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\ PergamonActa mater. Vol. 46, No. 1, pp. 353–367, 1998

7 1997 Acta Metallurgica Inc.Published by Elsevier Science Ltd. All rights reserved

Printed in Great Britain1359-6454/98 $19.00+0.00PII: S1359-6454(97)00145-6

DAMAGE EVOLUTION AND ACOUSTICEMISSION MECHANISMS IN a2 + b/SCS-6

TITANIUM MATRIX COMPOSITES

D. J. SYPECK and H. N. G. WADLEYSchool of Engineering and Applied Science, University of Virginia, Charlottesville, VA 22903, U.S.A.

(Received 9 January 1997; accepted 10 April 1997)

Abstract—Damage evolution and acoustic emission mechanisms have been investigated during the tensiledeformation of two a2 + b titanium aluminide matrix composites reinforced with SCS-6 silicon carbidefiber. The alloys had distinctly different b phase morphologies and resulting ductilities. A Ti–14 Al–21 Nbmatrix composite with a matrix failure strain significantly greater than the fiber exhibited annularmicrocracking of a brittle b-depleted matrix zone surrounding the fibers. Acoustic emission measurementsindicated that this damage process increased rapidly near the composite yield point and continued at aconstant rate thereafter. Acoustic emission detection of fiber fracture indicated that failure occurred afterabout four fiber fractures at a significantly lower stress than predicted by a global load sharing model.A Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta matrix composite with a matrix failure strain less than the fiberexhibited multiple matrix cracking. Acoustic emission measurements indicated that matrix crackinginitiated well below the stress where primary matrix cracks were first visually observed. Failure occurredafter numerous fiber fractures at a significantly lower fiber stress than predicted by a fiber bundle model.Damage evolution data obtained from the calibrated acoustic emission measurements were combined witha simple micro-mechanical model to predict the inelastic contribution of matrix cracking to the overalldeformation behavior. 7 1997 Acta Metallurgica Inc.

1. INTRODUCTION

Intermetallic matrix composites (IMC) consisting oftitanium or nickel aluminides reinforced withcontinuous silicon carbide fiber have attractedinterest because of their potentially high specificstiffness, strength and creep resistance over a widerange of operating temperatures [1–3]. Compositeswith matrices based on Ti3Al+Nb (a2 + b) alloysand creep resistant SCS-6 SiC fibers are beingexplored for use above the temperature range ofconventional titanium alloys (0600°C). The mechan-ical properties of these a2 + b/SCS-6 composites area function of their constituents properties [4–6], theinterface debond and/or sliding stress [7] and themethod or conditions used for their fabrication [8]. Avariety of micromechanical models [6, 8–12] havebeen proposed to predict the mechanical behaviorof this class of composites. These analyze theconsequences of fiber fragmentation and/ormatrix yielding/cracking. Interface debond/slidingbehavior is often included [8, 11, 12] while some alsoconsider residual stresses arising from the fiber–matrix thermal expansion coefficient mismatch[13, 14] or additional fiber microbending stresses andfiber breaks incurred during consolidation processing[8]. A key aspect of understanding and modeling themechanical behavior of these composites involves acorrect form for the evolution of damage duringloading.

Since damage processes in IMCs are often brittle,they are likely to be accompanied by detectableacoustic emission (AE) [15–18]. Numerous investi-gations have reported AE from metal matrixcomposites (MMCs) [19–21]. In some, attempts havebeen made to locate sources [20, 21]. In others,parameters of the recorded signals (e.g. amplitude,frequency spectra, etc.) have been proposed to‘‘characterize’’ the AE events and to attempt thedifferentiation of one source ‘‘type’’ from another[19]. Many of these studies have relied upon ad hocor empirical methods using data collected withinstrumentation that is not capable of reproducingmany important characteristics of the AE signal.Combined with an absence of models that establishfundamental relationships between damage mechan-isms and signal parameters, such studies have been oflimited value for characterizing damage evolution.

Here we pursue an alternative approach. Thetheoretical relationship between damage events andAE signals is briefly reviewed [22, 23]. Because thedynamic elastic Green’s tensor (this maps an AEsource to the motion responsible for an AE signal) isuncalculated for conventional composite test pieces,a pulsed laser calibration method is used to determinean empirical relationship between the dipole magni-tude (i.e. AE moment strength) of an AE event anda scalar parameter related to the energy of itscorresponding AE signal. This allows recovery of the

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Table 1. Elastic residual stresses (at the fiber-matrix interface) in MPa

Ti–14Al–21Nb/SCS-6 Ti–13Al–15Nb–4Mo–2V–7Ta/SCS-6Stresscomponent Fiber Matrix Fiber Matrix

Radial −194 −194 −260 −260Circumferential −194 323 −260 484Axial −665 222 −812 348

magnitude of the damage event (e.g. the crackopening volume) from the recorded AE. We do notattempt to seek its time dependence, its location norits orientation within the sample, though this couldbe accomplished in principle. Two different a2 + b/SCS-6 composites are studied. Correlations betweenthe differing damage mechanisms, their acousticemissions and the observed tensile behavior are thenused to access the effect of damage evolution upontensile performance.

