur 3

.

1

O4

times at most during a

life cycle of an engine. All these service stresses must be

assessed using mean-stress-amplitude diagrams which

can be only determined experimentally from

S-N

curves

with

R

=

-1

and

0.

Local endurable fatigue properties

The local endurable stresses are determined using the

manufactured ceramic valves. Two type of tests are

necessary, valve seat bending by pulsating axial loading

(R

=

0,

f

=

170s-')

of the valve head, and fully-reversed

rotatory bending

(R

=

-1,

f

=

17s')

of

the valve shaft,

Fig. 9.

a. Valve

seat

bending

b.

Rotatow

shaft

bending

T

=

RT,

300°C,

9OO'C

Fig. 9 Loading principles of valves

250

The failures are produced in the valve seat and in the

transition from the head to the shaft, respectively. FE-

calculations deliver the relationship between the applied

loads and the local stresses in the failure locations. The

data obtained for the mentioned critical locations under

room temperature,

300

and

900"

C, Fig.

10,

contain al-

ready the influence of the material, maximum detectable

defects (a

<

40

pm),

surface manufacture, residual

stresses and stress gradients

on

the endurable stresses.

All test results are covered by the proposed uniform

slope and scatter of the S-N curve for ceramics, Fig.

10.

The fatigue strength unter

900"

C

is slightly higher than

for the lower temperatures, probably because of the

beginning softening of the glass phase and increased

ductility.

e8

e9

el0

0

T=

20T

Vahesafterengmetestng

A

T.300

'C

+

T=300'C(tntake)

0

T=900Y

x

T=900Y(uhaust)

100

'

'..I

.

...I

'

.*.I

'

...I

10'

2

4

68105

2

4 6810~

2

4

6810'

2

4

6810*

2

Nurrber

of

cyder

to

falure

N,

+65.9

f

65.4

65.6 I70 2.6

+58.2

f

58.2

58.2 170 2.9

-60.0

f

60.0

0

170

m

Fig.

10

S-N curves of Si,N, (GPSN)-ceramic valves

The mean-stress-amplitude diagrams, Fig. 1

1,

are

derived from the S-N curves in Fig.

10

using the stress

amplitudes for

R

=

-1

and

0

at

3

.

lo4

and

2

.

lo9

cycles.

The comparison in Fig. 11 shows the dependency of steel

from temperature while ceramic is not effected.

a. Diagrams for N

=

3

*

lo4

cycles

-600

-400

-200

0

200

400

Warn

Local mean

stress

a,

b. Diagrams for N

=

2

.

lo9

cycles

-600 -400

-200

0

200

400

Wa

600

Local mean

stress

q,,

Fig.

1

Comparison of Si3N4 with valve steel

in

mean-

stress-amplitude diagrams

Fatigue strength assessment and verification by

laboratory engine testing and field tests

Tables

3

and

4

compare the occuring local service

stresses for the most critical loading states

in

different

locations of intake and exhaust valves with the endurable

stresses.

a. Maximum stresses for start-stopp-events

(N

=

3

.

10')

I

...

e3

I

+67.7

f

67.7

I

67.7

I

188

I

2.8

e4

I

-173.2

f

221.9

I

24.3

I

188

I

7.7

+31.7

f

31.7 31.7 188 5.9

+65.7

f

65.7 65.7

188

2.9

+58.2

f

58.2 58.2

188

3.2

I88

m

b. Maximum stresses during operation

(N

=

2

.

lo9

)

Tab.

3

Evaluation of calculated occuring stresses on a

Si3N4-intake valve

25

1

Heinrich J.G., Aldinger F. (Eds.) Ceramic Materials and Components for Engines

Подождите немного. Документ загружается.