application of the cruciform specimen geometry to...

Application of the Cruciform Specimen Geometry to ObtainTransverse Interface-Property Data in a High–Fiber-Volume-Fraction SiC/Titanium Alloy Composite

C.J. BOEHLERT, B.S. MAJUMDAR, and D.B. MIRACLE

A combined experimental and computational methodology was used to determine the relevant strengthand residual-stress parameters in a manufactured, high–fiber-volume-fraction multiply metal matrixcomposite (MMC). The method was similar to that previously demonstrated on single-fiber composites,which had an extremely low fiber volume fraction. Variabilities in residual stresses and debondstrengths in high–fiber-volume-fraction multiply composites, as well as current demands on themicromechanics-based computational prediction and validation of complex composite systems, neces-sitated the establishment of the test methodology described here. The model material chosen forthis investigation was a plasma-processed six-ply, unidirectional Sigma-1240/Ti-6Al-2Sn-4Zr-2Mo(wt pct) MMC containing 32 vol pct continuous fibers. Room-temperature transverse tensile experi-ments were conducted on cruciform specimens. In addition, rectangular specimens were also evaluatedin order to verify their applicability in obtaining valid interfacial property data. Debonding events,evaluated at different positions within a given specimen geometry, were captured by stress-straincurves and metallographic examination. Analytical and finite-element stress analyses were conducted toestimate the geometrical stress-concentration factors associated with the cruciform geometry. Residualstresses were estimated using etching and computational procedures. For the cruciform specimens,the experimental fiber-matrix debond strength was determined to be 22 MPa. Separation occurredwithin the carbon-rich interfacial layer, consistent with some previous observations on similar systems.Thus, the cruciform test methodology described here can be successfully used for transverse interfacial-property evaluation of high–fiber-volume-fraction composites. For the rectangular specimens, thestrain gages at different positions along the specimen width confirmed that the interface crack hadinitiated from the free edge and propagated inward. Hence, rectangular specimens cannot be used forvalid interface strength measurements in multiply composites.

I. INTRODUCTION validation experiments on a single aluminum rod embeddedin an epoxy specimen have confirmed the effect of theTHE off-axis properties of continuously reinforced metalsingularity.[16]

matrix composites (MMCs) are dependent upon the abilityThe results of the single-fiber cruciform specimens haveof the interface to transfer load from the matrix to the fiber.

necessitated a re-evaluation of manufactured MMCsTherefore, the stress at which the fiber-matrix interfaceintended for structural application. They are high–fiber-vol-debonds is a critical parameter in design. Recently, a novelume-fraction (r) composites (typically, with r . 0.2) incruciform specimen geometry, which forces the maximummultiply configurations. Residual stresses and interfacialtensile stress at the fiber-matrix interface to occur at thedebond strengths may vary within the bulk of such MMCcenter of the cross (Figure 1(a)), was introduced to providesystems, due partially to uncontrolled fiber-matrix spacings.a means to obtain valid data on the fiber-matrix interfaceAlso, the average debond strength can differ from laboratorystrength for MMCs containing a single silicon carbide (SiC)specimens because of different fabrication processes.fiber.[1–5] This geometry overcame the major drawback ofAlthough one may argue that rectangular-geometry speci-previously used rectangular specimens,[6–11] where a tensile-mens would promote premature interfacial debonding andstress singularity exists at the fiber-matrix interface locationprovide a lower bound on strength, there are a number ofwhere the fiber intersects the free surface (Figure 1(b)).[12,13]

applications where fibers indeed may not be exposed to theThis stress singularity would produce premature interfacialfree surface. One example is the fiber-reinforced disk, wheredebonding near the free surface, thereby providing invalidfibers may be arranged in a helical fashion in a multiplyinterface data.[14,15] More recently, asymptotic analysis andconfiguration. In addition, there is a current thrust to usecomputational procedures to predict the performance ofangle-ply and woven composites, especially in polymer-C.J. BOEHLERT, Assistant Professor, is with the School of Ceramicmatrix and carbon-carbon systems. These approaches relyEngineering and Materials Science, Alfred University, Alfred, NY 14802.

B.S. MAJUMDAR, Associate Professor, is with the Department of on advanced computational characterization of interfaces,Materials Science and Metallurgy, New Mexico Institute of Mining and such as the use of Needleman’s cohesive zone models,[17,18,19]

Technology, Socorro, NM 87801. D.B. MIRACLE, Research Group Leader, and need validation of interface properties at high–fiber-is with the Materials and Manufacturing Directorate, Air Force Researchvolume-fraction multiply levels. Whereas past approachesLaboratory, Wright-Patterson AFB, OH 45433-7817.