2. ACOUSTIC EMISSION FUNDAMENTALS

2.1. Natural acoustic emission

Burridge and Knopoff [22] treated an abruptfailure process in an elastic body as an expandingdislocation loop and expressed spatial and materialcharacteristics of the defect in terms of a distributionof ‘‘equivalent’’ body forces. Ignoring spatialvariations of the source region (i.e. point sources), asingle source centered at x' can be modeled by asource moment tensor [23]

Mij = cijkl [uk ]Sl (1)

where i and j indicate the direction and separation ofbody force dipoles, cijkl is the elastic constant tensor,[uk ] is the displacement discontinuity across the defectin the kth direction and Sl is the area of the sourceprojected on to a plane having a normal in the lthdirection.

Consider the creation of a penny-shaped crackin an isotropic linear elastic medium under ModeI loading. If the crack face displacement in thex'1 direction is D, and the crack face area, A, hasa normal also in the x'1 direction, then threeorthogonal dipoles model the source [16, 22];

(l+2m) 0 0Mij =G

K

k[0] l 0G

L

l·DA (2)

0 0 l

where l and m are the Lame constants. The product,DA, is the crack’s interior volume.

For a fiber fracture source in a unidirectionalcomposite under tensile load in the fiber direction,Mode I cracking of the fiber is usually accompanied

Table 2. Properties summary (25°C)

ValueSymbol Units [Reference]

SCS-6Radius rf mm 70 [30]Young’s modulus Ef GPa 400 [30]Poisson’s ratio nf — 0.14 [31]Linear expansion coefficient af 1/K 4.8·10−6 [31]Weibull modulus m — 17.3Weibull normalizing constant s0 MPa mml/m 5270

TitaniumYoung’s modulus E GPa 116 [32]Poisson’s ratio n — 0.32 [32]Linear expansion coefficient a 1/K 8.5·10−6 [32]Mass density r g/cm3 4.5 [33]Specific heat capacity cp J/(kg K) 522 [33]Electrical conductivity s 1/(mV m) 2.38 [32]Relative permeability mr — 1 [32]Thermal conductivity k W/(m K) 21.9 [33]Melting temperature Tm K 1953 [33]

Ti–14Al–21NbYoung’s modulus Em GPa 100Yield stress sy MPa 580

Ti–13Al–15Nb–4Mo–2V–7TaYoung’s modulus Em GPa 114Fracture stress su MPa 601

Ti–14Al–21Nb/SCS-6Fiber volume fraction Vf — 0.25Interface sliding stress ts MPa 113Temperature change DT K −900Processing induced fiber breaks rx 0 Break/m 6

Ti–13Al–15Nb–4Mo–2V–7Ta/SCS-6Fiber volume fraction Vf — 0.30Interface sliding stress ts MPa 123Temperature change DT K −1155Processing induced fiber breaks rx 0 Break/m 10

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Fig. 1. Details of the strain and AE instrumentation. A knife edge extensometer and miniaturepiezoelectric sensors were used.

by Mode II shear at the fiber–matrix interface.Static equilibrium considerations necessitate thatsliding must occur along a shear recoverylength, l= rfT/2ts, where rf is the fiber radius, ts isthe sliding stress at the interface and T is thefiber stress at the time of fracture and theremote stress thereafter. It is simple to show a crackopening:

D=rfT 2

2Efts(3)

where Ef is the Young’s modulus of the fiber. Since

far field contributions to the source moment tensorfrom shear at the fiber–matrix interface cancel due tosymmetry, we find:

(l+2m) 0 0Mij =G

K

k0 0 0G

L

l·pr3

f T 2

2Efts(4)

0 0 lf

where the ‘‘f’’ subscripts indicate parameters for thefiber.

The far field surface displacements (i.e. the AEsignal) can also be modeled. Provided the sourceto receive distance and the wavelengths of interestare much larger than the source dimensions [24],the time-dependent displacement in the ith direction,ui(x,t), at location, x, and time, t, due to wavemotion excited by body force dipoles at (x',t') isobtained by a convolution:

ui(x,t)=Mjkgt

0

Gij,k(x;x',t− t')S(t')dt' (5)

where S(t') is the source time-dependence (e.g. thecrack volume history) and Gij,k(x;x',t− t') is thespatial derivative of the dynamic elastic Green’stensor [23]. It represents the displacement at (x,t)in the ith direction owing to a unit strengthimpulsive body force dipole concentrated at (x',t'),acting in the jth direction, with separation in thekth direction. The dynamic elastic Green’s tensortherefore represents the body’s elastic impulseresponse. Presently, this is uncalculated for conven-tional composite test pieces.

Fig. 2. Acoustic emission calibration curve. A lasergenerated thermoelastic source produced artificial AE of

known moment strength for calibration.

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Fig. 3. Ti–14 Al–21 Nb/SCS-6 composite (microstructure). A 0.25 volume fraction of SCS-6 fiber in aTi–14 Al–21 Nb (wt%) matrix. Consolidation processing damage included a cracked b-depleted matrix

zone.

2.2. Artificial acoustic emission

The absorption of a laser pulse at the surface ofa metal causes a transient thermal expansion thatcan be used for generating artificial AE [25, 26].For a uniform pulse of duration t0, the maximumincrease in surface temperature is

DTs =2I0X t0

prcpk(6)

where r is the mass density of the metal, cp is thespecific heat capacity at constant pressure, k is thethermal conductivity and I0 is the absorbed laser fluxdensity [26]. The thermoelastic source is well modeledby two orthogonal dipoles oriented in the plane of theirradiated area [26]:

M11 =M22 =0l+23m13a

rcp(1−R)E0 (7)

where a is the linear expansion coefficient ofthe metal, R is the reflectivity [26] and E0 is thepulse energy. Thus, laser pulses can create dipolesof known magnitude which can be used tocalibrate the acoustic response function of testsamples.

