Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK
(Received I0 August 1990; revised version received 20 September 1990; accepted 29 October 1990)
ABSTRACT
It is well known that mechanical character&tics of the fibre-matrix interface in MMCs have a strong influence on various properties. However, there is much uncertainty surrounding the question of how best to control the structure of the interfacial region in order to optimise particular types of composite performance. In this paper current thinking on how interfacial characteristics affect composite properties is briefly summarised. The importance of different types of stress relaxation processes is emphasised. This is followed by some observations about testing procedures designed to measure bond strength in MMCs. It is noted that these invariably involve predominantly shear loading, whereas there is a need to explore the response of interfaces to tensile and mixed mode conditions. Finally, some observations are presented on interfacial chemical reactions and the development of fibre coatings.
1 I N T R O D U C T I O N
When compared with material produced in the early 1980s, significant improvements in the mechanical properties exhibited by metal matrix composites (MMCs) have been obtained over the last few years. This has for the most part been achieved by processing route improvements, leading to a reduction in the level of gross defects such as matrix porosity and inhomogeneities in the spatial distribution of reinforcement. Further progress now requires a fundamental understanding of the interplay
between microstructural features and mechanical performance in these materials. Prominent among the features of critical importance are the factors controlling the mechanical characteristics of the interface, including the stress state resulting from externally applied loads and temperature changes. As a simple example, a high bond strength (often favoured by a localised chemical reaction) will tend to improve the stiffness and work- hardening rate but give a low toughness and ductility. In general, it is likely that a compromise will need to be struck between achieving efficient load transfer with a strong bond and promoting greater ductility via inelastic processes occurring at the interface.
In this paper a brief survey is first given of how interfacial characteristics can affect the performance of metal matrix composites. This is followed by an outline of certain tests designed to characterise the mechanical response of the interface. Finally, some examples are presented of means by which a degree of control can be exercised over interracial structure. Much of the treatment is oriented towards short-fibre composites. Particulate and long- fibre reinforcement may be considered as special limiting cases; in most instances the effect is a fairly obvious simplification.
2 THE ROLE OF THE INTERFACE IN MMC P E R F O R M A N C E
2.1 The meaning and significance of bond strength
A common problem in characterising interfacial behaviour in MMCs lies in incomplete identification of the various parameters which may be significant. Relevant system properties include a critical shear stress for shear debonding, z. , and a coefficient of sliding friction, #. The value of r . will dictate the onset of frictional sliding, which will then progress at a rate determined by the shear stress rfr, given by
gfr ~--- - - ~ 0 " r (1)
where a t is the radial stress (normal to the interface) at the point concerned, which must be negative (compressive) if rr~ is to have a non-zero value. (This is usually the case in MMCs as a result of differential thermal contraction.) Under applied load parallel to the fibre axis (x-direction) differential Poisson contraction effects often cause the value of a r to vary along the length of a (discontinuous) fibre:
or(x) = a~aT + O',av(X) (2)
where cry,, T is the radial stress from differential thermal contraction (see below). It is common to assume that the shear stresses at which both debonding and frictional sliding take place are independent of other
Inter facial mechanics in fibre-reinforced metals 27
components of the stress state. (This is somewhat analogous to the basis of the Tresca criterion for plastic flow.)
While the ease of debonding and frictional sliding are important for the behaviour of the composite, particularly in terms of energy absorption and fracture mechanics, there is also interest in the conditions under which decohesion may occur, causing interfacial cavitation and/or the opening of a crack along the interface. It might be expected that it would be possible to identify a minimum (tensile) value of the radial stress, at., or, more probably, the hydrostatic component of the stress state, all,, necessary for decohesion to take place. Among other interfacial processes essentially governed by the local stress field are mass transport by diffusion and local dislocation rearrangements. While these do not involve the breaking of a fibre-matrix bond, they may be sensitive to the structure of the interface. A further point to note is that the stress field will be determined not only by the partitioning of the applied load between the two phases but also by differential thermal contraction (and possibly by prior plastic deformation of the matrix). In Fig. 1 a schematic illustration is given of the nature of these stresses and of the interfacial processes triggered by them.
Drawing a distinction between interfacial decohesion and sliding in the way described above is equivalent in conventional fracture mechanics to identifying mode I and mode II loadings respectively acting on a crack front. (The equivalent of mode III loading, which would arise from a twisting of the fibre about its axis, would be very unusual in a fibre composite.) In practice, an interface will often be subjected to a stress state tending to cause both shearing and decohesion at the interface, i.e. a mixed mode loading situation. The propagation of a planar crack constrained to follow an interface between two dissimilar materials under mixed mode elastic loading conditions can be analysed to give an interfacial tYacture toughness. L- 3 This approach can in principle be extended to treat fibres in a metallic matrix, but there are various complications, particularly as matrix plastic flow is likely to occur. Evans 4 has identified the ratio of the critical strain energy release rate for the interface to that for the matrix, Gic/Gm¢, as determining the ease of debonding in ceramic matrix composites, with a small value favouring propagation of the interfacial crack. There is as yet, however, very little information available on Gic values in MMC systems and reliable measurement of this parameter presents certain difficulties with a non- planar interface.
Few direct correlations have been established between interfacial characteristics and composite performance indicators. However, poor bonding has been shown to result in a reduced elastic modulus 5 and work- hardening rate. 6 In the following sections the implications of interface structure for a number of key areas are discussed in general terms.
Fig. 1. A schematic view of the interracial stresses in a short-fibre M MC subjected to (a) a temperature decrease and (b) a superimposed axial tensile load. Also shown are schematic illustrations of some of the processes which might take place at the interface under the
influence of the stress field.
