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

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Here

denotes the initial crack length,

the crack

length at the end of the dwell time or at the time of

failure during the dwell time, respectively. If the crack

lengths in eq.

are

replaced by the corresponding

strengths, i.e. the initial crack length by the initial

strength

and the final crack length by the residual strength

eq.

the initial strength, that the specimen would have had

in a short time tensile test, results from eq. 4.

If fracture occurs during the dwell time

has to

be set;

is the time to fracture. Some specimens have

been tested under compressive loads. In this case

$, =

has to be set, as under compressive stresses no crack

growth is expected.

For the initial strength a Weibull-distribution is as-

sumed:

Elimination of

(3i

by eq.

in eq.

yields

eq.

whereas

contains parameters of fracture mechanics:

K[c2-n

eq.

The experimental fracture probability usually is deter-

mined by allocation in the order

failure whereby the

criterion is the time to fracture or the fracture stress,

respectively:

i-0.5

pe,,(oi)

eq. 11

As tensile tests and flexural tests are to be analysed

at the same time, the difference in the effective tested

surface, respectively effective volume, has to

re-

garded. Here the geometry

the tensile specimens is

considered as the reference: thus

00 in eq.

is the char-

acteristic strength of the tensile specimens.

If only damage at the surfaces

the specimens is

regarded, the equivalent strength results in

Aeff,B

0.z

=gBL\

eq. 12

Aeff.z

)

where

denotes the strength of the tensile specimens

and

that

the bending bars. The effective surface

of the tensile specimens AeffZ corresponds to the cylin-

drical surface of across the tested length (here:

471

mm2).

The stressed surface of the bending bars

Aeff,B depends on the Weibull modulus

itself:

eq. 13

is the outer span of the fixture,

the width of the

specimen and k the ratio of the spans (here 20

mm).

If only flaws in the volume are considered, for the

equivalent strengths

eq.'14

follows, where

Veffz

results from the tested length and

the diameter of the tensile specimens to

707

mm3.

The

effective volume of the flexural specimens depends

like the effective surface

on m.:

km+1

2(m

112

Veff,B

eq. 15

Here k denotes the ratio

the spans and

the volume

between the outer rolls

4 x 40

mm3).

Fitting Sequence

and

Calculation

Fig.

shows the applied fitting procedure. The pa-

rameters of the two-parameter Weibull-statistic (m and

oo)

and the parameters for subcritical crack growth

and n) are calculated by eq.

at the same time. An

experimental data set consists of the loading time t,, the

testing stress

and the residual strength

ow.

Since in

regarding the residual strength

and the time to

fracture

at the same time a definite ranking is impos-

sible, for each data set a value for the initial strength

(3i

has to be calculated, assuming plausible initial values

for

oo,

and n. The tests are ranked according to

their initial strength. Then the experimental fracture

probability after Weibull (eq.

11)

is associated. By

means of the Levenberg-Marquardt-Algorithm eq.

fitted to the experimental probabilities

Pexp,

whereas

oo,

m, B and n are the variable parameters. The obtained

values are used to recalculate the initial strengths

(3i.

flexural test data are included, the dependence of the

effective surface, respectively effective volume, on the

Weibull modulus m according to eq. 12 and eq. 13,

respectively

eq.

and eq.

has to be considered.

Normally the new parameters lead to a different order

ranked after

than assumed before the first run. The

tests now are ranked regarding their new values of

(~i

and

after association of the respective probabilities

322

according to eq.

are fitted again to eq. 9 by the

Levenberg-Marquardt-algorithm.

This step of iteration

has to be repeated until the sequence of the tests re-

garding the initial strengths does not change anymore.

The thus stabilised values for the parameters

oo,

and n are the wanted values.

changed

associate

P-

Leven

berg-

Marquardt-

-1

-2

m~le

spurnen.

fracture dunng

uwptest

msle

spearnen.

fracture

restdual strength

bending

t8t

rpearnm

u,~,

residual swngm

rnedlanica Imd dunng

creep

test

Weitull

rarneters

Van

Fit

111

130

148

199 250

301

352

Fig.