3. EXPERIMENTAL

3.1. Materials

Two a2 + b/SCS-6 composite samples (4-ply) weresupplied by General Electric Aircraft Engines(GEAE) (Cincinnati, OH). They were fabricatedusing plasma sprayed monotapes [27] by consolida-tion at 900–950°C [28]. The gauge sections of thedogbone samples were 25 mm long, 6 mm wide and1 mm thick. One sample contained a 0.25 volumefraction, Vf, of SCS-6 fibers in a Ti–14 Al–21 Nb(wt%) matrix while the other contained a 0.30 fibervolume fraction in a Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta (wt%) matrix. The Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta matrix sample received a post fabrication heattreatment consiting of 1180°C/6–10 min/He quench;870°C/1 h/He quench; 705°C/8 h/vacuum cool. Simi-larly processed fiberless matrix samples were alsosupplied.

Elastic residual stresses were computed using thetwo phase composite cylinder methodology [29](Table 1), with input properties found in Table 2.For the matrices, the linear expansion coefficient,a, and Poisson’s ratio, n, of titanium were used.The matrix radii of the concentric cylinderswere 140 mm and 128 mm, which corresponded tomatrix volume fractions, Vm =1−Vf, of 0.75 and0.70, respectively.

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Fiber push-out tests on 0.50 mm thick sampleswere used to estimate fiber–matrix interface debond/sliding stresses [34]. For the Ti–14 Al–21 Nb/SCS-6system, the mean of five tests gave a complete debondstress of 116 MPa and an initial sliding stress, ts, of113 MPa. The respective standard deviations were14 MPa and 10 MPa. For the Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta/SCS-6 system, the complete debondstress was 154 MPa and the initial sliding stress was123 MPa. The respective standard deviations were18 MPa and 4 MPa. The debond surfaces of theTi–14 Al–21 Nb/SCS-6 system were rough while thatof the Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta/SCS-6 sys-tem were smooth [35].

A Weibull type analysis was used to characterizethe tensile strength of the SCS-6 fiber in its pristinestate [36, 37]. For fibers having a length L, theexpected value is of the form [38]

T� =s0

L1/mG01+1m1 (8)

where G(h)= fa

0zh−1exp(−z)dz is the Gamma func-

tion. Mean strengths [39] of tests with 10–70 mmgauge length samples [40] gave m=17.3 ands0 =5270 MPa mm1/m [35].

3.2. Mechanical testing

An electromechanical testing machine equippedwith a 50 kN loadcell, serrated face wedge actiongrips and a 10% capacity extensometer with a12.7 mm gauge were used to measure stress and strainat 025°C. Pressure clips and a thin layer of epoxyheld the extensometer knife edges firmly in place (Fig.1). Fiberless matrix samples were tested at a constantdisplacement crosshead rate of 0.025 mm/min whilecomposite samples were tested at a slower rate of0.005 mm/min to accommodate the large amount ofon-line AE data processing. Stress, strain and timewere recorded on a personal computer at 2 s intervals.

3.3. Acoustic emission measurement

Two point contact piezoelectric sensors weresymmetrically located near either end of the testsamples (see Fig. 1). The sensors were our ownversion of a broad-band conical device [41] designedto measure out of plane displacement with no

Fig. 4. Ti–14 Al–21 Nb/SCS-6 composite (stress–strain behavior and AE activity). A bi-linear behavior.The rate of AE activity increased rapidly near the composite yield point and continued at a constant ratethereafter. (a) Stress–strain behavior and AE moment strength. (b) AE event count and integrated

moment.

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Fig. 5. Ti–14 Al–21 Nb/SCS-6 composite (anular b-depletedmatrix zone cracks). These were more severe and werenearly twice as frequent as those observed in theundeformed grip section. (a) Micrograph of a single crack.

(b) Three-dimensional schematic of several cracks.

every 010 mJ up to 0100 mJ (Fig. 2). The AEmoment strength of the thermoelastic source,

M=M11 +M22 (9)

was obtained from equation (7) as M=0.54 E0. Therelation between the AE signal r.m.s., VRMS (in mV),and the AE moment strength, M (in N mm), was wellfitted by

VRMS =270·lnM−233. (10)

This procedure indicated a logarithmic dependence ofsignal upon source strength similar to that used forseismic magnitude scaling [44–46].

4. THE Ti–14 Al–21 Nb/SCS-6 SYSTEM

4.1. Microstructure characterization

The fibers were more or less uniformly spaced (Fig.3), while the matrix consisted of an equiaxed a2

(ordered h.c.p.) Ti3Al intermetallic phase withintergranular b (b.c.c.). By-products of the consolida-tion process included a 03 mm thick fiber–matrixreaction product, broken fibers (rx 0 0 6 breaks/m) andfiber microbending [27]. Radial (01 per fiber, see Fig.3) and annular cracks (06–7 crack/mm) were alsopresent. Both types of crack often extended into asurrounding (010 mm thick) b-depleted matrix zone(see Fig. 3) and sometimes partially through the SCSlayers. Apart from the b-depleted zones, the fiberlessand composited matrices were quite similar.

4.2. Stress–strain—AE behavior

The fiberless Ti–14 Al–21 Nb matrix behaved in anelastic–nearly perfectly plastic fashion with a Young’smodulus, Em, of 100 GPa [35]. Yielding initiated at astress, sy, of 580 MPa and a strain of 0.60%. Failureoccurred at a stress of 612 MPa and a strain of4.50%. Ten acoustic emissions were detected with amean AE moment strength of 2.6 N mm (0.2 N mmstandard deviation) during nominally elastic loading.