2.2 Stress relaxation processes
The stress-strain curve of a short-fibre or particulate M M C can be divided into several regimes, as depicted schematically in Fig. 2(a). The elastic portion is short or non-existent, because local plastic flow takes place very readily in regions of the matrix (near the interface) where there are already high residual deviatoric stresses as a result of differential thermal contraction. As this plastic flow becomes global throughout the matrix, linear stress-strain behaviour is expected. This regime should exhibit a high work-hardening rate (even if the matrix itself were to undergo no strain hardening) because a uniform plastic deformation of the matrix wilt raise the
Interracial mechanics in fibre-reinforced metals 29
Global _ . , UnrelaxedWo~ • . ~ Harlning
G Plastg'tYr'~"~'/ .,'~"~Failure
, , : Relaxation
,:" ~al I ~ El~iic
(a)
Applied Stress (MPa)
~ 1 U.Zi ...:.r ...TF~ _ ._.~. ~ I o o / [ M - ' ~ " ~ ~ S i C ~ (s=lO) I
o d.s~ 11o~ 115~ S/rain (b)
300- Applied Stress i [ as.received SiC ] (MPa)
200 - [ pre-oxidised SiC ] x
100 [ AI (A356-T6) - 10qo SiC ]
i i I
Su'ain 0 2% 4% 6%
tc)
Fig. 2. The influence of stress relaxation processes on the tensile stress-strain behaviour of short-fibre or particulate MMCs: (a) a schematic curve showing the processes controlling the shape; (b) three curves for a SiC whisker-rein forced Mg-Li alloy at different temperatures and strain rates; s and (c) two curves for SiC particulate-reinforced AI alloy, with and without the
prior formation of an oxide layer on the SiC. 9
misfit between the (stress-flee) shapes of the fibre and the corresponding hole in the matrix; this transfers load strongly to the fibre and hence raises the load-bearing capacity of the composite.
In practice, various stress relaxation phenomena tend to be stimulated by the resulting sharp gradients of stress within the matrix, these being processes which transfer load back from the fibre to the matrix. An example of how stress relaxation can affect the behaviour can be seen in the stress- strain curves of Fig. 2(b). These are for a matrix in which diffusive processes are fast at room temperature. 7.s Testing at high imposed strain rates or low temperature gives little scope for diffusive stress relaxation processes. The
30 77. ~|i Clvne, M. C, Watson
effect of this is to raise the work-hardening rates but to reduce the ductility. If the high fibre stresses caused by matrix plasticit.v are not relaxed in some way then cavitation or fibre fracture are likely, leading to t:ailure of the specimen. A similar type of effect is seen in Fig. 21c). In this case the provision ot'a thick oxide laver on the interti~ce appears to p romote stress relaxation, raising the ductility. This is probably 9 due in large part to decreased resistance to intertitcial sliding, which also has the effect of reducing the stress in the reinforcement. (It should, however, be noted that magnes ium in the alloy migrates to the oxidised inter[itce, reducing the age-hardening capacity of the matrix and probably contr ibut ing to the observed effect.}
The simplest picture of stress relaxation mechanisms as a group oF processes is obtained by considering the reduction the) effect in the misfit strain between the shapes of fibre and hole. This is illustrated in Fig. 3 t'or punching of prismatic dislocation loops'~'-" '~ inot to be confused with global
/
I- .4 !- -i
tat
1 a,'%
1 tbl
Fig. 3. Schematic depictions of t~o stress relaxation mechanisms. (a) Punching of secondary prismatic dislocation loops and (bi mass transfer by diffusion (vacancy transport). Both of these are shown relaxing the misfit strain l~r a short-fibre MMC resulting from a
temperature decrease.
lnterfacial mechanics in fibre-reinforced metals 31
plastic flow) and interfacial diffusion (vacancy transport) in response to the misfit from differential thermal contraction.
Quantitative studies of sliding phenomena have often been hampered by uncertainties about reinforcement shape effects. Figure 4 shows photoelastic fringe patterns, obtained by the 3-D 'frozen stress' technique ~2 around an ellipsoid and a cylinder of the same aspect ratio, stressed parallel to the axis. It is immediately apparent that high order fringes, corresponding to high shear stresses, appear at the 'corners' of the cylinder. Evidently local plastic flow and/or interracial sliding will tend to occur very readily in these regions.
%
(a)
(b) Fig. 4. Two photoelastic fringe patterns in the matrix around short ellipsoidal and cylindrical fibres under axial loading. Note the high shear stresses (high fringe orders) near the
'corners' of the cylinder.
32 77. ~i C/yne, M. C. ~ t s o n
2.3 Cavitation and failure
Under most loading configurations high tensile stresses build up at the fibre ends and these can cause interracial cavitation. Conditions for cavity nucleation and growth at a stiffinclusion are uncertain, with some attthors, 1:~ for example, predicting an increase in the critical plastic strain for cavitation with particle size and others t.* the reverse. Nevertheless, it is again evident that fibre ends are preferred locations, and FEM computations have been used to explore this. is
Much of the difficulty in laying down ground rules for tailoring interracial properties lies in establishing a criterion (related to interracial strength parameters) for the onset of interracial debonding/cavitation lwhich is thought to lead rapidly to composite failure by growth and link-up of cavities). One approach is to consider the hydrostatic component of the stress state, o H, expecting a critical {tensile) value for cavity formation. dependent on the bond strength (but with a maximum value corresponding to nucleation within the matrix). A variation ofo H with position predicted by the Eshelby model 16'~v is shown in Fig. 5ta). This confirms the sharp peak in the matrix at the fibre end. This may be reduced by the differential thermal contraction stresses expected at room temperature but, on the other hand, it will be greater when the fibre end is fiat rather than rounded. A cavity formed at the end of a fibre lying parallel to the applied stress axis can be seen in Fig. 5(b). It may be deduced from the above that a useful goal for composite production would be an interface prone to sliding but resistant to cavitation.
3 BOND STRENGTH M E A S U R E M E N T
Techniques for measurement of interfacial characteristics can be classified according to the phase angle of interracial loading generated during the test.* (Interracial critical strain energy release rates will vary with this phase angle.) Compact tension, flexural (4-point bend) and fibre pult-out push-out tests respectively have phase angles of about 0, re/4 and rr/2--corresponding to pure opening (I), mixed (I + II) and pure shearing (II) modes (see Section 2.1). Most measurements on MMCs have focused on shear debonding and sliding (often using simple variants of the shear lag theory to interpret the data), with little or no attempt to introduce substantial mode I components to the loading. It might be argued that an interface exhibiting a high shear debonding stress would also be expected to resist decohesion strongly. That this is not necessarily true can be seen from the fact that pronounced interracial roughness is expected to raise the former (in shearing mode) while having little effect on the latter (in opening mode), This type of argument
Inter facial mechanics in fibre-reinforced metals 33
"°"°I-. I t"7/ I "",.. iii
150~P~ (a.)
GH
(b)
Fig. 5. Cavitation is stimulated by high tensile hydrostatic stresses, particularly when these occur at the interface.and the bond strength is not high. (a) A map of the hydrostatic stress around an isolated ellipsoidal SiC particle in an Al matrix subjected to 100 MPa tensile load; this prediction was obtained using the Eshelby method, t6''~ (b) A TEM micrograph showing
a cavity formed at the end of a SiC whisker in an A1 matrix after tensile straining.