Results under assumption of volume defects

bsnding

tee

spearnen

0,.

revdual strength

rneChantca

bad during

a~ep

test

Welhll

pararnetsr

fmm

Qlgin

Fit

tmde

speamen.

fradure

rerldual rtmgth

Strengtl

kaf

111

130

148

199 250

301

352

w--.-....U..-

NPaI

Fig.

Results under assumption

surface defects

Fig.

Fitting algorithm

the combined lifetime model

DISCUSSION

The advantage of this procedure is the possibility to

get four characteristic values for a material at the same

time, requiring only a comparatively small amount of

experiments.

In an exemplary calculation for Hexoloy

four-point-bending tests and 20 tensile tests were used.

For three of the tensile specimen tested under compres-

sion the aforementioned assumption (no crack growth,

was applied. The complete data sets are

documented in

[6].

Fig.

shows the stabilised ranking at the end of the

described fitting process under the assumption of pure

volume defects. The fitted parameters become

214,s

1,2 MPa, m

6,s

0,4,

92 689

39 509

MPa2h and n

12,4

13.

In the case of surface de-

fects (Fig.

6) the results are

258,s

0,6 MPa, m

6,7

0,2,

576

666 MPa2h and

13,7

0,4.

Limits

the

Model

In these calculations it is assumed that the fracture

mechanism for all the tested specimens is the same, i.e.

brittle fracture starting from flaws after preceding slow

crack growth dependent on the testing conditions. The

assumption would be disproved, if the initial strengths

of the high temperature and the room temperature tests

arrange in discrete groups. This assumption is sup-

ported, if the initial strengths of the different types of

testing are mixed up. That the initial strengths of the

tensile tests are divided up into two groups was to

expect and is no argument against the evaluation pro-

cedure: the specimens fracturing during the dwell time

have necessarily lower initial strengths than the speci-

mens reaching the given dwell time.

These both cases are the limits within which the

actual flaw population must lie. The lower divergence

from the Weibull-straight in the case of surface defects

is in good accordance with the fractographic investiga-

tions, which revealed that a big portion of the fracture

origins lies near the surface, often with a noticeable

oxidation on the crack surface.

Although this evaluation method leads to a mixing

up of the different types of testing one must be aware

of the postulations. The following restrictions have to

be taken into account:

323

REFERENCES

Besides the surface defects fractures in the vol-

ume occur.

The parameters of the crack growth A and n

may strongly depend on the environmental

conditions. However in the present investiga-

tions no identifiable influence of moisture was

found.

A and n are surely dependent on temperature.

But the difference in temperature of

“C in

the high temperature tests doesn’t influence the

results in such a way that groups in the initial

strength values

are

formed.

If the value of the fracture toughness varies

with temperature, a correction in eq.

has to be

made: with knowledge of the temperature-

dependent behaviour of KIc results:

Klc,RT denotes the fracture toughness at room tem-

perature, on which the initial strength

refers, KI~,BT

the fracture toughness at that temperature, at which

fracture of the specimen occurred. Parameter B (eq.

10)

then contains Klc,~~. For the tested sintered a-SSiC no

correction is necessary: Investigations on comparable

material show only very little shifting of KIc up to

600

“C

[7,8].

ACKNOWLEDGEMENTS

Parts of this work were funded by the “Deutsche

Forschungsgemeinschaft” (DFG) in the framework of

the “Graduiertenkolleg Technische Keramik”, Karlsru-

he.

Westerheide, T. Hollstein, K. A. Schwetz, Ten-

sion-Compression Testing of HIP-Treated Sintered

Sic for Gas Turbine Applications at Temperatures

Between

1400

“C and

600

“C.

Proc.

6”

Int.

Symp. Ceramic Materials and Components for

Engines, Arita, Japan

(1997) 253

258.

