The strength of ceramics bonded with metals

Acta metall. Vol. 36, No. 8, pp. 2029-2035, 1988

0001-6160/88 $3.00+0.00 Copyright © 1988 PergamonPress pie

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THE STRENGTH OF CERAMICS BONDED WITH METALS B. J. DALGLEISH, M. C. LU and A. G. EVANS Materials Department, College of Engineering, University of California, Santa Barbara, CA 93106, U.S.A. (Received 11 January 1988)

Abstract--The strength of AI203 materials bonded using thin Pt layers is investigated. The measured strength levels are interpreted by conducting elastic/plastic stress analysis in conjunction with weakest link statistics. Comparisons between theory and experiment includes bond thickness effects, coupled with the role of interracial flaws and the flow stress of the Pt. Rfsumf---Nous 6tudions la rfsistance mfcanique de matfriaux A1203 lifs d l'aide de couches minces de platine. Nous interprftons les valeurs expfrimentales de la rfsistance mfcanique grace ~i une analyse des contraintes 61astiques et plastiques menfe conjointeraent avec une statistique des liaisons les plus faibles. La comparaison entre la thforie et l'experience tient compte des effets d'fpaisseur de liant ainsi que du rfle des dffauts ~ 1'interface et de la contrainte d'fcoulement du platine.

Zusammenfassung--DieFestigkeit von Materialien aus A1203, verbunden mit dfinnen Pt-Schichten, wird untersucht. Die gemessenen Festigkeitswerte werden mit einer Analyse der elastisch/plastischen Spannungen in Zusammenhang mit Statistiken der schwachsten Verbindung gedeutet. Vergieich zwischen Theorie und Experiment nmfaBt Einflfisse tier Dicke der Verbindungen, einschliel31ich der Relic yon unverbundenen Bereichen an der Grenzfl~che und tier Flie~pannung des Platins.

I. INTRODUCTION The bonding of ceramics to other ceramics and to metals in order to produce bonds having a strength that exceeds the strength of the ceramic can be accomplished by using a soft metal [1-3]. The strength of the bonded system is governed by a number of variables: the thermal and elastic mismatch, the plastic flow stress of the metal, the relative metal layer thickness, the fracture resistance of the interface and the flaw distributions in the ceramic and at the interface. Some of these variables are analyzed in the present study. Specifically, a material system has been selected, AI2OflPt, for which the thermal expansion mismatch is small, such that residual stress effects are minimized [1] and strength is dictated by considerations of load induced stress distributions [4], flaw populations and the interracial fracture resistance. The stress distributions at and near the interface in the presence of such soft metals must be appreciably influenced by the plasticity in the metal. Generalized trends in stress can be elucidated using a combination of methods. Elastic solutions provide estimates of the

tWork hardening causes the stress to continuously increase [6] somewhat above d.

small scale yielding extreme, slip line solutions are applicable to the fully plastic extreme (without appreciable hardening) and finite element results establish the intervening characteristics. Each of these approaches is utilized in the present investigation. Fracture tests conducted on AI203/Pt/AI203 specimens, followed by examination of the prevalent fracture flaws, provides information about the interfacial flaw population, as well as bond strengths. The results are interpreted using the stress analysis in conjunction with a fracture criterion and a weakest link statistical analysis. The correlation between theory and experiment allows trends in bond strength to be predicted as a function of the predominant material variables. 2. STRESS ANALYSIS The stress/displacement characteristics of a bond consisting of a thin metal layer between two ceramics has the characteristics depicted in Fig. 1. In the absence of fracture, a limiting stress # is reached for a non-hardening metalf that depends on the yield strength and the relative metal layer thickness. This stress can substantially exceed the yield strength of the metal, and can be predicted by using slip line solutions [5]. At small stresses (~ < Y), where Yis the uniaxial yield strength, small scale yielding obtains

2029

DALGLEISH et al.: THE STRENGTH OF CERAMICS BONDED WITH METALS

2030

CERAMIC 1

i'~io

W ~c l-

Y

. ~---J

/

/ V~

(b)

Previous elastic solutions [4] pertinent to small scale yielding have indicated the existence of stress concentrations near edges, governed largely by the mismatch in elastic properties (Fig. 3), as expressible by the bielastic parameters [7],