34 77. W Clyne, M. C. Watson
provides an immediate insight into the dependence of Gi~ on the phase angle of loading referred to above. It may also be noted in this context that there may be practical benefits in promoting interfacial sliding {to encourage energy absorption at the interface) while inhibiting decohesion and cavitation (which tend to promote failure of the component). Under these circumstances more sophisticated tests are required in order to monitor and control the interracial mechanical characteristics and this is an area of ongoing research.
3.1 Single fibre pull-out testing
This test, devised for long fibres, has been extensively applied to polymer composites. It comprises the extraction or" a single fibre, half embedded within a matrix, under simple tensile forces. Its main virtue is simplicity, with the load/displacement data normally interpreted from a minor adaptation of the shear lag theoryJ 8'19 A schematic illustration is given in Fig. 6 of the axial distributions of normal stress in the fibre and shear stress at the interface. These distributions are shown at three stages in the process, corresponding to elastic distortion up until debonding, propagation of the debonded portion and subsequent pure frictional sliding. Basic assumptions of the shear lag model, such as no shear strain in the fibre and no transfer of normal stress across the fibre end, are retained in most treatments of this problem.
Analysis is usually divided into two distinct parts; the first corresponds to the point of debonding and the second to the subsequent frictional sliding process. It is conventional to assume that the peak in the load/displacement plot corresponds to the debonding event, occurring at an applied stress %.. (This may not necessarily be the case: depending on the values of T,, l~ and ara T, the load could in principle rise during the propagation of debonding, shown as stage 2 in Fig. 6. However, Poisson contraction of the debonded fibre will reduce a r (see eqn (2)), and hence limit the contribution to the load from the debonded portion, so that this possibility is often ignored.)
For the relatively high values of the fibre aspect ratio, s (= L/2r), typical of this type of test the stresses are very low along most of the fibre length. Some variants of the basic model have been published. For example, Hsueh 2° incorporated the possibility of stress transfer across the fibre end and ensured that the load carried by the free fibre is balanced by that in the composite. This model leads to more complex equations, but the general form of the curves are similar. In particular, the ratio of T. to a o. is usually very close to that for the basic shear lag treatment. None of these models takes account of the fact that the shear stress in the matrix should fall to zero at the free surface from which the fibre emerges.
Interfi~cial mechanics in fibre-reinforced metals 3 5
t g
Applied Stress
(50* ~ ( 5
x=O x=L (50
/ j d e b o n d e d
• ent f
q
.-----.]i-
G_(x) = G ._+ G ~v(X)
: 121
Fig. 6.
°F i ~t (sr (x)"
L'
Schematic illustration of stress distributions during the pull-out test.
The frictional sliding behaviour has also been analysed, taking account of the effect of the Poisson contraction of the fibre in reducing the radial compressive stress. On the basis of a crude assumption that only the fibre carries an axial normal stress (with the resulting radial strain at the interface producing a reduction in radial stress proportional to the matrix stiffness), relationships are obtained between pull-out stress and length remaining
36 77. ~~ Civne M. C. Hatson
Applied Stress
G 0
Displacement of Loading Point
@
X=( X = X )
debonded
Fig. 7.
I Or(X),= (J + G ' x l ,
(J0s ~ ! !i i.! i!
" < (o rx a . ' , ~ v 0 ; ' 0 , ~TJ
u%~x, .... ~ " ~
S c h e m a t i c illustration of stress distributions d u r i n g the p u s h - o u t test.
embedded , E, It is therefore possible for ,~ and ara- r to be eva lua ted f rom a single pull-out load/displacement curve by finding the combination of these two parameters giving the best fit.
Al though single fibre pull-out testing has been successfully applied to M M C s (e.g. see Ref. 21), there are practical difficulties in specimen preparation and handling when applying the procedure to composites with a relatively stiffmatrix. In general, it is rather more convenient to use the push- out test described below.
Interfacial mechanics in fibre-reinforced metals 37
3.2 Single fibre push-out testing
This test is now being widely applied to MMCs and CMCs. -'2-26 It is usual to examine a series of specimens with different fibre aspect ratios, all of these being much smaller than those typical of pull-out testing. In this case the Poisson effect raises, rather than lowers, the frictional sliding stress. Schematic illustrations of the stress distributions and load/displacement curve are shown in Fig. 7. Recording of the latter requires sensitive, purpose- built equipment (particularly for fine fibres), but the basic operation can be carried out with a conventional microhardness indenter. The SEM micrograph in Fig. 8(a) shows a monofilament that has been pushed down in
(a)
(b) Fig. 8. SEM micrographs of a Ti-SiC monofilament specimen after push-out testing with a conventional microhardncss machinc, showing (a) the indented fibre and (b) the pushed-out
fibre end protruding from the rcvcrsc facc.
38 T I,~-2 C(vne, M. C. ~¢btson
Interracial shear stress
(MPa) i
0.08 i !
0"06 1
0.04
0.02 i [ r ob
¢~ _)xperiment 0 2 0.4 0.6
" Pv'r = 5 "3
L Oo= o.29.,,P
~., 4 - -9, I P
0.8 1.0 Fractional distance along fibre
Fig. 9. Photoelastic measurements can be used to explore the validity of models for the elastic behaviour during bond strength testing, From the comparison shown here it can be
seen that the Hsueh model is in fair agreement with a set of such measurements.
this way: for such large diameter fibres a quick examination in the optical microscope will reveal whether the fibre has been displaced after the application of a particular load. However, a difficulty then arises rrom the uncertainty about whether the load found to be necessary for push-out corresponds to the onset of debonding (ao,) or to frictional sliding along the complete length (%s). An advantage of the test. however, is that a comparison can be made with the load needed to push the partially pushed- out fibre back into the matrix. The recording of a load similar to that for initial push-out suggests that a0~ is being measured.
Again the analysis is carried out in two regimes, corresponding to the elastic case and to pure frictional sliding. Hsueh 27 has presented treatments, based on the shear lag analysis, for both of these. Figure 9 shows a comparison between predicted curves and experimental data obtained with the 3-D frozen stress photoelastic technique. These data were obtained by using two photoelastic resins (with a stiffness ratio of about 2) for matrix and fibre. Measurements of the fringe order, and of the principal stress directions, as a function of position along the fibre were combined in a simple Mohr's circle calculation to give the variation along the fibre length of the shear stress parallel to the interface. It can be seen that this is in reasonable agreement with the Hsueh model for this case.