Carborundum Corporation, Sic Ceramic Materials

for Design of High-Performance Applications,

product information on Hexoloy, Form

A-12,047

(

1997)

Cercom Inc., product information on Cercom PAD

Sic, Internet:

http://www

.cercom.thomasregister.com,

K. G. Nickel, P. Quirmbach, Gaskorrosion nicht-

oxidkeramischer Werkstoffe, Technische Kerami-

sche Werkstoffe, Ed. J. Kriegesmann, Kijln: Deut-

scher Wirtschaftsdienst, Chapter

5.4.1.1.,

(1991)

D. J. Baxter, Oxidation Round Robin (Monolithic

Technical Ceramics), Final Report European

Commission, EUR

19039

(2000)

E. Nestle, Charakterisierung des Schadigungsver-

haltens von Siliciumcarbiden fur den Einsatz in

Gasturbinen unter komplexen Beanspruchungsbe-

dingungen, doctoral thesis at the University of

Technology Karlsruhe, Germany

(2000)

Himsolt, T. Fett, K. Keller, D. Munz, Fracture

Toughness Measurements on Silicon Carbide,

Materialwissenschaft und Werkstofftechnik,

Campbell, B. J. Dalgleish, A. G. Evans,

Brittle-to-Ductile Transition in Silicon Carbide,

Journal oft the American Ceramic Society,

[8]

1402-408 (1989)

2OOO-06- 15

148-153 (1989)

324

MECHANICAL FAILURE OF

ELECTROCERAMIC COMPONENTS

P. Supancic, M. Lengauer,

Danzer

Materials Center Leoben

and Institut fur Struktur- und Funktionskeramik

Montanuniversitat Leoben, Peter-Tunner-Str.

A-8700 Leoben, Austria

ABSTRACT

Electroceramic current driven devices, such

varistors and power switching PTC- and NTC-com-

ponents, are primarily loaded electrically.

conse-

quence of the intrinsic Joule selfheating process, heat

expansion of the material occurs. The corresponding

thermomechanical stresses can be

high that mechani-

cal failure occurs. The stress amplitudes are governed by

a large number of geometrical, electrical and thermo-

elastic properties. Two examples of electroceramic com-

ponents are discussed in detail: a power varistor (where

temperature changes arise

fast that inertial effects

play a dominant role for the mechanical loading) and a

high-power PTC-switching device (where a highly non-

linear electrical resistance characteristic causes strong

thermal gradients).

INTRODUCTION

Although electroceramic devices are primarily elec-

trically loaded, high power devices can suffer mechani-

cal failure [l-31. To a large extent, this is

consequence

of Joule heating, which causes temperature differences

and locally different thermal strains and stresses in the

components. Due to the general demand of industry for

increasing power densities, the mechanical loads of

these components increase and problems with insuffi-

cient mechanical strength get more and more severe.

Therefore, and despite the large costs, proof testing of

highly loaded electroceramic components is

commonly

used practice [22]. In the light of these facts it is sur-

prising that relatively little literature exists about the

mechanical failure of electroceramics.

In principle the necessary procedure for a proper

mechanical design of electroceramic components is

quite similar to that for structural ceramic components:

In a first step, the loading analysis, the temperature and

mechanical stress fields in the component has to be

determined. Input parameters are the external loading

conditions of the component, its geometry and some

material properties. In a second step, the reliability

analysis

life time prediction, the loading of the com-

ponent

compared with the relevant strength

the

material.

Loading analysis

In structural ceramic components the external me-

chanical loading

in general determined by the action

of external forces

by the action of temperature differ-

ences

changes [4-61. The determination of the result-

ing strains and stresses is a standard problem. Numerical

solutions can be obtained by using commercial Finite

Element codes (e.g.: Abaqus, Ansys, Nastran, etc.).

In electroceramics additional strains and stresses

may occur due to a coupling of electrical with thermal

andor

mechanical properties. This fact is well

known

for piezoelectric ceramics, were an applied electrical

field induces mechanical strains

[7].

Other examples are

thermistors (temperature dependent resistors), where the

electrical current causes a Joule selfheating process,

which may cause thermomechanical stresses [8]. In

thermistors the resistivity (and therefore also the

strength of the heat source) strongly depends on the

temperature. In these materials thermal gradients (which

occur in any component) cause a strongly inhomogene-

ous distribution of heat sources which again influence

the temperature and the electric field. This highly non-

linear problem of mutual interactions has to be solved in

order to determine the temperature field and the ther-

momechanical stress and strain field.

Over a long time scale, the load spectrum might

change due to degrading electrical properties

[9,10].