The Ti–14 Al–21 Nb/SCS-6 composite initiallyexhibited a slight non-linearity owing to samplebending (Fig. 4). A linear (Stage I) behavior thenoccurred up to a stress, s, of 475 MPa and a strain,o, of 0.29%. A brief transition (indicative of matrixplasticity) and a second (Stage II) linear region ofdiffering slope followed [38, 47, 48]. The measuredmodulus in Stage I was 178 GPa while in Stage II itwas 88 GPa. Tensile failure occurred at a stress of925 MPa and a strain of 0.79%. 1851 emissions (seeFig. 4) were detected throughout the loading. Themean AE moment strength was again 2.6 N mm(1.3 N mm standard deviation). The rate of AEactivity for the composite increased rapidly as theapplied stress exceeded about 400 MPa and ap-proached steady state just beyond the point where thetransition to Stage II occurred. The final integratedmoment strength of all composite AE activity was4710 N mm. Four strong events having Mq 10 Nmm were recorded towards the end of the test.

significant resonance in the 10 kHz to 2 MHz range[42, 43]. They were connected via short coaxialleads to charge amplifiers having a rated 250 mV/pCsensitivity and 10 kHz to 10 MHz bandwidth; 20 kHzhigh-pass and 2 MHz low-pass filters were usedafter the amplifiers to attenuate environmentalnoise.

A LeCroy (Chestnut Ridge, NY) 7200 PrecisionDigital Oscilloscope recorded the AE; 20,000 datapoints were recorded per channel with 8 bit resolutionover a 5 ms time interval (i.e. a 4 MHz sampling rate).The trigger point was offset to allow 4.5 ms of databeyond the trigger point and full capture of theexponential ‘‘ring-down’’ of most signals. A 0.1 V/division setting was used as the primary channel.When strong events overloaded the primary channel,a 1 V/division channel also captured the signalensuring no loss of data. The time of the AE and theirroot mean square (r.m.s.) voltages were written to thefixed disk drive of the oscilloscope.

3.4. Acoustic emission calibration

A 1.064 mm Nd:YAG Q-switched pulse laser witha 7 ns (FWHH) pulse duration and 6 mm spotdiameter was used to generate the thermoelastic AEsource. Using t0 0 7 ns and properties of titanium(Table 2), equation (6) indicated that melting beginsat E0 0 108 mJ for a sample at 025°C. Ten r.m.s.voltage and laser energy measurements were made

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4.3. Damage observations after testing

Metallographic examinations of the longitudinallysectioned sample revealed annular b-depleted matrixzone cracks (these extended into the reactionproducts) which were more or less uniformlydistributed along all fibers (Fig. 5). The cracks in thegauge section after testing were more severe (had alarger area and opening displacement) and werenearly twice as frequent (011–12 crack/mm) as thosein the undeformed grip section. Occasionally thesecracks extended all the way through the SCS layersand are similar to the observations of otherresearchers [49–51]. The ends of the annular crackswere not found to directly nucleate fracture of theunderlying SiC.

The fracture surface exhibited significant crackdeflection with typical fiber pull-out lengths of up toa fiber diameter or two [35]. Far (several mm or moreaway) from the fracture surface, there was noevidence of fiber fracture (other than processingdamage). However, higher magnification uncoveredthe occasional occurrence of clusters of arrested

annular fiber cracks (Fig. 6). These crack clusterswere randomly distributed throughout the gaugesection, but within a cluster they exhibited a regularaxial spacing with a 050–60 mm separation. Thecracks extended 010–15 mm radially inward fromnear the midradius boundary (039.5 mm from thefiber center) and towards the carbon core forming anannular ring (see Fig. 6). Nearer to (within a few mmof) the fracture surface, many closely spaced fiberfractures (less than one fiber diameter apart) andarrested annular fiber cracks were present. Just below(within a few fiber diameters) the fracture surface,several of the fibers had been extensively shatterd,and some into very small wedge-shaped fragmentsrunning perpendicular to the direction of loading.Other researchers have related similar fragmentationto stress waves [52].

4.4. Acoustic emission mechanisms

A typical annular b-depleted matrix zone crackhad a radial length of 013 mm and thus a crack facearea, A, of 06200 mm2. The crack opening, D, was

Fig. 6. Ti–14 Al–21 Nb/SCS-6 composite (annular fiber cracks). Clusters of these cracks extended radiallyinward from near the midradius boundary and towards the carbon core forming an annular ring.

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Fig. 7. Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta/SCS-6 composite (microstructure). A 0.30 volume fraction ofSCS-6 fiber in a Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta (wt%) matrix. Consolidation processing damage

included cracked reaction products and SCS decohesion.

01.0 mm (see Fig. 5 and note that tensile loadingopens the crack), and so the AE moment strength:

M=M11 +M22 +M33 (11)

was 01.8 N mm where equation (2) and Ti–14 Al–21 Nb moduli (Table 2) have been used. This damageprocess was therefore near the limit of detectability(M0 2.5 N mm) and was probably responsible forthe numerous ‘‘weak’’ signals observed during testingof the composite.