The Hsueh model for the frictional sliding behaviour predicts, at least for MMCs, a much more uniform distribution of shear stress along the fibre length than in the elastic regime. This is a strong function of the fibre Poisson ratio and the matrix stiffness. Figure 10 shows plots ofrrr for SiC fibres in Ti. It is evident that for this combination (and most MMCs) the value of ~rr
Inter facial mechanics in fibre-reinforced metals 39
Interracial shear stress 30 (MPa)
20
(~raT ~
10
s= 10
S = 2
I I
0 0.2
SiC monofilament in Ti |
J R/r = i0
1.1.=0.3 (~r&T = " 50 MPa
0:4 0:6 o18 1:o Distance along fibre (mm)
Fig. 10. The frictional sliding stress in the pull-out test varies along the length of the fibre as a result of the Poisson expansion of the compressed fibre. The significance of this effect is greater for large values of the fibre Poisson ratio and matrix stiffness. Predicted variations are shown here for SiC fibres of 100/~m diameter, with various aspects ratios, in a Ti matrix.
remains close to/ tara r. A consequence of this is that the frictional push-out stress, O-os, is predicted to rise in an approximately linear manner with fibre aspect ratio. Predictions for ao. and aos as a function of fibre aspect ratio are compared in Fig. 11 with experimental data for SiC monofilaments in an as- sprayed t i tanium matrix. These data were obtained with a simple microhardness machine, so that there is initial uncertainty as to whether the peak loads represent the onset or completion of debonding. However, it can be seen that the experimental data are not consistent with the predicted ao.(S) curves but conform to those for frictional sliding with a zfr value of about 35--40 MPa. This conclusion is supported by the observation of similar loads for push-out and push-back operations. However, one effect of the limited variation in frictional sliding stress along the fibre length is that good agreement with experiment can be obtained over a wide range of # and Or/, r combinations (giving the same product zfr)-
3.3 The full fragmentation test
A method that has been used for MMCs is the so-called 'full fragmentation' technique. This procedure for deducing a shear strength involves embedding a single fibre in a matrix, then imposing a large plastic strain in tension and measuring the mean aspect ratio of the resulting fibre segments. Analysis is based on a constant z, with the Weibull modulus of the fibre taken into account. 2s'2s One of the problems with the method is that it is unclear precisely what is being measured, although it is presumably related to z. .
Pushout 0 1 2 3 4 . . . . l . . . . L . . . . i . . . . l
stress ( SiC raonofilament in ") (~ = - i00 MPa (MPa) isprayed Ti (E _ 60 GPa)l raT/
% =oo I r=50 m | | R/r = 10 l . / " - 75 MPa
400 o Experimentall~~ "- 50 MPa
0 ~ " , , ~ 4 Maximum undisp lacedJ . i . . . . t . . . . i . • : - J. , i , , I
0 0.1 0.2 0.3 0.4
Specimen thickness (ram)
(h) Fig. l l . When the push-out test is done with a conventional microhardness tester, there is uncertainty about whether the recorded minimum push-out loads correspond to debonding or frictional sliding. It can be seen here that, for these data obtained with SiC monofilaments in sprayed Ti, the form of the debonding curve (a) is not consistent with the observed results,
while reasonably good agreement is observed with the frictional sliding predictions (b).
3.4 Other tests
A procedure can be applied to push the fibres into a bulk matrix, 22 with accurate sensing of load and displacement: interpretation of data is complex and application to MMCs has been limited. Estimates based on thermodynamic arguments and debonding observations 29'3° have sug-
Inter facial mechanics in fibre-reinforced metals 41
gested a high af. value (several GPa) for AI-SiC: it certainly appears that this bond is normally stronger than that for Ti-SiC, although the details are probably sensitive to interfacial contamination or precipitation. More experimental data are needed in order to confirm such effects. Various other procedures have also been suggested, although all those for fibres tend to generate predominantly mode II loading conditions. The development of mixed mode loading conditions at fibre/matrix interfaces has been discussed 31 for ceramic matrix composites, in which differential thermal contraction can generate tensile radial stresses when the matrix has the lower expansivity.
3.5 Some data for the Ti-SiC system
It is not appropriate here to attempt any systematic survey of published data, but a limited comparison of results for Ti-SiC monofilament composites is shown in Table 1. The strengths for an as-sprayed matrix appear low and somewhat variable. These composites have little or no interfacial reaction and the matrix also has some porosity (---5-10%), leading to reduced radial compressive stress. The carbon-rich coatings on the SCS fibres are expected to shear very readily when unreacted. However, the pull-out values seem a little low and test data often appear less reproducible with MMCs than those obtained by the push-out procedure. The other composites were all given a heat treatment during fabrication sufficient to form reaction layers. This raises T, compared with the as- sprayed composites, although further heat treatments have little effect. 23 Strength values obtained from the fragmentation test often seem a little high; this may be a consequence of the simplifications in the analysis or of the fact that the continued plastic flow of the matrix will raise the radial compressive stress.
TABLE 1
Interfacial Shear Strength Data for Ti-SiC Monofi lament Composites
Matrix SiC Fabrication Test r, rfr Reference fibre route procedure (MPa) (MPa) number
Ti Sigma a Spray deposit Pull-out 50 12 32 Ti SCS-6 a Spray deposit Pull-out 5 1 32 Ti Sigma Spray deposit Push-out - - 35 33 Ti-25AI-10Nb-3V SCS-6 Powder hot press Push-out 110 60 23 Ti-6AI-4V SCS-6 Diffusion bond Push-out 150 90 24 Ti-15V-3AI-3Cr-3Sn SCS-6 Diffusion bond Push-out 120 80 24 Ti-25Al-10Nb--3V SCS-6 Diffusion bond Push-out 120 50 24 Ti-rAI-4V SCS-6 Hot press Fragment 180 - - 34 Ti-rAI-4V Sigma Hot press Fragment 345 - - 34
"lO0~am diameter, stoichiometric SiC, W core. b 140/~m diameter, C-rich surface, C core.