These not fully understood kind of aging processes lead

to a change of the heat source distribution and conse-

quently also influence the thermo-mechanical loads.

These additional changes in strains and stresses

must also be accounted for, but up to now, only rela-

tively little theoretical work on these problems were

performed. In the present work a short summary on state

of the art of the mechanical loading and failure of high

power varistors and PTC-devices will be given.

Reliability analysis

In ceramics failure generally originates at flaws,

which are sparsely distributed inhomogeneities in the

material and which can, in general, be described like

cracks

1, 121. Fracture starts if

at the location of the

"crack"

the stress intensity factor exceeds the fracture

toughness (this criterion is called the Griffith criterion).

The failure stress (the strength) depends on the size and

orientation

the flaws and on the fracture toughness

the material [13]. For

given material the strength is

high if the most critical flaw is short and vice Vera. In

general the size of flaws is not exactly

known

and differs

from component to component. Therefore the strength

325

of ceramic materials scatters and has to be described by

statistical methods [14, 15, 111.

widely used strength

distribution function is the well-known so-called

Weibull function [16, 171. On the basis of these ideas a

probability of failure can be determined for any given

stress field (the result of the loading analysis).

Mechanical design in the field of structural ceramics

is based on the ideas described above. The developed

methodology should be applicable to electroceramics

the failure (the fracture toughness, the strength) is not

influenced by an applied electric field (the development

of mechanical stresses can be influenced). Up to now

such an influence has not been reported for ceramic

resistors but recently such an influence has been ob-

served on piezoelectric materials

[

18-21]. Therefore the

loading analysis can be applied for resistors but has to

be modified for piezoelectric ceramics.

In many ceramics cracks slowly grow under the in-

fluence of a subcritical load [14, 221. This results in a

decrease of strength with time under load. If the strength

approaches the loading stresses an increasing fraction of

the components will fail. The life time is exhausted

this fraction reaches a predetermined limit. Although

these ideas are well

known

for structural ceramics

application of a life time prediction on electroceramics

has as yet not been reported in the literature.

absorbs energy and heats up rapidly. After establishing

the normal voltage, also the varistor returns to the highly

resistive state. The reason for their unusual electrical

behaviour can be located at the grain boundaries: they

act

electrostatic potential barriers.

certain limit of

electrical field strength has to be exceeded

that elec-

trons can overcome these barriers.

excellent review

on many different aspects of varistor ceramics can be

found in [23,24].

The ceramic bodies of power varistor devices are

typically shaped as cylinders. Both flat surface areas of

the disc

are

coated with a metallic electrode layer

provide a conducting surface to the circuit. The width of

an uncovered gap at the rim of the disc is in the range

about

mm.

The peripheral surface

covered with an

insulating glassy coating to protect the ceramic against

chemical attacks and to avoid flash-overs.

FAILURE

VARISTOR

COM-

Fig. 2a: Puncture failure of

power varistor (indicated by

arrow). Diameter of the disc:

mm.

PONENTS

Varistor ceramics, based on doped ZnO, show

highly non-linear electrical fieldresistivity characteris-

tics (voltage dependent resistor).

typical relation is

plotted in Fig. 1 on a double logarithmic scale.

Fig. 2b: Separation

two parts, the fracture origins are

located

the peripheral surface (indicated by arrows).

Diameter

the disc:

mm.

Current

density

[A/cm2]

Fig.

Typical electric field/current characteristic curve

high

power

varistor.

Varistor components are nearly electrical insulators

at low electric fields and good conductors above a

threshold field strength (i.e. a certain switching voltage).

Typically varistors are used in parallel with circuits to

protect them from voltage surges. In normal use, volt-

ages below the switching voltage are applied to the

varistors and they act as insulators. When the voltage

exceeds the threshold (for instance during a voltage

transient), the varistor becomes highly conducting and

draws the current through it. By this process, the varistor

Fig. 2c: Separation

two

parts, the fracture origin is located

near the centre

the disc (indicated

arrow).

Diameter of the disc:

mm.

Three modes of failure have been observed, see Fig. 2a-

2c.