/TL------J Plastic

~,~ ,Limit

f

Stress,6

tr~.~

11

Fig. 2. The slip line solution for a fully plastic metal layer bonded to ceramic plates.

i~Ceramic [ ~ . _ L et~I ~ ~ - ~ ' F ully

,gst ~

,-..~y 2d

CERAMIC STRAIN

2

CERAMIC

°zz,

METAL-

METAL

(a)

if)

n

X(kc+ l ) - (kin + l) T~(kc+ 1) + (kin+ l)

Ceramic

~ PlasticZone ~--Metal Smallscaleyielding

'

Strain

Fig. I. Stress-strain curves for bonded systems. (a) The separate behaviors of the metal and ceramic. (b) The behavior of the bonded system indicating the various regions of plastic flow.

fl

~ ( k c - 1 ) - (kin- l) =

(2)

£(kc - 1) + (k,,, - I)

where k = 3-4v for plane strain, v is Poisson's ratio and Z = #c/#=, with # being the shear modulus and the subscripts m and c referring to the metal and ceramic, respectively. The amplitude and scale of the elastic stresses at the interface may be expressed by the approximate relation,

a=/tr~ ~ A(ot, fl, d/h)(h/Y) ~ O'
# / Y = 3/4 + (1~4)(h/d)

tr=/croo~ B(a, fl, h/d).

(y > y * )

(3)

1.6 ~/

AI203/Nb '

(1)

where 2d is the layer thickness and 2h the bond dimension (Fig. 1). It is immediately apparent, therefore, that very soft metals can be used to create strong bonds provided that the layer thickness is small. Indeed, it is shown that the bond strength is rarely limited by the yield strength of the metal, at least when the bond is subject to axial loads.t tShear loads on the bond cause yield limited behavior at stresses of the order of the yield strength.

1.o F L 0

I ,,

I 0.1

1

I 0.2

Distancefrom Edge, y/h

I 0.3

Fig. 3. Trends in elastic edge stress concentrations for different material couples.

DALGLEISH et al.:

THE STRENGTH OF CERAMICS BONDED WITH METALS

Table I. Summary of elastic field p a r a m e t e r s

~

Materials AI,O~/Nb AI20~/Au

/~c//x,~ 4.3 5.9

vc,'v,n 0.64 0.57

:c 0.68 0.78

B 0.24 0.29

AI,O3/Cu

3.3

0.73

0.58

0.23

d/h

A

2

.v*/h

,o

00 0.04

06,

0 0.16

0.34 0.08 0.38 0.16 0.1 0.38 0.19 0.2 0.38 0.20 0.40.480.200.13 0.8 0.60 0.21

Stress coefficients (~ = 0.55. fl =0.15)

J

~

-

~

INTERFACE

02,

/7" ///y

002 0.06 0.08 0. I0 0.12

-

2031

?,

0.87/" , / /~

. I'/

~r /Y 1.04 ~ . , . . ~ , , , , , , ~

t

0.20

f EDGE --~

Some characteristic values of the parameters A, 2 and

y*/h are summarized in Table 1 for a material couple characteristic of many ceramic/metal systems: viz. IXc/IXm~ 4, VclVm = 2/3. For such materials, A ~ 0.1 ln(h/d) and 2 ~ 0.2. At the simplest level, the stresses in small scale yielding may be estimated by truncating a= at, (Y/2)(I + n/2) (Fig. 4). More appropriately, however, the equivalent stress may be calculated

2a~=(ai-tr2)2 +(a:-a3)2 +(trs-trl) ~"

(4)

and the plastic zone shapes estimated by equating tr~ to the shear yield strength, Y/2. Some typical plastic zone shapes and sizes evaluated for a material couple characteristic of AI203/Pt are depicted in Fig. 5. Such elastic calculations are relatively straightforward and thus have merit for examining the small scale yielding regime. It is also useful to note that the extent of the plastic zone along the interface. ).p, can be deduced

ELASTIC~PLASTIC

' ELASTIC

Fig. 5. Plastic zone profiles in small scale yielding predicted from the elastic equivalent stresses and by elastic/plastic analysis.

from equation (3) by equating a= to (Y/2)(1 + n/2) giving;

yp/h = [2A/(1 + n/2)l~';(a~/Y)~;

(5)

Finite element solutions have been derived for a bielastic constant representative of the AI,O 3/Pt system. The stress/strain curves, plastic zones and stress distributions are summarized in Figs 6-8. Comparison with the analytical solutions reveals that the limit stresses d agree closely with the slip line solutions (Fig. 6), validating the utility of equation (1), and that plastic zones and stresses in small scale

,O'~

Plastic Zone b

/I t

0.1

i

!