42 T. W. Clyne, M. C. Watson
4 I N T E R F A C I A L C H E M I C A L ATTACK
4.1 Types of attack
In some cases reaction is limited because one of the reactants becomes consumed. An example is provided by 'Saffil' alumina fibres, which contain a few per cent of SiO2, concentrated at the grain boundaries and on the free surface. This silica is readily at tacked by a strong reducing agent, such as magnesium, present during fabrication. A common complication is that Saffil composites are often made by infiltration of a fibre preform held together by a silica-based binder, which also tends to react during processing. 35 The surface analysis data 36 shown in Fig. 12 give concentrations in the top few nanometres of the fibres after various treatments. (Stripping with H F removes several nanometres of material.) These data confirm that during infiltration magnesium from the melt penetrates the fibres to a depth of a few nanometres, corresponding to the silica-enriched layer. This localised attack of the fibre surface does not appear to occur with magnesium-free melts, and this has been correlated with a significantly lower interracial bond strength exhibited by such composites. 3
There are a number of cases where uninhibited interfacial reaction causes progressive degradation of properties. This is true of most titanium composites, in which reactions are difficult to avoid. The reaction between titanium and SiC to form TiC and TisSi338'39 has a large thermodynamic driving force. It occurs during fabrication of SiC-reinforced titanium and under high temperature service. Figure 13(a) and (b) shows reaction layers formed with Sigma and SCS6 fibres. ̀ *° The latter has a carbon-rich surface,
As-Received
-SiO2 binder added -SiO2 binder added -HF stripped -AI-Mg infiltrated -AI-Mg infiltrated -SiO2 binder -matrix d sso red -matrix d ssolved
-HI: stripped
2 5 -
.hi5
% 10
' m 0
AI
Fig. 12. Shown here are XPS analyses of AI, Si and Mg levels in the surface layers of'Saffil' fibres after various treatments. A brief exposure to HF acid is used to remove a thin surface layer on the fibre, while prolonged immersion of a composite in sodium hydroxide solution dissolves away all the matrix. These data confirm that the thin silicon-rich surface of the fibre
becomes impregnated with Mg during manufacture of the composite.
blterfacial mechanics in fibre-reinforced metals 43
(a)
(b) Fig. 13. SEM images of(a) Sigma (stoichiometric) SiC and (b) SCS-6 (C-rich surface) SiC monofilaments after 50 h at 800°C in titanium, showing thick reaction layers and extensive
cracking.
44 77 14": Clyne, M. C. Watson
often thought to be protective; in I:act, it is consumed at a similar rate to stoichiometric SiC, but it appears to act as a mechanical buffer against the propagation of cracks into the fibre.
In many cases fibre-matrix reaction is very limited because, although thermodynamically favoured, its kinetics are such that it progresses very little during the heat treatment needed for fabrication or in service. Most A1- SiC composites fall into this category, although a fabrication route involving prolonged exposure of SiC to the aluminium melt causes extensive reactions. "*~ The extent of reaction can be reduced by raising the level of silicon in the aluminium alloy. Chemical reactivity at reinforcement/matrix interfaces is reviewed in several papers in a recently published conference proceedings/2
4.2 Effect on mechanical behaviour
A thick reaction layer normally impairs composite performance. This again may be illustrated by reference to the Ti-SiC system. The effect is clear in Fig. 14, showing fracture energy as a function of reaction layer thickness for particulate composites. One interpretation of such data involves a simple fracture mechanics approach, assuming flaws to be present of a size equal to the reaction layer thickness. "~3-'~5 In fact, fracture appears to occur rather differently in some systems when thick layers are present. For example, in Ti-SiC particulate composites there is a strong tendency (apparent in Fig. 15) for the crack to follow the boundary between the unconsumed SiC and the reaction layer) 6 It is thought that the deleterious effect of the reaction layer may in this case be aggravated by the 5% volume contraction associated with this reaction, which sets up tensile interfacial stresses, These counteract the effects of differential thermal contraction and even a relatively thin layer is predicted to put the interface into net tension before any external stress is applied. '~6
nominal fracture energy 300
(10 m 2 )
2OO
2
I00
• . r . . . . .
4 reacuon layer thickness (p.m)
Fig. 14. Nomina l fracture energy of Ti -SiC part iculate composi tes dur ing impact loading. as a funct ion of the thickness of the interracial react ion layer produced by heat t reatments . ~6
Interfacml mechanics in fibre-reinforced metals 45
(a)
(b)
Fig. 15. Optical micrographs of Ti-SiC particulate composites after impact testing, sectioned normal to the fracture surface, showing specimens with reaction layer thicknesses
of about (a) 0-2pm and (bt 5pro.
5 FIBRE COATINGS
5.1 Coating techniques
Certain surface modifications, such as the promotion of an oxide layer, can often be achieved by a simple procedure such as heating. However, carefully specified structures may require the use of highly specialised techniques.
46 T. ~~ Clyne. M. C. Watson
Coatings have been deposited by techniques such as sputter deposition, physical vapour deposition ~" (PVD) and (plasma-assisted) chemical vapour deposition (CVD). The CVD process relies on the thermal decomposition of a gas on a hot fibre. This is used to manutacture the SiC monofilaments considered above, so that the prospect of incorporating the coating operation into the fibre manufacturing process seems commercially attractive. Problems may arise in finding a suitable carrier gas and establishing a deposition procedure for selected coating materials. In addition, control over factors such as deposition temperature, and the microstructure and stress state of the deposit, will in general be limited. Sputter deposition is an alternative technique, offering good control over deposit density, stress state, "ts composit ion and thickness, but at a penalty in cost and processing time.
5.2 Structure and thermodynamic stability
From a thermodynamic point of view, highly stable oxides emerge as strong contenders for barrier coatings. As an example, consider the Gibbs free energy of formation of several candidate oxides (Y203, HfO2 and ZrO2 in Table 2) for use in titanium matrix composites (the free energy of formation of TiO2 is also shown). It can be seen that Y 2 0 3 is the most stable of the candidate oxides. Further data concerning entropy changes during oxygen dissolution in titanium are needed for detailed predictions, but it may in any event be noted that there is some evidence "~9 that both ZrO 2 and HfO2 can undergo appreciable reaction with solid titanium, while Y203 is essentially stable. These thermodynamic data give no information on the possible formation of other compounds such as mixed oxides or the possibilit5 of
T A B L E 2
S u m m a r y o f T h e r m o d y n a m i c a n d Dif fus ion D a t a R e l e v a n t
for C h o i c e o f Ba r r i e r L a y e r M a t e r i a l s'~-5"
Element For o_ride o f X X
AGloooK D x at tO00 K Do at IO00 K (kJmole - l) (m 2 s - ~i (m" s - l)
Ti - 7 1 0 - - - -
A1 - 8 9 3 --- - -
M g - 996 --- - -
Y - 1 0 8 0 1-3 x 10 -21 l ' 0 x 10 -Z6
Zr - 8 4 0 18 x 10 -26 4-t x 10 -1'~
H f - 892 N A N A
Interfacial mechanics in fibre-reinforced metals 47
reaction with the fibre (e.g. carbide formation). Information on possible fibre/coating reactions are incomplete (especially for yttrium compounds), although in most cases the high stability of the oxide will prohibit any such reaction. It may be noted that other types of coating are also being explored for titanium composites, notably TiB2.