The four ‘‘strong’’ events having Mq 10 N mmwere unlikely to be associated with b-depleted zonecracking. For example, the two emissions whichoccurred at stresses of 877 MPa and 884 MPa hadmoment strengths of 18.0 N mm and 51.5 N mm,respectively. We believe that these signals were due tofiber fractures. Superposing elastic residual andapplied stresses, the fiber stress, T, at the time of thesefractures was 02200 MPa. From equation (3), usingproperties found in Table 2, the computed crackopening is 03.8 mm. Equations (4) and (11) then givea moment strength of 032.0 N mm which iscomparable to the range of values observed.

The short annular fiber cracks were probably notdetected if they occurred one at a time in these tests.They had a typical radial length of 015 mm, an outerradius of 039.5 mm and hence an area of03000 mm2. Their crack opening was 00.3 mm (see

Fig. 6 and note that tensile loading opens the crack)which corresponds to a moment strength of 00.5 Nmm. This is below the baseline noise level (M0 2.5 Nmm) of the tests (their significance is discussed later).

4.5. Modeled stress–strain behavior

A global load sharing model modified to accountfor the effect of fiber breakage induced duringconsolidation processing [8] was used to predict thestress–strain behavior. Elastic residual stresses andmatrix plasticity were additions to the model. Theremote axial fiber and matrix stresses were found(elastic residual and applied stresses superimposed)using the composite cylinder methodology[29, 53, 54]. Composite strain (which was primarilycontrolled by elastic deformation of the unbrokenfibers) entered the constitutive relation in thismanner. Because the shear recovery length, l= rfT/2ts, is a positive quantity, the absolute value of thiswas used as a model input during the early stages ofloading (i.e. when the fiber is in residual axialcompression) to ensure that consolidation fiberbreaks were properly accounted for.

In Stage I, the modeled behavior was similar tothat measured (see Fig. 4). The onset of matrixplasticity (i.e. Stage II behavior) was estimated usinga von Mises criterion. Yielding was taken to initiatenear the edge (080 mm from fiber center) of the

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b-depleted zone (where the more deformable b phasebegins) rather than at the fiber–matrix interface. Thepredicted axial strain at yielding was 0.28% whichcompared well with the measured value of 0.29%. InStage II, axial constraint imparted by the fibersinhibited plastic flow of the matrix. Furthermore,since the maximum strains were small (0.79% axialstrain at failure), remote fiber and matrix stresseswere approximated by superimposing elastic yieldpoint stresses with the additional incremental stressesdeveloped after the matrix was deforming perfectlyplastically [55]. The latter were computed using theelastic composite cylinder solution with an axialstrain equal to the incremental strain beyond the yieldpoint and tangent Stage II moduli. For thenon-hardening matrix, the tangent Young’s modulusand Poisson’s ratio tended to zero and one half,respectively, the plane strain bulk modulus wasreplaced by the elastic bulk modulus, kpm:Em/3(1−2 nm) and the shear modulus remained un-changed [56]. The fiber retained its original elasticmoduli. The measured Stage II modulus (see Fig. 4)was 012% less than predicted. Since few fiber

fractures occurred prior to sample failure, thisreduced modulus is believed to be connected with theannual b-depleted zone cracking.

The computed fiber and matrix axial stresses atsample failure, sf = 2464 MPa and sm =535 MPa,were reduced from their precomposited values. Thus,neither the fiber nor the matrix had achieved the fullload bearing capacity exhibited prior to compositing.Although additional test data reported by GEAEusing samples machined from the same panel hadcomputed fiber stresses that were as much as 034%higher (private communication), they were stillsignificantly less than the model prediction basedupon a retention of the pristine fiber strength.Strength measurements of fibers extracted fromuntested composites of similar composition to thosetested here indicate that a 020% loss of strength canaccompany consolidation [57]. The underlyingorigin of this is at present unclear. It may be linkedto chemical depletion of SCS layers or to theirphysical damage during processing. While processingdamage (including fiber microbending) may leadto reductions in fiber strength when composited,

Fig. 8. Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta/SCS-6 composite (stress–strain behavior and AE activity).Unstable tensile behavior was observed. The strength of AE activity increased dramatically at the pointwhere the first primary matrix crack was observed. (a) Stress–strain behavior and AE moment strength.

(b) AE event count and integrated moment.

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Fig. 9. Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta/SCS-6 composite (primary and secondary matrix cracks).Primary cracks traversed the whole cross-section and were present along the entire gauge length.Secondary cracks which arrested before traversing the whole cross-section were also present. (a)

Micrograph. (b) Three-dimensional schematic of primary and secondary matrix cracks.

fragmentation theory suggests that cumulative failureof the fibers should have occurred prior to samplefailure. This was observed neither acoustically normetallographically in our tests and indicates anon-cumulative mechanism.

Lastly, we note that some fibers far from thefracture surface contained arrested annular cracks(see Fig. 6). Flaws of such a large size can usuallyexist in brittle silicon carbide fibers only when thetensile stress is less than a few MPa. They could havebeen caused by a combination of added static anddynamic stresses arising from damage, includingnearby fiber breaks [52, 58]. Displacement constraintimparted by unbroken fibers in the same cross-sec-tional plane, the sometimes large compressive stressesfound in regions of SCS-6 fibers [59] and microstruc-tural changes at the midradius boundary [60] mayhave contributed to their arrest. Daniel [61] has usedhigh-speed photoelastic techniques to observe fiberdamage of this type in model glass–Homalitecomposites. Were large fiber defects of this type tohave occurred before the final catastrophic event,they would have significantly weakened the fibers andled to premature failure.