Limit Stres~ Slip Lines 3.3~

l

,, \ i % .

(1/2) (1 + ~/2) 0.2

cr~/Y 1.0

2.0~

0.4 0.8

1.4~ 1.1~

0.5 I 0.05 Distance from edge: y/h

Fig. 4. Schematic trends in interfacial stress for small scale yielding.

I 0.10 Engineering strain :

I 0.15

Fig. 6. Predicted stress-strain curves for a non-hardening metal calculated for various metal layer thicknesses. Also included is a comparison with the slip line solution for the limit stress, ~.

DALGLEISH et al.: THE STRENGTH OF CERAMICS BONDED WITH METALS

2032

~tr~

distributions (see Fig. 13) suggest the simple statistical form;

f ~ g (S) dS = (S/So)'~Ao ~

~rJY = 1.3 ~ J Y = 1.4

INTERFACE

where m is a shape parameter and So and A0 are scale parameters, such that

/CERAMIC

1 - • = exp

EDGE

ZONE~"

(9)

/ SMALLSCALE YIELDING

Fig. 7. Predicted evolution of the plastic zone for d/h = 0.2.

yielding agree quite well with values provided by the elastic solutions, when tr < Y (Fig. 5). Additional information provided by the finite element solutions include the shape evolution of the plastic zone (Fig. 7), as well as the relative uniformity of the interfacial stresses in the transition zone (Fig. 8).

{

-(4bh/Ao)

[;0

T}

a~(z)/So

dz

(10)

where Z = y/h and b is the specimen width. A full analysis of the statistics of interface failure is cumbersome. Notably, because the stress fields are not self-similar, equation (10) must be integrated numerically using the fracture stress as a variable integration limit. However, for cases wherein fracture occurs subject to small scale yielding (o~ /Y < 1.5), as obtained for the present Al,OflPt system (see Fig. 14), the analysis can be simplified and the results expressed in terms of insightful non-dimensional parameters. Specifically, the stress field is separable into three distinct segments: a==(Y/2)(l+n/2) for y y*. Consequently, the probability of failure for specimens subject to uniaxial tension can be ascertained readily from equation (10), and by using equation (5), as; - I n ( l - ¢~) = (4bh/Ao)(S/So)"

[(Y/S)"-~:~f(m, d/h, Y/S)] (11) 3, STATISTICS OF INTERFACE FAILURE Brittle fracture governed by a distribution of flaws is a statistical problem, wherein the fracture probability can be related to the flaw size distribution. The development of appropriate relationships is contingent upon a fracture criterion. For example, when a critical strain energy release rate G~ determines the onset of interface fracture, the normal stress at fracture, S, is related to the interfacial flaw radius, a, by [8];

where S is now the applied stress at the fracture criticality and f = [(1 + n/2)/2~'-t/aA i,~

3.0 --

S 2 = (4 cos h2nE)G~(I + 4E2)[(1 - v~)/#~ -t-(1 -- Vm)/#m]/Tta. (6)

x[2m -

(>.~ty*y" lf(2m -

2d ]

¢rJY / / 2.32 ;// 2"3/2/~Slip line

I'~T

2.5

At the very simplest level, G~ = ~ Wad

where W=d is the .work of adhesion and ~ is a coefficient governed by crack tip plasticity in the metal, microstructural interactions, etc. [9]. Flaw strength distributions, deduced using equations (6) and (7) are the basis for further statistical analysis. If it is further assumed that weakest link statistics obtain, the survival probability becomes [10]

E

1 -- ¢, -- exp --

dA

f"

j0

g(S)dS

]

•~

1.5

0.87

1.0

0.52

0.5

(8)

where .4 is the total interface area and g (S) dS is the number of flaws in unit area having strength between S and S + dS. Present measurements of flaw size

/

2.0 ~o .=

(7)

I)1.