Manuscript submitted May 7, 2001. for introducing new fiber-matrix systems in applications

METALLURGICAL AND MATERIALS TRANSACTIONS A U.S. GOVERNMENT WORK VOLUME 32A, DECEMBER 2001—3143NOT PROTECTED BY U.S. COPYRIGHT

(a) (b)

Fig. 1—(a) Cruciform specimen, showing that the free edges are stress-free and that the maximum stress occurs at the center. Thus, debond is forced tooccur away from any stress singularity location. (b) Illustration of a standard rectangular transverse specimen. Singularity at the fiber-matrix interface occursat the free edges.

relied on a large test-matrix database incorporating different geometries. Metallographic observations were used to iden-tify the separation location and rationalize the interface-fiber lay-ups, it is now realized that a more efficient method-strength data in terms what is known about carbon-richology is to use a computationally intensive micromechanics-interfaces.based approach utilizing data from simple unidirectional

multifiber configurations. Clearly, a test methodology needsto be established to obtain valid transverse fiber-matrix inter- II. EXPERIMENTAL PROCEDURESface-property data for high–fiber-volume-fraction multiply

The material system evaluated consisted of unidirectional,composites.100-mm-diameter Sigma-1240 fibers in a Ti-6Al-2Sn-4Zr-The present work extends the previous work on single-2Mo (wt pct) matrix. It is noted that the interfacial debondfiber cruciform specimens to a multiply MMC system manu- strength for this MMC system has not been previously char-

factured by a plasma-deposition process. The fiber volume acterized, either in single- nor multiply form. Sigma-1240,fraction considered (r 5 0.32) is typical of composites that produced by BP Metal Composites Ltd., United Kingdom,are intended for application in advanced aerospace systems. consists of SiC, which is chemical vapor deposited onto aBecause of the relatively high volume fraction of fibers, one tungsten filament substrate and has an outer coating (,3has to account for the anisotropic properties of the material. mm) made up of three layers. The initial two layers containThis was not an issue in past cruciform specimens. Residual carbon and TiB2, respectively. Due to the poor thermal-stresses were estimated in this work using etching experi- shock resistance of the TiB2 coating, which causes fiberments, and analytical and computational procedures were degradation during composite manufacture, a protectiveincorporated to determine the local stress at the fiber-matrix coating was developed to reduce this problem. This thirdinterface at the onset of nonlinearity of the stress-strain layer has a composition between that of TiB and TiB2.[20]

plot. In addition to the cruciform geometry, the effect of a The matrix material was a near-a a 1 b alloy. The six-plyrectangular specimen width, not evaluated previously, was composite was produced at Howmet (Whitehall, MI) byexamined for the multiply composites. The rationale was to plasma melting the Ti alloy powder to deposit the matrixevaluate their validity in obtaining interface-strength data material around a fiber array, precision wrapped around aand also to understand the progression of the debond from mandrel. Monotape lay-ups were subsequently produced bythe free edges to the specimen interior. The characteristic cutting and arranging the fiber-reinforced monotapes. Multi-

layered fiber-reinforced composite panels were produced bylocal debond stress was compared for the different specimen

3144—VOLUME 32A, DECEMBER 2001 METALLURGICAL AND MATERIALS TRANSACTIONS A

(a) (b)

Fig. 2—The geometry of the (a) cruciform and (b) wide-uniform rectangular specimens (not drawn to scale) indicating the positions of the strain gages.L and T represent the long and transverse strain gages, respectively. Tensile loading was applied along the vertical axis and the fibers were aligned alongthe horizontal axis.

hot consolidation of monotape lay-ups using a hot isostatic perpendicular to the fiber from the consolidated, unidirec-tionally reinforced MMC panel using a wire electrodischargepressing procedure at 105 MPa/954 8C for 4 hours. No

attempt was made to change the as-processed interfacial machine (EDM). The EDM surface layers were removedthrough polishing with consecutively finer grits of SiC papercondition.

The axial residual stress in the fiber was measured using (up to 600 grit) prior to testing. The following specimengeometries were machined: (1) a rectangular specimen ofan etching procedure. A 28 3 10 mm rectangular section,

with the long axis along the fiber direction, was diamond cut a 23 mm uniform width (designated as the wide-uniformspecimen), (2) a rectangular specimen of an 8 mm uniformfrom the composite panel. The edges were slightly beveled so

that the fiber centers could be observed under an optical width (the narrow-uniform specimen), and (3) a cruciformspecimen. Figures 2(a) and b depict the geometry of themicroscope, which was fitted with a precision micrometer

stage. The center-to-center distance between the ends of cruciform and wide-uniform specimens, respectively. Ten-sile loading was applied along the vertical axis, and theindividual fibers (i.e., the gage length) was measured to a

resolution of 1 mm. The faces of the coupon were partially fibers were aligned along the horizontal axis. As indicatedearlier, the cruciform geometry isolates the free edges in themasked with a lacquer, such that the mask strip was 0.5-

mm wide and stretched across the entire 10 mm width of horizontal arm from the applied mechanical load, while thecentral portion is highly stressed. Thus, debond initiationthe sample. The rationale was that this thin matrix strip

would hold the fibers in place after the matrix in the and propagation is forced to occur in the center of the cross,away from the free edges. Small fillets were used on theremaining regions was fully dissolved. A modified Kroll’s

etch, which contained a slightly higher-than-normal concen- inside corners of the cross to ensure that they had minimaleffect on the stress in the central region. However, there istration of HF, was used to dissolve the matrix. The lengths