5. THE Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta/SCS-6 SYSTEM

5.1. Microstruture characterization

The fibers were more or less uniformly spaced (Fig.7), while the matrix consisted of an equiaxed a2 phasein a matrix of transformed b that contained a fineacicular a2 + b microstructure. By-products of theconsolidation process included a 03 mm thickfiber–matrix reaction product zone, occasionalbroken fibers (rx 0 0 10 breaks/m) and fiber mi-crobending. Short radial (see Fig. 7) and annularmicrocracks were observed in the reaction product.No b-depleted matrix zone existed near the fibers.However, islands of 03–5 mm diameter not havingtypical a2 or a2 + b morphologies were observed nearthe fibers (see Fig. 7). These etched more slowly thanthe a2 phase and were not found in the correspondingneat matrix. The fibreless and composited matriceswere otherwise quite similar. Portions of the SCS-6layers were observed to have decohered from thefibers and were trapped in the matrix (see Fig. 7). Thiscoating damage has been linked to fiber thermalshock during the plasma spray deposition process [27]

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and may have contributed to the higher interfacedebond/sliding stresses measured for this system.

5.2. Stress–strain—AE behavior

The fiberless Ti–13 Al–15 Nb–4 Mo–2 V–7 Tamatrix behaved in a brittle fashion with a Young’smodulus, Em, of 114 GPa [35]. Failure occurred at astress, su, of 601 MPa and a strain of 0.50%. Fiveacoustic emissions were detected with a mean AEmoment strength of 2.8 N mm (0.3 N mm standarddeviation).

The Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta/SCS-6 com-posite exhibited a linear (Stage I) behavior up to astress, s, of 370 MPa and a strain, o, of 0.19% (Fig.8). Thereafter, unstable tensile behavior (includingstrain reversals and hysteresis) was observed. Otherunpublished test data reported by GEAE haveexhibited similar behavior for this system (privatecommunication). The strain reversals were consistentwith the formation of cracks (and an accompanyingincreased compliance) outside the extensometer knifeedge contact points. If the opening displacement ofthese cracks exceeded that needed to accommodatethe imposed displacement rate, an elastic contractionof the gauge section can occur. Tensile failureoccurred at a stress of 758 MPa and a strain of0.88%. 1121 emissions (see Fig. 9) were detected witha mean AE moment strength of 38.6 N mm (248.4 Nmm standard deviation). The AE activity for thecomposite began at a stress of around 50 MPa andoccurred at an approximately constant rate up to astress of 370 MPa and a strain of 0.19%. At thispoint, dramatic increases in signal strength ac-companied abrupt changes in stress–strain behavioruntil tensile failure. The integrated moment strengthwas found to be well fitted by a power-law relation;

gs

0

M(h)dh=10−6s3.7

1.05(N mm) (12)

where the composite stress, s, has units of MPa.

5.3. Damage observations after testing

Metallographic examinations of the longitudinallysectioned sample revealed extensive matrix cracking(Fig. 9) and many fractured fibers (some wereassociated with consolidation processing but themajority occurred during testing) (Fig. 10). Annularreaction product and fiber cracks similar to thoseseen in the Ti–14 Al–21 Nb/SCS-6 system (see Figs 5and 6) were also found. The primary matrix crackstraversed the full cross-section and were spaced00.3–0.9 mm along the entire gauge length (see Fig.9). The secondary matrix cracks (see Fig. 9) werearrested before traversing the full cross-section.Often, multiple fiber fractures with spacings of lessthan a fiber diameter (see Fig. 10) were observed far(several mm or more away) from the final fractureplane. The annular fiber cracks were again regularlyspaced with a 050–60 mm separation; however, they

Fig. 10. Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta/SCS-6 composite(closely spaced fiber fractures, annular fiber cracks and aprimary matrix crack). Fiber fractures were numerous andoften very closely spaced. Large matrix crack openingdisplacements were indicative of extensive sliding at the

fiber–matrix interface.

occurred much more frequently, and were moreevenly distributed than in the Ti–14 Al–21 Nb/SCS-6system. While matrix cracks and fiber fractures oftenpenetrated at least one of the SCS layers, neither wasobserved to nucleate damage in the adjacent phase(with the possible exception of consolidationprocessing damage like that shown in Fig. 9). Largematrix crack opening displacements (see Fig. 10) wereindicative of extensive sliding at the fiber–matrixinterface. Even so, a relatively planar fracture surfacewith minimal fiber pull-out was observed [35]. Justbelow (within a few fiber diameters) the fracturesurface, several of the fibers had been extensivelyshattered, and some into very small wedge-shapedfragments like that observed in the Ti–14 Al–21 Nb/SCS-6 system.

5.4. Acoustic emission mechanisms

Primary matrix cracks were the most likely originof the many abrupt strain reversals seen in thestress–strain curves (see Fig. 8). The crack face areas,A, for these were 04.2 mm2. The first primary crackevent appeared to occur at a stress, s, of 370 MPa.A simple (one-dimensional) micro-mechanical model(see the Appendix) can be used to estimate the crackopening. Using equation (A8) and data from Table 2,the crack opening, D, is estimated to be 03.0 mm.From equation (2), the moment strength, M=M11 +M22 +M33, was therefore 04000 N mm. Thisis a very strong event and appears to be the sourceof the significant number of observed signals in the01000–10,000 N mm range (see Fig. 8). The manyevents with smaller moments, 100 QMQ 1000 Nmm, occurring after the first primary matrix crack arelikely to have been caused by either (partial) matrixcracks that were arrested at fibers, or the intermittentextension of eventual primary cracks.