0

I

I

I

0.25 0.50 0.75 Distance from edge: y/h

1.00

Fig. 8. Interracial normal stresses predicted for the case 0.2, with elastic properties appropriate to Al:O3/Pt.

d/h =

DALGLEISH et al.: THE STRENGTH OF CERAMICS BONDED WITH METALS = 2mA

lla(Y/S)~-lla [(1 +

rr12)12]'- lja.

2033 (14)

Furthermore, when ~ is large, the trend in strength S can be deduced by using the approximate expressions for A and 2 indicated in Section 2, viz., such that equation (13) gives s~ r ~ (so / r ) "a In (d/h ).

(15)

These predicted trends will be compared with experimental data in the following section. 4. EXPERIMENTAL MEASUREMENTS 4.1. Procedures

(a)

Specimens have been prepared by emplacing a thin Pt foil between two AI203 surfaces and exposing to normal compressive stress ( ~ 1MPa) at elevated temperatures (-,,0.9 Tin, where Tm is the melting temperature) in argon [1-3]. The metal foil thicknesses ranged between 25 and 250/~m. Flexure specimens have been cut from the bonded block and polished. Fracture experiments have subsequently been conducted in four point flexure, at room temperature. The resulting fracture surfaces have been examined in the scanning electron microscope. Hardness indentations e~placed in the metal after bonding have also been conducted, as needed to estimate the flow stress. 4.2. Measurements and observations

(b)

Fig. 9. Fracture characteristics. (a) Fracture in the ceramic. (b) Interface fracture.

The implications for fracture prediction are governed by the magnitudes of m and 2. Most bonded systems of practical interest have m > l/it, viz. a relatively narrow size distribution of interfacial flaws. Then fracture is largely dominated by the concentrated stress field near the edges and is thus sensitive to the metal layer thickness and the yield strength.t For the case, m > 1/2, y* >yp, and when a~ < 1.5Y the function f i n equation (11) reduces to: f ~ Area J/a[(l + n/2)/2] m- J/a.

(12)

Strength tests have indicated that all bonds exhibit essentially linear behavior prior to fracture. The highest strengths typically corresponded with failure initiating within the A1203 [Fig. 9(a)]. Otherwise, fracture occurred at the interface [Fig. 9(b)]. Inspection of the interface fracture surfaces revealed voids on the metal side (Fig. 10) and microstructural heterogeneties on the ceramic side (Fig. 11). The voids are presumed to derive from incomplete diffusion bonding, while the heterogeneities are formed by impurity diffusion within the ceramic. It is presumed that these defects are the fracture origins. Indeed, when low stress fractures occurred, large unbonded areas were invariably detected near the

The fracture trends are then governed by the expression (Ao/4bhZ)[-ln(1 - 0)1 = (S/So)" x [itmA ]/a((l + n12)12)m- Ua(y/s)m-IIX].

(13)

Clearly, at any specified probability level, the measured strength S decreases as Y increases and depends on bond thickness by virtue of trends in A and it (Table 1). Bond thickness effects are most effectively examined by inspecting the term in parentheses in equation (13) ?Conversely, when m is small, there is a high probability of fracture away from the surface and the fracture trends are insensitive to Y and to d/h. A.M. 36/8-.-K

Fig. 10. Residual voids on the metal side of the interfacial fracture surface.

2034

DALGLEISH et al.:

THE STRENGTH OF CERAMICS BONDED WITH METALS

10m=6 i

to r~

~5 s

I

I

0 Fig, 13.

A

I-'l

0.3 0.5 0.7 O.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 VOID SIZE (#m)

typical void size distribution measured on a fracture surface,

At. \

"

~

_._'-'~~--'~'~

Fig. 11. A microstructural heterogenerity on the ceramic side of the interface, formed during diffusion bonding.

tensile surface on the metal side of the fracture surface (Fig. 12). The statistics of interface fractures are related to the size distribution of the interracial defects (Section 3). Consequently, various size distribution measurements have been made, as exemplified b y the void size distributions presented in Fig. 13. ..The strength results are plotted by grouping into thr~e categories: those that fail in the ceramic; those thaVfail from the interface from large unbonded regions (Fig. 12) and, finally, interface failures that occur from a defect distribution (Figs l0 and I l). The mean and standard deviations obtained using censored statistics are plotted in Fig. 14. It is apparent that interfacial failure is sensitive to the metal layer thickness, whereas failure in the ceramic is essentially thickness independent. Indentation of the Pt bonds after diffusion bonding gave hardness levels of ,,,450 MPa. The corresponding uniaxial flow stress is Y ~ 150 MPa. The presence of voids at the interface has been used to provide an estimate of the work of adhesion: W=d = ),,~(i + cos 0)

(16)

1.8

. ~,I'ENSILE EDG E~,~

'

.'