of 50 individual fibers were compared before and after disso- a significant stress concentration at the free surfaces of theuniform section of the vertical arm due to the exposed fiberslution to provide an averaged total axial strain associated

with loss of constraint by the matrix. Poisson’s effect was present. Thus, debonding is likely to occur in the verticalarms prior to debonding in the center of the cross. As longincluded in obtaining the axial residual stress in the fiber

from the measured axial strains. From the axial residual as the former debonding does not lead to immediate failureof the specimen, the strain at the center of the cross can bestress, the residual radial stress in the fiber was obtained

using the theoretical relation between the axial and radial used to identify the onset of the debonding (from a knee in thestress-strain plot) that is free from edge effects. In addition tostress in a thermally stressed concentric-cylinder model.

Mechanical test specimens of 100 mm in length were cut the composite specimens, a monolithic Ti-6Al-4V (wt pct)

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 32A, DECEMBER 2001—3145

specimen was tested in the cruciform geometry, and thestress-strain behavior was compared to the composite data.This specimen also provided a validation for the stress analy-sis for a matrix-only specimen.

Room-temperature (RT) tensile experiments were per-formed using an Instron servohydraulic test frame anddisplacement rates between 7.5 3 1022 and 1.8 3 1021

mm/s. Both uniaxial and biaxial strain gages were utilizedat various locations to help detect the onset of fiber-matrixdebonding. A single uniaxial strain gage, containing anactive area of 3 3 3 mm, was placed on the surface of thenarrow-uniform specimen’s face halfway along its length.For the wide-uniform specimens, a biaxial strain gage, withan active area of 2 3 2 mm, was placed at the midplanecenter, and uniaxial strain gages were placed across thespecimens’ width (Figure 2(b)). For the cruciform geometry,biaxial strain gages were applied to the center of the horizon-tal arm and in the uniform section of the vertical arm (Figure2(a)). Mechanical tests were performed to failure. After test-ing, the specimens were sectioned and polished normal tothe fiber axis and in a plane which contained both the fiberand the loading axis. In addition, fracture surfaces provided (a)information on the debonding and failure events. All suchsamples were evaluated using optical microscopy and aLeica 360 FE scanning electron microscope (SEM).

In addition to microscopy, the stress-strain responses wereused to assess debonding. This technique, which has beenpreviously used in studies of single-fiber and multifibercomposites,[1–8] relies on determining the onset of debondingfrom (1) a knee in the stress-strain curve, and (2) a sharpchange in the Poisson’s ratio as a function of the appliedstress. The same approach was used here, and, in particular,an incremental method was used to determine the onset ofthe slope change in the initially linear stress-strain plot. Forthe cruciform data, the debond stress was converted into aninterfacial debond strength using the experimental data fromthe biaxial strain gages along with stress-strain analysis fororthotropic lamina and finite-element analysis (FEA). Thegeometrical stress-concentration factors (SCFs), associatedwith the cruciform geometry and the matrix-embedded circu-lar fiber, were evaluated by FEA. The local radial stress atthe fiber-matrix interface was, thereby, obtained by multi-plying the overall SCF with the applied stress and subtractingthe local radial residual stress.

(b)III. RESULTS Fig. 3—SEM images of the as-processed Sigma-1240/Ti-6Al-2Sn-4Zr-

2Mo composite indicating the (a) fiber distribution and the (b) well-consoli-A. As-Processed Microstructure dated interfacial region.

Figure 3(a) illustrates the as-processed composite micro-structure. The fiber distribution was not uniform, and, insome cases, the edge-to-edge distance between neighboring 0.75-mm-thick layer consisted of a needle-like TiB2 structure

and was uniformly distributed. The third layer ranged infibers within a ply was less than 20 mm. These local high–fiber-volume-fraction regions introduce large residual thickness between 0.25 and 1 mm and was surrounded by

the reaction zone enriched in a-phase titanium. Diffusionstresses and were responsible for isolated radial cracks, aswill be described later. The overall fiber volume fraction of boron and/or carbon, both a-phase stabilizers,[21] most

likely played a role in enriching the a phase. Carbon diffu-was 0.32 6 0.1. Figure 3(b) depicts the interfacial region,which consisted of the three layers of the fiber coating and sion has similarly affected the reaction zone in SCS-6/Ti-

6Al-4V (wt pct)[22] and SCS-6/Ti-25Al-17Nb (at. pct) com-the approximately 1.5-mm-thick reaction zone between thematrix and the outer coating. The initial 1.3-mm-thick layer posites.[23] Outside the reaction zone was a ring of b phase

(the white region of Figure 3(b)). In general, the interfacesurrounding the SiC was richest in carbon and, although itwas typically uniform, there were cases in which it extended was well consolidated. However, in some regions, concen-

trated traces of Mo and Zr were found between the C-richto 2.0 mm and had a “bumpy” appearance. The intermediate


(a) (a)

(b)

Fig. 4—Stress vs strain plots for the wide-uniform rectangular (a) U9 (b)and (b) U11 [90]6 composite specimens. The location of the strain gagesare indicated.

layer and the reaction zone. This was most likely a resultof the plasma matrix deposition technique. In some cases,fine radial cracks were present within the reaction zone,most likely a result of the large residual stresses developedduring fabrication in locations of nearly touching fibers. Thematrix contained approximately 80 vol pct of a phase, withb-phase islands primarily dispersed at a grain boundaries.