Fiber fractures were estimated to have momentstrengths in the 010–50 N mm range (see Section

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Fig. 11. Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta/SCS-6 composite (micro-mechanical model of primary matrixcracking). A relatively simple (one-dimensional) elastic analysis was used to model the tensile strain

response of the cracked composite; (a) x'q l'. (b) x'R l'.

4.5). Thus, many of the numerous events havingsimilar strengths (see Fig. 8) were consistent with theextensive, metallographically observed, fracturing offibers.

Annular reaction product cracks typically propa-gated through the entire 03 mm thick fiber–matrixreaction product zone surrounding the fibers and thushad crack face areas of 01350 mm2. Crack openingswere 00.5 mm or less and so the correspondingmoment strengths were in the neighborhood of00.2 N mm. Similarly, arrested annular fiber crackswere expected to have moment strengths of 00.5 Nmm (see Section 4.5). Since the estimated strengths ofboth crack types is well below the detection threshold(M0 2.5 N mm), we conclude that these were notacoustically detected in these experiments unlessoccurring many at a time.

5.5. Modeled stress–strain behavior

A simple matrix cracking (with no fiber fracture)micro-mechanical model (see the Appendix) was usedto model the stress–strain behavior. The crack densityevolution can be estimated from the AE data bynoting that the moment strengths of matrix crackingevents were much greater than those associated withother damage mechanisms. Let the number ofcompleted matrix cracks at a given stress, s, beproportional to the magnitude of the integratedmoment data [equation (12)]. Since there were about45 cracks observed along the 25 mm gauge length atsample failure (i.e. when s=758 MPa), the crackhalf spacing dependence on stress is simply

x'0 1013s−3.7

0.8(mm) (13)

where s has units of MPa.

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To compute the strain, o, of the composite at agiven stress, s, equation (13) was first solved for x'.This was then compared to the shear recovery length,l', obtained using equation (A1) with the remotematrix stress, sm, predicted using equation (A2) andparameters cited in Table 2. The residual fiber andmatrix stresses were sT

f =−812 MPa andsT

m =348 MPa, respectively (see Table 1). Whenx'q l, the situation was that depicted in Fig. 11(a),and equation (A9) gave the strain. When x'R l, thesituation was that depicted in Fig. 11(b), andequation (A15) gave the strain.

Comparing results, the measured Stage I modulusof 0199 GPa slightly exceeded the model prediction(see Fig. 8). This occurs because the (continuous)power-law fit of the integrated moment curve (Fig. 8)slightly overestimated the amount of (discontinuous)cracking in this region. A rule of mixturesapproximation gives a Stage I modulus of 200 GPa,indicating that the effect of secondary crackingdamage on Stage I stiffness is negligible. After thefirst primary crack event (at 370 MPa), the modeledstress–strain behavior compared favorably with thedata up to a strain of about 0.5%. Beyond this, themodeled stiffness was slightly greater than measured(probably a consequence of neglecting fiber fracturesin the model) and increased as the matrix crackingbegan to saturate.

The first primary matrix crack occurred at a strainof 0.19%. This corresponded to a strain which was0.31% less than the measured failure strain (0.50%)of the fiberless matrix. By superimposing the elasticresidual and the applied stresses, sm = sT

m + oEm, thecomputed axial matrix stress at the onset of matrixcracking, 565 MPa, is close to the value measured(601 MPa) for failure of the fiberless matrix sample.This may be somewhat coincidental since the flawpopulation that gives rise to a stochastic matrixstrength is likely to be affected by compositing. Evenso, the measured mean crack spacing (00.56 mm) atfailure agrees well with that predicted (00.53 mm)using the Kimber–Keer model [62].

The mean fiber stress at failure for fibers bridginga primary matrix crack was 2527 MPa. Similar resultswere reported by GEAE using samples machinedfrom the same panel (private communication). As alower bound prediction, a fiber bundle model [38](with a 25 mm bundle length and the SCS-6parameters cited in Table 2) suggests bundle failureat a fiber stress of 3502 MPa and strain of 0.93%.Thus, the measured maximum fiber stress for our testwas about 1 GPa less than the typical tensile strengthof a bundle of pristine, unprocessed fibers. Like theTi–14 Al–21 Nb/SCS-6 system, the reinforcing fibershave performed in a weakened fashion whencomposited.

Since the amount of damage to the fibers (fracturesand arrested annular cracks) was significant and oftenso closely spaced (see Fig. 10) that static equilibriumconsiderations could not explain the phenomena,

dynamic stresses are thought to have contributed totheir weakening. In fact, the acoustic emissionsindicated that the stress wave intensity was muchgreater in this composite system than in theTi–14 Al–21 Nb/SCS-6 system. This, along withprocessing induced damage and microbendingstresses, is thought to be the origin of fiber weakeningand premature failure of this composite.

6. SUMMARY

A laser calibrated acoustic emission approach wascombined with relatively simple micro-mechanicalmodels to deduce the evolution of damage processesduring the tensile straining of two different inter-metallic matrix composites.

A ductile matrix Ti–14 Al–21 Nb/SCS-6 com-posite emitted most of its detectable AE by annularmicrocracking of a brittle b-depleted matrix zonesurrounding the fibers. This damage process in-creased rapidly near the composite yield pointand continued at a constant rate thereafter. Anestimate of the acoustic moment of a fiber fractureidentified the occurrence of about four fiberfracture events prior to sample failure. Clusters ofannular fiber cracks were observed metallographi-cally. Their mechanism of origin remains unclear,but may have been linked to the dynamicunloading waves which accompanied final samplefailure. A global load sharing model which includedconsolidation fiber breakage was modified toaccount for elastic residual stresses and matrixyielding. This model predicted a Stage II modulusthat was 012% greater than measured. The extrasoftening appears to be connected with the exten-sive b-depleted zone cracking. Cumulative fiberfragmentation was not observed, and a non-cumu-lative mechanism was suspected, and may havecontributed to a tensile failure at stresses signifi-cantly less than predicted.