5.3 Stresses and mechanical stability
In practice, the avoidance of mechanical damage to the coating is often the most important objective. The need for a large grain size (and low porosity) points to a relatively high coating formation temperature. Sputter deposition has been used, 5° with a substrate temperature of around 500°C. This leads to the danger of cracking as a result of differential thermal contraction stresses. The stress field calculations 5t shown in Fig. 16(a) indicate that large tensile hoop and axial stresses will tend to arise in a yttria coating on a SiC filament during cooling. Cracking caused by such stresses is apparent in Fig. 16(b). Matrix plastic deformation close to the interface during thermal cycling may also cause damage. Mehan et al. 52 demonstrated the value of a YEO3 layer in preventing attack of SiC in the presence of a Ni-Cr alloy, but also showed that (on a planar substrate) this layer underwent spallation after only one thermal cycle.
Fortunately, there is scope during the sputtering process for these stresses to be offset by the so-called 'atomic peening' effect '*a in which, depending on the sputtering gas pressure, energetic back-scattered neutral atoms can cause transient formation of interstitials and hence generate a large compressive stress. Schematic illustrations of this mechanism and of the contributions to the final stress state, as a function ofsubstrate temperature, are shown in Fig. 17. It has been confirmed 53 that a net compressive stress can be induced, giving good mechanical stability.
5.4 Duplex coatings
Mechanical considerations have led to suggestions 5° for a duplex barrier consisting of a metallic layer adjacent to the fibre with an overlayer of the metal oxide. This ductile metallic underlayer offers the possibility of reducing the deleterious effect of brittle interracial layers, by acting to prevent crack propagation into the fibre. In the case of titanium, since a residual oxygen content is always present in the matrix, a suitable choice of metal/oxide system also offers potential for oxide self-repair by means of oxygen gettering from the matrix (see below).
In practice, it is preferable to deposit a yttrium coating which can be partially oxidised to yttria, for example by heating in air. The resultant
48 77. ~t,: C(vne, M. (.7. Watson
Stress (MPa)
40O
30O
200
100
0
-I00
tfoop ]
, / Radial .~
0 10 2o 30 4o 50
tai
R a d i a l d i s t a n c e
(~.m)
Fig. 16. Predicted stress distributions ta) are shown here for W-cored SiC monofilament with a 2-!tin yttria coating, after cooling through 500 K. That these stresses can be sufficient to cause serious damage is evident from the SEM micrograph (b), which is of a SiC monofilament with a yttria layer about 1-2 ~m in thickness, after cooling down from 900:C.
Both hoop and axial cracking has taken place.
Interfacial mechanics injbre-reinforced metals
Iorkwtion
, (TE)
Sputteting target
In-plane Stress in Coating at Room
t/
Quenched-in Vacancies etc
Temperature
-0.3 T, I
Growing deposit
Differential *- thermal
.’ .* I. contraction I’ .- -- I-
ROOlll Compression Tcmpcratun
Substrate Temperature
t
__._.-._._._._._.-.-.-.-.- “Atomic Peening”
Fig. 17. ‘Atomic peening’ during sputter deposition can induce large compressive stresses in a coating. Shown here are (a) a depiction of the process and (b) a schematic illustration of the effect of formation temperature on the final (in-plane) stress in a sputtered layer. for a case
where the layer has a higher expansivity than the substrate.
structure is shown in Fig. 18. A better method of actually forming the outer yttria layer is to allow the yttrium to getter oxygen from solution in the titanium, so that the protective layer is formed in situ. The X-ray maps shown in Fig. 19 demonstrate that this gettering operation has taken place. Finally, Fig. 20 illustrates the protective action of the coating, with the effect of mechanical damage apparent over a portion of the interface.
Fig. 18. An SEM micrograph of a duplex Y 'Y203 coating on a SiC monofilament, produced by heating a Y-coated fibre in a limited oxygen supply
i
I 50 t.tm '1
Fig. 19. X-raymapsofaY-coa tedS iCf ib re inTia f t e r2ha t950°C, showing the distribution of yttrium and oxygen.
Interfacial mechanics in fibre-reinJbrced metals 51
Fig. 20. SEM micrograph showing an interface in a composite exposed to 950:C for 2 h. The coating is intact over most of the circumference; note, however, that there is a region near the bottom left where it has become mechanically damaged and some attack has taken place.
6 SUMMARY
The nature of the fibre-matrix interface influences the performance of MMCs in a number of ways. The following points have been identified.
(a) A strong bond promotes load transfer to the fibres, raising the stiffness and work-hardening rate for short-fibre and particulate composites.
(b) The onset of failure in MMCs is frequently provoked by fibre fracture or cavitation in the matrix at the fibre ends. These arise from high fibre stresses, which are rapidly stimulated by unrelaxed plastic flow throughout the matrix. The nature of the interface has a strong influence on stress relaxation processes, which include interfacial sliding, interfacial diffusion and generation of secondary dis- locations. The promotion of such relaxation mechanisms can improve the ductility of MMCs by postponing the onset of catastrophic processes.
(c) It follows that, in measuring the strength of an interface, a distinction should be drawn between the resistance to shear debonding/ frictional sliding and the resistance to normal debonding/cavitation. It may be advantageous to reduce the former but raise the latter. Ideally the interfacial fracture toughness should be measured for mode I (opening), mode II (shearing) and for mixed mode loading
52 T. ~ Clyne, M. C. Watson
conditions. In practice, although this can be done for planar bi- material interfaces, virtually all tests developed so far for fibre composites involve pure shear (mode II) loading.