B. Stress-Strain Behavior

The stress-strain plots for two wide-uniform specimens(U9 and U11) are shown in Figures 4(a) and (b). SpecimenU9 contained a uniaxial strain gage located at the specimenedge and a biaxial strain gage located in the center (Figure2(b) illustrates the locations of the respective strain gages). (c)Specimen U11 contained one uniaxial strain gage very close

Fig. 6—Stress vs strain plots for the (a) T1 and (b) T2 cruciform [90]6to the edge and another in-between the edge strain gagecomposite specimens where the locations of the biaxial strain gages wereand the central biaxial strain gage (designated as midedge). within the uniform section of the vertical arm (referred to as Uniform) and

Figures 4(a) and (b) show that the local strain near the the center of the horizontal arm (referred to as Wing). Also illustratedsample edge is always greater than or equal to that for the in (c) is the stress-strain response of the monolithic Ti-6Al-4V (wt pct)

cruciform specimen.interior strain gages. No noticeable strain jump was observed


Table I. RT Tensile Properties of Composite and Monolithic Specimens

Geometry, Specimen, Strain-GageLocation sonset* (MPa) «onset* (Pct) Et** (GPa) ytl at s 5 100 MPa ytl at s 5 325 MPa

narrow-uniform, U2, center 255 0.18 148 na nawide-uniform, U9, center 284 0.18 160 0.22 0.21wide-uniform, U9, edge 266 0.18 151 na nawide-uniform, U11, center 299 0.20 155 0.21 0.20wide-uniform, U11, edge 279 0.20 152 na nawide-uniform, U11, midedge 286 0.19 157 na nacruciform, T1 uniform† 285 0.20 155 0.25 0.23cruciform, T1 wing‡ 308 0.21 150 0.31 0.31cruciform, T2 uniform† 246 0.17 159 0.21 0.19cruciform, T2 wing‡ 277 0.18 156 0.32 0.31cruciform, Ti-6Al-4V§ uniform 516 0.65 86 0.29 0.30cruciform, Ti-6Al-4V§ wing 494 0.60 84 na na

*Onset refers to the onset of nonlinearity observed using the longitudinal (i.e., loading direction) strain gage data.**Calculated using the applied remote stress and the local strain.†Uniform refers to the gage placed in the uniform-width region of the vertical arm.‡Wing refers to the gage placed in the center of the horizontal arm.§Data from monolithic specimens.na: not available.

in the multiply composites, unlike that for single-fiber where w 5 (h 2 1)/(h 1 j) [2]MMCs.[1–4] Therefore, the debonding event was correlated and h 5 Ef /Em [3]with the onset of nonlinearity in the stress-strain curve. This

in which Em and Ef are the elastic moduli of the matrix andmethod introduces larger errors than those in which a strainfiber respectively, and r is the fiber volume fraction. Thejump is detectable. However, the use of an incremental-value of j is between 0.5 and 2, and for the current study,slope method helps to keep the error low and provides aa value of 2 was used. The values of Ef and Em were assumedconsistent method of establishing a debond event. Specifi-to be 390 and 102 GPa, respectively; the latter is the averagecally, the incremental slope is plotted vs the applied stress,of data taken for plasma-processed Ti-6Al-2Sn-4Zr-2Mo (wtand the point where it deviates from a constant value ispct).[26,27] A value of 390 GPa has been used in the literatureeasily detectable.for BP Sigma-1240 fibers[5,20,28] and is based on actual modu-For specimen U9, the far-field applied stress at the onsetlus measurements.of nonlinearity was determined to be s 5 266 MPa for the