The first mode, the puncture failure, is commonly

associated with thermal run away, the two other modes

are consequences of thermal strains, which occur due to

selfheating in service.

326

Puncture failure

The varistor component is designed to absorb the

Joule heat homogeneously during a voltage surge. In

some cases (predominantly at longer voltage pulses)

some current paths draw relatively higher currents and

result in melting of the ceramic.

typical fusion channel

of molten varistor ceramic is shown in Fig. 2a, which

connects both electrodes. This phenomenon of current

concentration is accounted for by inhomogeneities in the

microstructure, essentially by large grains

[23].

Since

the material is destroyed after

breakdown of this kind,

the failure causing defects cannot be found afterwards.

The dimensions of high power varistors are in the range

of several cm and there is no simple, non-destructive

way of detecting potential microstructural inhomogenei-

ties. For an experimental investigation, special thin

plates of about

0.5

thickness, were prepared. By

measuring the resistance of the plates at low field

strength and successive splitting of the plates, the low

resistive parts could be isolated. Finally the large grains,

causing the resistance deficiency, were detected by se-

rial sectioning. In Fig.

two large grains bridging the

whole thickness of the sample could be made visible by

etching techniques. It is a reasonable assumption, that

large grains also exist in real high power components

and

cause current localisation at high voltages.

Fig.

Two

large grains in the varistor

microstructure,

indi-

cated

white

arrows

(approx.

length:

300

400

pm).

Brittle failure from the surface

mentioned earlier, there is a thin glassy coating

(width:

100

pm) at the peripheral surface of the

disc. Since this layer

electrically insulating, the glass

is not actively heated by a current pulse. The time span

of these pulses

are

typically in the range of one

few

tens of

ps.

Since there is no significant heat conduction

from the heated ceramic body to the glass layer within

this short time interval, strong thermal mismatches are

induced between the glass and the ceramic.

second

geometrical feature of the varistor component can in-

crease this thermoelastic mismatch: the uncovered gap

between the circular electrode layer and the rim of the

disc leads

a reduced current intake at the ceramic-

regions near to the whole peripheral surface.

con-

sequence less electrical energy

absorbed in these

regions. The worst case concerning thermal stresses is

found immediately after a current surge: The glass layer

has still nearly the ambient temperature, the varistor

ceramics next to the glassy surface is less heated com-

pared to the massive bulk of the varistor component.

The cold glass and the cooler ceramic material at the

peripheral surface are put into tension by the expanding

core material of the varistor. For a typical mean tem-

perature increase of 120

the corresponding thermal

stress maxima are found in the range of the materials

strength of about

100

MPa in the varistor ceramics and

about

MPa in the glass layer. After reducing the

temperature differences by heat conduction the ampli-

tude of tensile stresses decrease. In Fig. 2b the fracture

surface of a varistor is shown, which is split into two

parts. The fracture origins are found in the highest

loaded area, namely close to the outer surface of the

cylinder.

Brittle failure from inside

The loading

case

described above leads to a tensile

stress free field in the whole core of the varistor. From

this point of view there

no reason for starting failure

from the inner regions. But in experiments, especially in

short pulse tests of duration spans of some

ps,

also these

cases

are

found.

example is shown in Fig. 2c, where

the cracking starts obviously in the centre of the cylin-

der.

pore was found to be the fracture origin on the

one hand, and there was no evidence for any kind of

puncture failure on the other hand. The mechanism

this fracture mode can be understood as the result of

inertia forces in response to the rapid Joule heating. The

conceptual basis for this effect can be found in [2],

where a one-dimensional model is presented. By as-

suming a homogeneous heating process during a power

pulse in the order of

lops,

compressive stresses are

built up in the centre, since the top planes cannot follow

the heat expansion that fast. This inertia effect can be

made evident by evaluating the time span, which is used

by an elastic wave to move from one top plane to the

other: since the velocity of sound

of varistor material

4300m/s,

a components height

h,,

propagated within a time interval of

z,,=

ps.

After

this initialisation phase the compressive stress state

changes to tensile stresses. Elastic waves are running

-20

-40

-60

60 80

100

Time

[ps]

Fig.