A brittle matrix Ti–13 Al–15 Nb–4 Mo–2 V–7 Ta/SCS-6 composite emitted strong AE from multiplematrix cracking. Matrix cracking initiated well belowthe stress where primary matrix cracks were firstvisually observed. Many of the smaller AE signalsafter the first primary crack event were consistentwith mostly secondary cracks which had beenarrested at fibers or intermittently extended tobecome primary cracks. Failure occurred afternumerous fiber fractures at a fiber stress significantlylower than predicted by a fiber bundle model. The AEowing to damage increased with stress in a power-lawfashion. Damage evolution data deduced from theacoustic emission measurements were combined witha relatively simple micro-mechanical model to predictthe inelastic contributions of matrix cracks to theoverall deformation behavior. Good agreementbetween the predicted and measured stress–strainbehavior was found. Significant annular fiber crackswere observed and thought to be associated with the

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unloading waves associated with primary andsecondary matrix cracking providing a mechanism forreducing the effective fiber strength.

Acknowledgements—We are grateful to A. G. Evans fordiscussions about the mechanisms of composite damage andto General Electric Aircraft Engines who supplied thesamples. Thisworkhas been supported by theDARPA/ONRURI at UCSB (S. Fishman, Program Manager).

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APPENDIX

Tensile Response of a Unidirectional Brittle MatrixComposite Loaded in The Fiber Direction

The prediction of inelastic deformation owing to brittlematrix cracking in unidirectional fiber reinforced com-posites has been studied by Aveston et al. [63], Budianskyet al. [64] and more recently Curtin [65], who notedsimilarities between the matrix cracking process and thestochastic fiber fragmentation that often occurs in ductilematrix composites. He et al. [12] have conducted detailedfinite element calculations of the inelastic strains associatedwith matrix cracking that compared favorably with analysesusing shear lag models [66]. Here, a relatively simple(one-dimensional) elastic analysis is used.

If the faces of a matrix crack remain approximatelystraight, equilibrium considerations necessitate that fiber–matrix interface sliding must occur along a shear recoverylength given by [63]:

l '= rfsmVm

2Vfts. (A1)

Along this length, matrix stress, s'm, increases linearly fromzero (at the crack plane) to the remote isostrain value, sm.Conversely, fiber stress, s'f , decreases linearly from s/Vf tothe remote isostrain value, sf. Hence, the matrix supportsless load than what would be expected for an uncracked(isostrained) composite while the fiber supports more. Thedifference in their changes of length gives rise to a matrixcrack opening, D. Composite strain, o, is simply theelongation of the (unbroken) fibers divided by their originallength. Both are a function of the matrix crack spacing.

Since the site of cracking events is governed by thedistribution and severity of defects [65], it is convenient towork with a mean crack spacing 2x' [12]. Two situationsmust be addressed. The first involves sliding along lengthsless than one half the mean crack spacing [i.e. when x'q l',Fig. 11(a)], while the second involves sliding along the entirelength [i.e. when x'R l', Fig. 11(b)]. The equilibriumrelation, s=Vfsf +Vmsm, is satisfied throughout. Sub-scripts f and m differentiate the fiber and matrix.

When x'q l' (in the region xE x'− l'):

Stresses:

sf = sTf + ox Ef sm = sT

m + ox Em (A2)

Isostrain:

ox = sVfEf +VmEm

(A3)

Displacement (at x= x'− l '):

ux = ox (x'+ l ') (A4)

When x'q l' (in the region xe x'− l'):

Stresses:

s'f = sf +Vmsm

Vf 01− x'− xl ' 1 s'm = sm0x'− x

l' 1 (A5)

Strains:

o'f = s'f − sTf

Efo'm = s'm − sT

m

Em(A6)

Displacements (at x= x'):

u'f = l 'Ef0sf − sT

f +Vmsm

2Vf 1+ ux

u'm = l 'Em0sm

2 − sTm1+ ux (A7)

When x'q l':

Matrix crack opening:

D=2(u'f − u'm)=

rfVm[sEm +Vf(sTmEf − sT

f Em)]2

2V2f EfEm(VfEf +VmEm)ts

(A8)

Composite strain:

o= u'fx' (A9)

When x'R l':

Stresses (at x=0):

sf =sVf

− 2tsx'rf

sm =2tsx'Vf

rfVm(A10)

Stresses:

s'f = sf +Vmsm

Vf 0xx'1 s'm = sm01− x

x'1 (A11)

Strains:

o'f = s'f − sTf

Efo'm = s'm − sT

m

Em(A12)

Displacements (at x= x':)

u'f = x'Ef$sf − sT

f +Vmsm

2Vf % u'm = x'Em0sm

2 − sTm1 (A13)

Matrix crack opening:

D=2(u'f − u'm)

=2x'$ 1Ef0 s

Vf− sT

f − tsx'rf 1+ 1

Em0sTm − tsx'Vf

rfVm 1%(A14)

Composite strain:

o= u'fx'=

1Ef0 s

Vf− sT

f − tsx'rf 1. (A15)