For the narrow-uniform specimen (U2), the onset of non-edge and s 5 284 MPa for the center gage. The correspond-linearity occurred at s 5 255 MPa and « 5 0.18 pct (Table Iing local strains were the same for both gages: « 5 0.18and Figure 5). Taking into consideration the scatter observedpct. For specimen U11, the onset of nonlinearity occurredbetween specimens, these values more closely resembleat s 5 279 MPa for the edge and at s 5 299 MPa for thethose from the edge locations of the wide-uniform speci-center gage. Once again, the local strains at debonding weremens. The stress/strain behavior of the composite cruciformthe same: « 5 0.20 pct. The onset of nonlinearity for thespecimens (T1 and T2) indicated differences between themidedge of specimen U11 occurred at a stress (s 5 286strain gage placed in the uniform section of the vertical armMPa) intermediate between the edge and center locations.and that placed at the center of the horizontal arm (FiguresComparing the data for the center gages from the two speci-6(a) and (b)). The strain at the cruciform center was alwaysmens, a 15 MPa difference (or approximately 5 pct of theless than or equal to that in the uniform of the vertical arm,stress value) in the applied stress at the onset of debondingand the onset of nonlinearity also occurred at higher stressesis observed. In addition to the comments in the previousand strains in the cruciform center. The onset of nonlinearityparagraph regarding data scatter, the stress difference mayat the center of the cross occurred at s 5 308 MPa andbe related to the different fiber distributions from specimen« 5 0.21 pct and at s 5 277 MPa and « 5 0.18 pct forto specimen.specimens T1 and T2, respectively. Correspondingly, theTable I lists the corresponding sonset, «onset, primary modu-onset of nonlinearity in the vertical arms occurred at s 5lus Et (determined using the applied stress and measured285 MPa and « 5 0.20 pct and at s 5 246 MPa and « 5local strain in the loading direction), and Poisson’s ratio (ytl) 0.17 pct for specimens T1 and T2, respectively. Althoughvalues at applied stresses of s 5 100 and 325 MPa. The ytl there is variation in the data from the two specimens, forvalues, measured from the biaxial strain gages in the centereach specimen, the difference in the far-field applied stressof the specimens, decreased with increasing stress aboveat the onset of nonlinearity is more than 20 MPa between250 MPa for both of the wide-uniform specimens, indicativethe gages at the cruciform center and the vertical arm. Aof a debonding event. The value of Et differed slightly fromslightly higher primary modulus, calculated using the appliedthe edge to center locations, ranging between 151 and 160stress, was measured within the uniform section of the verti-GPa. A value of 158 GPa is predicted using the Halpin–cal arm compared to the cruciform center (Table I). This isTsai equation:[24,25]

mainly due to a slightly complex stress state in the centerEt /Em 5 (1 1 jwr)/(1 2 wr) [1] of the cruciform, as is explained in Section IV.A.


Fig. 7—The fracture surface of the T1 cruciform specimen, which brokewithin the uniform section of the vertical arm near the fillet, indicatingFig. 5—Stress vs strain plot for the narrow-uniform rectangular U2 [90]6separation within the C layer and ductile dimpling within the matrix.composite specimen.

along the centerline of the horizontal arm.[2] In the currentComparing the data from all the composite specimens, material, failure in the fillet region occurred after debonding

the largest applied stress at the onset of nonlinearity, s 5 had initiated in the center of the cruciform specimen. There-308 MPa, occurred at the cruciform center for specimen T1. fore, it was possible to obtain a valid interface strengthThe lowest stress at the onset of nonlinearity, s 5 246 measurement from the current experiments. For a higherMPa, occurred in the uniform section of the vertical arm of fiber-matrix strength or lower matrix ductility, this situationcruciform specimen T2. The strains at the onset of nonlinear- may not always be realized. In such cases, additional geomet-ity were less widely dispersed and ranged between 0.17 and ric modifications, such as reducing the thickness at the cruci-0.21 pct. form center, may have to be incorporated to obtain valid

For the monolithic Ti-6Al-4V (wt pct) cruciform speci- bond-strength data.men, the stress-strain behavior was almost identical for the Fracture of the uniform-width rectangular specimenstwo strain-gage locations (Figure 6(c)). The onset of nonline- always occurred along the length of a single fiber or rowarity occurred at much greater stresses and strains compared of fibers. In each case, failure occurred after the knee in theto the composite specimens, and, considering the magnitude stress-strain curve was reached and always between 0.3 andof the stresses and strains, a smaller deviation between the 0.6 pct. Figure 7 shows the fracture surface of cruciformonset of nonlinearity at the two locations was observed for specimen T1, which failed in the uniform section, close tothe monolithic material compared to the composite. In fact, the fillet. The fiber surface shows bumps that are characteris-an opposite trend to that of the composites was exhibited, tic of chemical vapor–deposited grown fibers. Energy-where the onset of nonlinearity occurred at higher stresses dispersive atomic X-ray analysis revealed that this surfaceand strains in the uniform region of the vertical arm com- contained little, if any, Si or Ti, indicating that failure hadpared to the cruciform center (Table I). This is due to a occurred primarily in the carbon layer. The opening betweencompressive stress along the horizontal arm, as will be dis- the TiB2 layer and the fiber suggests that failure may havecussed in Section IV.A. Figure 6(c) also shows a different occurred at the interface between the C and TiB2 layer.Poisson’s ratio for the two locations, and this is a result of However, cross section samples revealed that failurea biaxial stress state at the cruciform center. occurred within the C layer, either close to the TiB2 layer

or close to the base SiC fiber surface. Figures 8(a) and (b)represent the debond crack for a polished section at locations

C. Debond Observations of more than 15 fibers away from the fracture surface. Figure8(a) illustrates a region where several cracks formed withinFracture for both the cruciform specimens occurred in the

uniform section of the vertical arm, very close to the fillet. the C layer. This was unusual, and typically a single C-layercrack formed close to the C/TiB2 interface (Figure 8(b)). InThis was a result of the higher stress concentration near the

fillet, aided by earlier debond initiation at the fiber-matrix many cases, the C-layer crack traversed the entire fiber. Thewidth of the debond crack was as large as 0.5 mm in polishedinterface at the free edges (due to stress singularity). This

fracture behavior was unlike that of single-fiber cruciform fracture surfaces close to the free edge (Figure 9). Althoughsome reaction-zone cracks existed in the untested material,specimens where no fibers were present in the uniform sec-

tion of the vertical arm, so that debonding and subsequent an extensive amount of reaction-zone cracks, some of whichwere linked to the C-layer cracks, were found in the testedplasticity-induced damage in those specimens were localized


(a) Fig. 9—C-layer cracking for a fiber two fiber spacings away from thefracture surface for a wide uniform-width rectangular specimen.