Stress oscillation in the centre

the disc, calculated

an one-dimensional

[2]

(dotted line) and three-dimensional

model

[25]

(solid line).

327

through the whole varistor and lead to oscillations. The

largest stress amplitudes are found in the centre of the

cylinder. This stress oscillation for a typical test pulse,

which leads to a temperature increase of 120"C, is

shown in Fig.

the dashed line. The solid line in

Fig.

corresponds to the results of a three-dimensional

model for the same heating process, published recently

[25].

this

case the reflections of the initial compres-

sive wave at different surfaces of the cylinder lead to a

complicated interference pattern in the centre. The ten-

sile stress maximum at about

MPa was found to be

higher in this case compared to the one-dimensional

model due to lateral contraction effects, which are trig-

gered by Poisson's ratio. Analysing the relation between

pulse duration and tensile stress maximum, by using the

simpler one-dimensional approach, leads to the follow-

ing essential results: for test pulses shorter than the time

interval needed for an elastic wave to propagate through

the length in the order of the mean varistor dimension

(in most cases: height

h,,),

the stress is proportional to

the product of the heat expansion coefficient

(i.e.:

7.10-6

OC-'), the Young's modulus

(i.e.: 100 GPa) and

the temperature change

during the pulse. For longer

pulses the influence of inertia forces decreases dramati-

cally. In Fig.

the stress amplitude

(nonnalised to the

maximum value

@Y.AT)

vs. the pulse duration is plotted

for a typical varistor height of

mm. This relation

explains the experimentally observed fact that short

pulses in the order of

z,,

and shorter can lead to

failure initiated in the centre of the cylinder. For longer

pulses in the order of multiples of

z,,

this mechanism

becomes unimportant concerning failure. Until now

inertia forces are the only explanation for a central ini-

tiation of fracture of varistor components.

100

Pulse duration

[ps]

Fig.

Calculated relation between

the

maximum normalised

tensile stress

and

the pulse duration (one-dim. model).

FAILURE

OF PTC-DEVICES

Positive temperature coefficient (PTC) resistors are

characterised by an increase in the electrical resistance

with temperature. Apart from special polymer compos-

ites, commercial PTC-components are based on a

doped, barium titanate ceramic.

ferroelectric-para-

electric phase transition at a critical temperature (the

Curie-temperature) in combination with screening ef-

fects of potential barriers at grain boundaries causes the

exceptionally strong PTC-effect

encompassing a

resistance increase of several orders of magnitude within

a temperature interval of a few tens of degrees.

typical

curve of the resistance/temperature characteristics is

shown in Fig.

The actual PTC-range spans a tem-

perature interval from

230

"C, but the strong onset

Temperature

["C]

Fig.

Resistance/temperature characteristics (normalised

p-)

at various electrical field strength.

of the resistance rise is found at about 120 "C, which is

called the reference temperature. While the solid line

corresponds to the resistance behaviour at nominally

zero electrical load, the dashed line represents the resis-

tance under an electrical field strength of 1 kV/cm. Gen-

erally the resistance drops by increasing the electrical

field. This additional resistance lowering effect is called

the varistor-effect of PTCs. Power PTC-resistors are

used as self-regulating switching devices for degaussing,

heating and overload-protection applications. However,

mechanical failure can occur during high-power

switching processes, which limits the magnitude of the

applied electrical voltage. One main mode of failure,

concerning the ceramic, is delamination fracture, which

splits the whole component (which is usually formed

a cylindrical disc) into two parts.

typical example of a

delaminated component is shown in Fig.

328

stat.

t=2

Fig. 7: Delaminated PTC-component (split into two parts).

In the following, the results of

theoretical analysis

will be presented

[3],

which explain the electrically

induced thermal stresses during the

PTC

switching pro-

cess, that can lead to the catastrophical delamination

failure.

mathematical model was developed, including

all relevant electrical, thermal and mechanical aspects of

the PTC. To demonstrate the main mechanisms, a sim-

ple trial PTC-component was chosen, which has a cylin-

drical geometry of

diameter and a height of

2.5

mm.