'

.'

_fFract'ureiriCer'arnic

1.6

.

1.4 I 1.2

/

1.0

0.8 0.6 0.4 0.2

Beam Section o 3x3 mm • 5x5 mm I

I

0.02

Fig. 12. A large unbonded region on the metal side of fracture surface responsible for a low strength bond.

I

I

0.04 d/h

I

I

0.06

I

I

0.08

•

Fig. 14. Trends in the strength of the bonded system with bond thickness for AI203/Pt bonds. Also shown is the trend predicted from statistical analysis.

DALGLEISH et al.: THE STRENGTH OF CERAMICS BONDED WITH METALS where 0 is the dihedral angle measured from the interface voids (Fig. 10) and 7= is the surface energy of the metal. With the choice, 7m = 1.25 J m -2, the work of adhesion is estimated to be, Wad ~ 0.3 J m -2. 4.3. Comparison with theory

The statistical data concerning flaw populations and the appropriate choice of the energy release rate coefficient, (, are inadequately established to allow a first principles prediction of trends in strength, in accordance with the scheme outlined in Section 3. Nevertheless, by noting from Fig. 13 that m > 1/2, the measured trends with bond thickness can be compared with predictions based on equation (15), by using the experimental results at one bond thickness (d/h = 0.01) to establish the strength level. The resultant, predicted trend with bond thickness, plot ted in Fig. 14, conforms with the experimental results. The basic notion, therefore, that edge dominated fractures are obtained when m is large is seemingly substantiated (a thickness dependent strength drives specifically from the edge effect). The effect of plasticity in limiting the edge stresses is not directly validated by the data. However, it is noted that layer thickness effects are expected to be considerably larger than those given by equation (15) when edge plasticity does not occur. 5. CONCLUDING REMARKS

The measurements and analyses presented in this paper constitute a preliminary attempt at under-

2035

~tii~it~irength of,~ramics bonded with metals. However, the full extent of the problem embraces additional issues. In particular, most metals have different thermal expansion coefficients than their ceramic counterparts and thus, bonded systems are subject to residual stress. Such stress can influence the strength characteristics of the bonded systems. Also, interfacial fracture resistances between metals and ceramics have yet to be systematically characterized. Much additional research is thus needed to fully understand the strength of ceramic/metal systems. REFERENCES

1. F. P. Bailey and W. E. Borbidge, Surface and Interfaces In Ceramic and Ceramic-Metal Surfaces (edited by J. A. Pask and A. G. Evans), p. 525. Plenum, New York (1981). 2. F. P. Bailey and K. J. J, Black, J. Mater. Sci. 13, 1045 (1978). 3. F. P. Bailey and K. J. J. Black, J. Mater. Sci. 13, 1606 (1978). 4. A. G. Evans, M. C. Lu, S. Schmauder and M. Riihle, Acta metall. 34, 1643 (1986), 5. R. Hill, The Mathematical Theory of Plasticity. Oxford University Press, Oxford (1983). 6. E, A, Almond, D. K. Brown, G. J. Davies and A. M. Cottenden, Int. J. Mater. Sci. 25, 175 (1983). 7. J. Dundurs, Discussion of Papers by D. B. Body, J. appl Mech. 36, 65 (1969). 8. J. R. Rice and G. C. Sih, J. appl. Mech. 32, 418 (1965). 9. R. M. Cannon, V. Jayaram, B. J. Dalgleish and R. M. Fisher, Electronic Packaging Materials Science, Mat. Res. Soc. Syrup. Proc. 72, 121 (1986). 10. A Freudenthal, Fracture (edited by H. Liebowitz), Vol. II, Chap. 6. Academic Press, New York (1968).