Fig. 10—Reaction zone cracking for a tested narrow-uniform rectangularspecimen indicating radial cracks transgressed the a-enriched zone andwere blunted by the b ring.

between post-tested specimens and the as-processed(b)composite.Fig. 8—SEM images of the cracking exhibited within the C layer at loca-

tions of more than 15 fibers away from the fracture surface. The loadingdirection was horizontal where (a) represents the top of the fiber and (b) IV. ANALYSIS FOR DETERMINATION OFrepresents a section 90 deg with respect to the loading direction.

BOND STRENGTH

This section is divided into three parts. In the first part,the experimental stress-strain data from the rectangular spec-

specimens (Figure 8(a)). Wider cracks connected the imens, as well as similar data from the uniform-width (verti-debonded layers of adjacent fibers located less than 20 mm cal-arm) region of cruciform specimens, are combined withapart. More frequently, smaller cracks were found emanating lamina analysis for unidirectional composites to determinefrom the a-enriched reaction zone (dark) to the b ring stiffness coefficients for the current orthotropic laminate. It(white), as shown in Figure 10. Generally, the b-ring blunted was assumed that in the uniform-width regions, the stresssuch cracks. The matrix exhibited a ductile fracture (Figure perpendicular to the fibers was the applied stress, and the7). It is noted that in the outer locations of the horizontal stress parallel to the fibers was zero. In the center of thearm of cruciform specimens, where a much smaller stress is cruciform, a biaxial stress exists. Those stresses were

obtained from the measured strains, taken from the biaxialapplied (Figure 1(a)), no noticeable difference was observed


gage at the cruciform center, using the same stiffness matrix. kl 5 «l /sa [9]Having thus obtained the local stress perpendicular to the

From the stress-strain slopes prior to any debonding infiber at the center of the cruciform, the interface radialthe uniform-width regions, we obtain Et 5 157 GPa andstress was obtained by multiplying that stress by a stress-ytl 5 0.23. The value of El was calculated using the rule-of-concentration factor (due to a stiff fiber embedded in amixtures equation,matrix).

In the second part of this section, FEA was conducted at El 5 rEf 1 (1 2 r)Em [10]two levels. First, a cruciform specimen was analyzed based

This led to a value of El 5 194 GPa. Using the relationshipon homogenized stiffness coefficients for the lamina. Plane-stress analysis was used, and good agreement was obtained ylt 5 ytl(El)/Et [11]between the FEA-calculated local stress at the cruciform

a value of ylt 5 0.28 was calculated. The value of Q11 wascenter and that from the strain-gage data and laminate analy-then calculated using the relationship listed previously, andsis. Second, a plane-strain unit cell FEA was conducted forthe Q22 and Q12 values were then calculated according tothe fiber-matrix system so as to obtain the local radialEqs. [6] and [7]. The Q22 and Q12 values agreed with thestresses along the periphery of the fiber.values based on the expressions given after Eq. [5].In the final part, the thermal residual stress was calculated

Within the center of the horizontal arm, the constraintsat the fiber-matrix interface, based on the etching experi-of Eqs. [6] and [7] do not apply; i.e., the right-hand sidesments. Axial stresses were obtained from the etching experi-of Eqs. [6] and [7] are no longer 1 and 0, respectively. Inments, and, therefore, a factor was needed to estimate theother words, the local nondimensional stresses, st/sa andlocal thermal radial stress from the measured thermal axialsl/sa , need to be calculated. The values of the stiffnessstress. This factor was obtained using a concentric cylindercoefficients (Q11, Q22, and Q12) remain the same. The valuesmodel. There was good agreement between the radial stressof Kt , and Kl were obtained from the slopes of the strainsthus measured and the limited radial-stress measurements«t and «l as a function of the applied stress, sa (applied loadthat had been conducted on similar materials using neutrondivided by the cross-sectional area in the uniform-widthscattering techniques.[29] To arrive at the tensile bondregion of the vertical arm). Here, the strains were obtainedstrength of the fiber-matrix interface, the thermal-stress con-from the biaxial strain gages located at the cruciform center,tribution was then subtracted from the local stress due toand the slope was taken before the knee in the stress-strainthe applied load.curve. In this way, the following geometric stress factorswere obtained: st/sa 5 0.98 and sl/sa 5 20.12, where