A copper wire is attached to the electrodes by

solder. The switching behaviour of

the

PTC-component

in a circuit, consisting of a serial connection of the

PTC

and a fixed shunt-resistor, was measured

monitoring

current and the voltage drop at the PTC. Taking all

experimental boundary conditions into account, the

mathematical model reproduces well the observed cur-

rent and resistance behaviour in time. The comparison

between experiment and theory is shown in Fig.

After

certain time span an initially strong electrical current is

dramatically reduced, since the PTC has switched to the

high resistive state due to selfheating. But the tempera-

ture rise within the PTC-component is not homogene-

ous.

Although the heat production rate is nearly constant

in the disc at the beginning of the switching process,

heat conducting leads to a solder-induced cooling

the

disc at both top planes. The central regions of the PTC-

disc reach the reference temperature faster,

that the

resistance increase starts locally in this range.

higher

resistance leads to a concentration of the heat generation

and consequently a strong temperature increase in the

centre of the PTC-disc. This positive feedback causes in

this case a transient temperature difference of more than

100

"C. The build-up of the axially varying temperature

0,30

0,25

0,zo

10'

0.15

0,lO

105

0,051

Time

[s]

Fig.

Current and resistance vs. time in a F'TC switching

process in air at

"C, the shunt

was

fixed to

kR.

Applied

total voltage:

300

DC.

all

.,,/;,

___.-.-._.

-,-,.

.,j

t=0.25

t=o

-1,0

-0,5

0.0

0,5

1,0

Axial position

[mm]

Fig.

Transient

axial

temperature profiles at several points

in time.

field is shown in Fig.

Finally the electric power is

reduced

much, that it is balanced by the heat loss

through the surface and a stationary temperature distri-

bution is achieved. Since the mechanical stresses have to

be known for the loading analysis, the corresponding

thermal stress field was calculated for that point in time

when the largest temperature differences occur. In Fig.

0,lO

k0.75

compression

/!!SqEs+q

.=loo

-0,lO

-0,15 -0.10 -0,05

0.00

0,05

0,lO

0,15

Diameter

[cm]

Fig.

10:

Isostress lines

the

1''

principal stresses

cross-sectional area

the PTC.

isostress lines on a cross-sectional area of the first

principal stress field are shown. While the centre of the

ceramic disc is under a compressive stress, the outer

regions are in tension. In the considered case a signifi-

cant stress maximum of about

100

MPa occurs near the

peripheral surface in the plane

symmetry between the

electrode layers. This significant stress concentration is

caused by the constraining effect

the relatively cold

disc-faces, which clamp the thermal expansion of the

warmer central planar regions. The amplitude of tensile

stress is in the range of the material's strength and it

should be expected that delamination fracture

origi-

nated by flaws in this ring-shaped region. By investi-

gating fracture surfaces using scanning electron micros-

329

copy, it was possible to iden@ these fracture causing

defects. In Fig. 11 a typical fracture origin is shown

(pore with a diameter of about 80 pm).

Fig.

pore as fracture

origin.

CONCLUSIONS

Mechanical failure of electroceramics due to elec-

trical loading is of great economic significance and

has to be avoided by a proper mechanical andlor

microstructural design

proof testing.

In general mechanical loading of active electro-

ceramics results from thermal strains, which are

caused by Joule heating. In most cases the loading

is “quasi-static”, but sometimes it is highly tran-

sient

that inertia forces have to be considered.

There is a similarity to the situation under thermal

shock

thermal cycling. The concepts used to

optimise geometric and microstructural design in

thermal shock-situations can be transferred to de-

signing electroceramic components.

In all investigated cases failure was caused by

“large” flaws. Reducing their size will directly lead

to a higher performance.

In order to improve the components reliability,

there is a demand for tools to analyse mechanical

stresses in electrical loaded components. Details of

understanding of the interaction between electrical

load, heat production and transport and thermo-

mechanical properties have to be taken into ac-

count.

ACKNOWLEDGEMENTS

The authors thank EPCOS AGDeutschlandsberg

(Austria) for supplying samples, and acknowledge the

collaboration of

Hahn (SIEMENShlunich), J. Riedler

and

Schoner (EPCOS) for providing some of the

requested material data and the helpful discussions on

related topics. This work was supported by the Austrian

Kplus-program.

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