(d) Fibre-matr ix chemical attack can have a strong effect on interfacial mechanics. A limited degree of reaction usually seems to raise the bond strength, but substantial attack makes the interface prone to cracking and can render the composite very brittle. This may be partly due in some cases to a change in the stress state caused bv the volume change on reaction.
(e) The design of fibre coatings is a complex area currently under intensive study. Some information has been given about the factors to be considered in optimising the structure of barrier coatings produced by sputter deposition for use in titanium composites.
(f) It has been emphasised throughout that an appreciation of the interfacial stress state during fabrication and service is of considerable importance.
A C K N O W L E D G E M E N T S
The authors are grateful to a number of their colleagues, notably Dr P. J. Withers, Dr R. R. Kieschke and Mr A. J. Reeves, for contributions to the work described and for useful discussions. Financial support for one author (M.C.W.) is being provided by the Interdisciplinary Research Centre for High Performance Materials at Birmingham, and the collaboration of Prof. M. H. Loretto, the Director of the Centre, is gratefully acknowledged.
R E F E R E N C E S
1. Hutchinson, J. W., Mear, M. E. & Rice, J. R., Crack paralleling an interface between dissimilar materials. J. App. 3/Iech. (Trans. ASME), 54 (1987) 828-32.
2. Rice, J. R., Elastic fracture mechanics concepts for interracial cracks. J. App. Mech. (Trans. ASME), 55 (1988) 98-I03.
3. Charalambides, R G., Cao, H. C., Lund, J. & Evans, A. G., Development era test for measuring the mixed mode fracture resistance of bimaterial interfaces. Mech. Mater., 8 (1990) 269-83.
4. Evans, A. G., The mechanical performance of fiber reinforced ceramic matrix composites. In 9th Rise Syrup., ed. S. I. Anderson, H. Lilholt & O. B. Pedersen. Rise National Laboratory, Rise, 1988, pp. 497-502.
5. Takehashi, H. & Chou, T. W., Transverse elastic moduli of unidirectional fibre composites with interfacial debonding. Metall. Trans., 19A (1988) 129-35.
6. Aboudi, J., Constitutive equations for elastoplastic composites with imperfect bonding. Int. J. Plasticity, 4 (1988) 103-25.
Inter facial mechanics in fibre-reinforced metals 53
7. Mason, J. E, Warwick, C. M., Charles, J. A. & Clyne, T. W., Magnesium-lithium alloys in metal matrix composites--a preliminary report. J. Mat. Sci., 24 (1989) 3934- 46.
8. Mason, J. F. & Clyne, T. W., Creep behaviour of whisker-reinforced Mg-Li alloys. Acta Met. (submitted).
9. DaSilva, R., Caldemaison, D. & Bretheau, T., Interface strength influence on the mechanical behaviour of A1/SiC particle metal matrix composites. In Interfacial Phenomena in Composite Materials 1989, ed. F.R. Jones. Butterworths, London, pp. 235-41.
10. Ashby, M. F. & Johnson, L., On the generation of dislocations at misfitting particles in a ductile matrix. Phil Mag., 20 (1969) 1009-22.
11. Taya, M. & Mori, T., Dislocations punched out around a short fibre in a short fibre metal matrix composite subjected to uniform temperature change. Acta Met., 35 (1987) 155-62.
12. Withers, P. J., Smith, A. N., Clyne, T. W. & Stobbs, W. M., A photoelastic examination of the validity of the Eshelby approach to the modelling of MMCs. In Fundamental Relationships between Microstructure and Mechanical Properties of MMCs, ed. P.K. Liaw & M.N. Gungor. TMS-AIME, Warrendale, PA, 1990, pp. 225-40.
13. Goods, S. H. & Brown, L. M., The nucleation of cavities by plastic deformation. Acta Metall., 27 (1979) 1-15.
14. Tanaka, K., Mori, T. & Nakamura, T., Cavity formation at the interface of a spherical inclusion in a plastically deformed matrix. Phil. Mag., 21 (1970) 267-79.
15. Nutt, S. R. & Needleman, A., Void nucleation at fibre ends in A1-SiC composites. Scripta Met., 21 (1987) 705-10.
16. Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion and related problems. Proceedings of the Royal Society, A241 (1957) 376-96.
17. Withers, P. J., Stobbs, W. M. & Pederson, O. B., The application of the Eshelby method ofinternal stress determination to short fibre metal matrix composites. Acta Met., 37 (1989) 3061-84.
18. Lawrence, P., Some theoretical considerations of fibre pullout from an elastic matrix. J. Mat. Sci., 7 (1972) 1-6.
19. Chua, P. S. & Piggott, M. R., The glass fibre-polymer interface. I: Theoretical considerations for single fibre pullout tests. Comp. Sci. Tech., 22 (1985) 33-42.
20. Hsueh, C. H., Elastic load transfer from partially embedded axially loaded fibre to matrix. J. Mat. Sci. Letts, 7 (1988) 497-500.
21. Kieschke, R. R. & Clyne, T. W., Pull-out testing of SiC monofilaments in a spray-deposited Ti matrix. In lnterfacial Phenomena in Composite Materials 1989, ed. E R. Jones. Butterworths, London, 1989, pp. 282-93.
22. Marshall, D. B. & Oliver, W. C., Measurement of interfacial mechanical properties in fiber-reinforced ceramic composites. J. Amer. Ceram. Soc., 70 (1987) 542-8.
23. Eldridge, J. I. & Brindley, P. K., Investigation of interfacial shear strength in a SiC fibre/Ti-24A1-11Nb composite by a fibre push-out technique. J. Mat. Sci., $ (1989) 1451-4.
24. Yang, C. J., Jeng, S. M. & Yang, J. M., Interfacial properties measurement for SiC fiber-reinforced titanium alloy composites. Scripta Met. et Mat., 24 (1990) 469-74.
54 T. W. Clyne, M. C. Watson
25. Verpoest, I., Desaeger, M. & Keunings, R., Critical review of direct micromechanical test methods for interracial strength measurements in composites. In Controlled Interphases in Composite Materials, ed. H. Ishida. Elsevier, New York, 1990, pp. 653-66.
26. Sachse, W., Measurement of the interfacial strength of fibres and thin films. Mat. Sci. & Eng., A126 (1990) 133-9.
27. Hsueh, C. H., Evaluation of interfacial shear strength, residual clamping stress and coefficient of friction for fibre-reinforced ceramic composites. Acta Metall. Mater., 38 (1990) 403-9.