A. Stiffness Coefficients and Determination of Local st and sl are the local stresses at the cruciform center,Stresses from Strain-Gage Data perpendicular to the fiber direction and parallel to the fiber

direction, respectively. There are two important points toConsider the strains measured in the rectangular speci-note here. First, the local stress in the loading directionmens and in the uniform-width (vertical arm) regions of theis very close to the stress in the uniform region, a usefulcruciform specimens. Designating the strains in the loadingcharacteristic of the cruciform specimen. Second, there is a(transverse-to-the-fiber direction) and perpendicular-to-compressive stress along the fiber direction. However, thisloading (fiber direction) directions as «t and «l , respectively,value is low and is not anticipated to have any major effectone can use orthotropic equations (for example, those ofon the debond stress through a Poisson’s effect. RecollectAgarwal and Broutman[25]) to calculate the stresses in thethat the average measured apparent Poisson’s ratio at theloading (st) and perpendicular-to-loading (sl) directions,center of the cruciform (ytl 5 0.315) was higher than in theaccording touniform section (ytl 5 0.23), and this was a direct conse-

st 5 Q12«l 1 Q22«t [4] quence of the biaxial stress state at the cruciform center.sl 5 Q11«l 1 Q12«t [5]

B. Finite-Element Analysis of the Anisotropic Cruciformwhere Q11 5 E1/(1 2 yltytl), Q22 5 Et/(1 2 yltytl), Q12 5 yltSpecimen and Unit-Cell AnalysisE1/(1 2 yltytl), and El and Et are the elastic modulus of the

composite in the longitudinal direction (i.e., fiber direction) Plane-stress analysis was conducted for the cruciformand the transverse direction, respectively. The major specimen. A homogenized material with the followingPoisson’s ratio, ylt , is the transverse strain caused by a longi- properties was considered: El 5 194 GPa, Et 5 157 GPa,tudinal strain (i.e., by loading only in the longitudinal direc- ylt 5 0.28, and ytl 5 0.23; refer to the previous sectiontion), and the minor Poisson’s ratio, ytl , is the longitudinal regarding the basis for these constants. In addition, thesestrain caused by a transverse strain (i.e., loading being only values were very close to results obtained using unit-cellperpendicular to the fiber direction). Dividing Eqs. [4] and analysis for the fiber-matrix system, the constituent proper-[5] by the applied stress in the loading direction (sa) and ties, and the fiber volume fraction.considering that the stress in the fiber direction is zero for Figure 11(a) shows the geometry that was analyzed, andthe uniform-width region, we have Figures 11(b) and (c) illustrate the stresses along the loading

direction and perpendicular-to-loading direction, respec-st /sa 5 Q12kl 1 Q22kt 5 1 [6]tively. Figure 11(b) shows that the wings of the cruciform

sl /sa 5 Q11kl 1 Q12kt 5 0 [7] specimen are indeed unloaded, and that the stress in theloading direction is fairly uniform around the cruciformwhere Kl and Kt are constants, defined ascenter. The maximum stress in this region is 0.95 times the

kt 5 «t /sa [8] applied stress, which is close to 0.98 as deduced in the


(b)

(a) (c)

Fig. 11—(a) Finite element model for calculating stresses in the anisotropic cruciform specimen. (b) Contour plot of stress (sxx) in the loading direction.(c) Contour plot of stress (syy) perpendicular to the loading direction. Note that the stress is negative at the center.

previous section. However, the overall maximum stress in loading face was integrated to obtain an average stress forthat face. The stresses along the fiber-matrix interface werethe loading direction occurs at the fillet and is approximately

1.5 times the applied stress. In single-fiber MMC specimens, then normalized with respect to that stress and plotted, asshown in Figure 12(b). In this plot, the angle u is measuredthis higher stress did not have any major effect, since local

plasticity occurred and was overshadowed by the long dam- from the loading line. The maximum radial stress obtainedwas 1.348 times the far-field average stress, and this isage region along the fiber-matrix interface. In the multifiber

specimen, however, the presence of fibers in the fillet region consistent with results in other multifiber systems.[28] Figure12(b) shows a slightly nonsymmetric stress pattern for themade the location vulnerable, and it was here that failure

initiated. Figure 11(c) shows the stress profile perpendicular tangential stress, and this is a result of the rectangular geome-try and the slightly nonsymmetric loading pattern.to the loading direction. The stress was compressive in the

central region, with a maximum value of 20.138 times thefar-field stress (sa). This value is comparable to that of