28. Le Peticorps, Y., Pailler, R., Lahaye, M. & Naslain, R., Modern Boron and SiC CVD filaments: A comparative study. Comp. Sci. & Tech., 32 (1988) 31-55.
29. Flom, Y. & Arsenault, R. J., Interfacial bond strength in an AI alloy 606I-SiC composite. Mat. Sci. & Eng., 77 (1986) 191-7.
30. Li, S., Arsenault, R. J. & Jena, P., A quantum chemical study of adhesion in AI- SiC. J. Appl. Phys., 64 (1988) 6246-53.
31. Charalambides, P. G. & Evans, A. G., Debonding properties of residually stressed brittle matrix composites. J. Amer. Scram. Soc., 72 (1989) 746-53.
32. Kieschke, R. R. & Clyne, T. W., Control over interracial bond strength in Ti/SiC fibrous composites. In Fundamental Relationships between Microstructure and Mechanical Properties ofMMCs, ed. P. K. Liaw & M. N. Gungor. TMS-AIME, Warrendale, PA, 1990, pp. 325-40.
33. Watson, M. C. & Clyne, T. W., The use of single fibre pushout testing to explore interfacial mechanics in SiC monofilament-reinforced Ti. Acta ~,Iet. (submitted).
34. Le Petitcorps, Y., Pailler, R. & Naslain, R., The fibre/matrix interfacial shear strength in titanium alloy matrix composites reinforced by SiC or B CVD filaments. Comp. Sci. & Tech., 35 (1989) 207-14.
35. Li, C. H., Nyborg, L., Bengtsson, S., Warren, R. & Olefjord, I., Reactions between SiO2 binder and matrix in 6-AI203/A1-Mg composites. In Interfacia/ Phenomena in Composite Materials 1989, ed. F. R. Jones. Butterworths, London, 1989, pp. 253-7.
36. Cappleman, G. R., Watts, J. F. & Clyne, T. W., The interfacial region in squeeze infiltrated composites containing 6-alumina fibre in an aluminium matrix. J'. Mat. Sci., 20 (1985) 2159-68.
37. Clegg, W. J., Horsefall, I., Mason, J. F. & Edwards, L. F., The tensile deformation and fracture of A1-Saffil metal matrix composites. A cta Met., 36 (1988) 2151-9.
38. Rhodes, C. G. & Spurling, R. A., Fibre-matrix reaction zone growth kinetics in SiC-reinforced Ti-6AI-4V as studied by transmission electron microscopy. In Recent Advances in Composites in the United States and Japan. ASTM STP 684, ed. J.R. Vison & M. Taya, Am. Soc. Testing & Mats, Philadelphia, 1985, pp. 585-99.
39. Choi, S. K., Chandrasekaran, M. & Brabers, M. J., Interaction between titanium and SiC. J. Mat. Sci., 25 (1990) 1957-64.
40. Kieschke, R. R., Titanium reinforced with SiC monofilaments. PhD thesis, University of Cambridge, 1990.
4t. Lloyd, D. J., The solidification microstructure of particulate reinforced aluminium-SiC composites. Comp. Sci. & Tech., 35 (1989) 159-80.
42. Ishida, H., Proceedings of Third International Conference on Interfaces in Composite Materials, Proc. ICCI-III. Elsevier, New York, 1990.
Inter facial mechanics in fibre-reinforced metals 55
43. Metcalfe, A. G. & Klein, M. G., Effect of the interface on longitudinal tensile properties. In Interfaces in Metallic Matrix Composites: Composite Materials, Vol. 1, ed. K. G. Krieder. Academic Press, New York, 1974, pp. 310-21.
44. Ochiai, S. & Marakami, Y., Tensile strength of composites with brittle reaction zones at interfaces. J. Mat. Sci., 19 (1979) 831-40.
45. Ochiai, S., Urakawa, S., Ameyama, K. & Marakami, Y., Experiments on fracture behaviour of single fibre-brittle zone model composites. Met. Trans., IIA (1980) 525-30.
46. Reeves, A. J., Dunlop, H. & Clyne, T. W., The effect of interfacial reaction layer thickness on fracture of Ti-SiC particulate composites. Metall. Trans. (submitted).
47. Nathan, M. &Ahearn, J. S., Interfacial reactions in Ti/SiC layered films with and without thin diffusion barriers. Mat. Sci. & Eng., A126 (1990) 225-30.
48. Hoffmann, D. W., Film stress diagnostic in the sputter deposition of metals. Proc. 7th ICVM, Iron & Steel Inst. Japan, Tokyo, Japan, 1982, pp. 145-57.
49. Tressler, R. E., Interfaces in oxide reinforced metals. In Interfaces in Metallic Matrix Composites: Composite Materials, Vol. 1, ed. K. G. Krieder. Academic Press, New York, 1974, pp. 286-301.
50. Kieschke, R. R., Somekh, R. E. & Clyne, T. W., Sputtered barrier coatings on SiC fibres for use in reactive metallic matrices. Part l--Optimisation of barrier structures. Acta Met., 39 (1991) 427-36.
51. Warwick, C. M. & Clyne, T. W., Development of a composite coaxial cylinder stress analysis model and its application to SiC monofilament systems. J. Mat. Sci. (in press).
52. Mehan, R. L., Jackson, M. R. & McConnell, M. D., The use ofYzO 3 coatings in preventing solid-state Si-based ceramic/metal reaction. J. Mat. Sci., 18 (1983) 3195-205.
53. Warwick, C. M., Kieschke, R. R. & Clyne, T. W., Measurement and control of the stress state in sputtered diffusion barrier coatings on monofilaments. In Interfacial Phenomena in Composite Materials 1989, ed. F.R. Jones. Butterworths, London, 1989, pp. 267-75.
54. Janaf Thermochemical Tables, US Department of Commerce, NSRDS-NBS, Publication 37, 1971.
55. Berard, M. E & Wilder, D. R, Self-diffusion in polycrystalline yttrium oxide. J. Appl. Phys., 34 (1963) 2318-27.
56. Berard, M. F. & Wilder, D. R., Cation self-diffusion in polycrystalline Y~O 3 and Er20 3. J. Amer. Ceram. Soc., 52 (1969) 85-91.
57. Kofstadt, P., Nonstoichiometry, Diffusion and Electrical Conductivity in Binary Metal Oxides. Wiley-Interscience, New York, 1972, pp. 268-74.