C. Residual-Stress Calculation and Bond Strength20.12 obtained in the previous section. Also, the apparent

DeterminationPoisson’s ratio was 0.33, which was close to the value of0.315 measured experimentally. A simple concentric cylinder model (CCM)[30] was used

to calculate the axial and radial residual stress in the fiberPlane-strain unit-cell FEA was also conducted for thefiber-matrix combination. The geometry is illustrated in Fig- using the constitutive properties and the imposed tempera-

ture differential. For the sake of simplicity, the analyticalure 12(a). Symmetric boundary conditions were used asshown. At the loading face, a uniform displacement, rather results are presented for the case where the elastic modulus

is independent of temperature and the Poisson’s ratio (y) isthan a constant stress, was imposed. The remaining edgewas considered to be stress free, given the thin section for identical for the fiber and the matrix. Given that the largest

source of uncertainty is the stress-free temperature, thethe composite. A fine mesh was used, particularly at thefiber-matrix interface. Following FEA, the stress along the effects of these two assumptions are small. The following


properties used for the constituents were Ef 5 390 GPa,Em 5 102 GPa, n 5 0.25 (a compromise between that ofthe fiber (0.22) and the matrix (0.3), and r 5 0.32. Theseprovide a ratio of 0.33. Multiplying this value by 21097MPa, our experimental estimate of the radial stress in thefiber is s f

rr 5 2362 MPa. Note that this value is higher thanthat for the SCS-6/Ti-6A1-4V system (s f

rr , 2300MPa)[2,28] and is likely related to the improved high-tempera-ture strength of the alloy.

Using the processing temperature of 954 8C and thethermal-expansion coefficients of 4.65 3 1026/8C and12.06 3 1026/8C for the fiber and matrix, respectively,[27]

the calculated radial and axial residual stresses using theCCM (Eq. [13]) are s f

rr 5 2347 MPa and s fzz 5 21052

MPa. These values are in good agreement with the values(a) quoted previously. Neutron-diffraction experiments on a

similar system, SCS-6/Ti-6Al-2Sn-4Zr-2Mo (wt pct) with 31vol pct fibers, provided axial and radial residual compressivestresses of 823 6 21 and 414 6 15 MPa, respectively.[29]

While the former is low, the latter is closer to what wasassessed in our material.

At this point, the following equation was used to determinethe bond strength of the fiber-matrix system:

sbond 5 Kslocal 1 sresidual [14]

where slocal (equal to k1 * sfar) is the local stress in theloading direction at the center of the cruciform, K (equal to1.35) is the stress-concentration factor from the unit cell,and sresidual is the radial residual stress (2362 MPa) deducedfrom the etching experiments. The value of k1, a factor whichrelates the local stress at the cruciform center to the far-fieldapplied stress, was taken to be 0.97 (i.e., averaged betweenthe strain-gage data (0.98) and the computational result(0.95)). Based on the average of the two cruciform experi-

(b) ments, sfar 5 293 MPa. Using these values, the bond strengthfor the Sigma-1240/Ti-6Al-2Sn-4Zr-2Mo system is deducedFig. 12—(a) Unit cell model for calculating the stresses along the fiber-to be sbond 5 22 MPa. The low value agrees well with thatmatrix interface. (b) Results from unit cell FEA analysis illustrating how

the stresses vary around the circumference. measured for the interfacial strength of a Sigma-1240/7040glass ceramic matrix composite (CMC): sbond , 5 MPa.[31]

results are obtained (refer, for example, to Majumdar et V. DISCUSSIONal.[31]): As indicated in the introduction, the rationale for testing

high–fiber-volume-fraction multiply cruciform specimens isthat the bond strength needs to be obtained from manufac-

s frr 5

1 1 hr

1 2 r

1 1 h1 1 r1 2 r

s fzz [12] tured composites rather than from laboratory-scale, single-

and multifiber single-ply specimens. This is because manu-facturing processes introduce residual stresses and bondstrengths that may be different from laboratory specimens,

s frr 5

(1 2 r)hEmDaDT

(1 2 r)(1 2 2n) 2 2 rnh 1 (1 1 r)h[13] even for the same fiber-matrix system. The experimental

results and analysis show that, indeed, valid bond-strengthdata can be obtained, and, thereby, establish a methodologywhere Da 5 (am 2 af), am and af being the coefficients of

thermal expansion for the matrix and fiber, respectively; and for obtaining such data. The use of biaxial gages at differentlocations within the cruciform specimen, the use of an etch-DT is the stress-free temperature (often referred to as the

processing temperature) minus the current temperature. ing procedure for residual-stress measurements, and theapplication of CCM analysis all provide a simple means ofEquation [12] shows that the ratio of the radial residual

stress in the fiber (s frr) to its axial residual stress (s f

zz) is obtaining bond-strength data from multiply specimens.In addition to the cruciform specimens, uniform-widthprimarily dependent on the fiber volume fraction and the

ratio of Ef to Em. Since these values are well known for the rectangular specimens were tested to evaluate debond propa-gation from the free edges and to assess their usefulness incurrent materials, the radial residual stress can be deduced

from the axial residual stress. The latter was obtained in the obtaining bond-strength data. The results show that, indeed,the stress singularities associated with specimen edges docurrent work using etching experiments, which provided

a compressive axial residual stress of 21097 MPa. The significantly effect the onset of debonding. The primary


transversely loaded SCS-6/Ti-6Al-2Sn-4Zr-2Mo (wt pct)composite containing 32 vol pct fibers[32] and, more recently,in Sigma-1140/Ti-6Al-4V (wt pct) single-fiber cruciformexperiments[34] and Sigma-1140/Ti-6Al-4V (wt pct) com-posites containing 8 and 21 vol pct fibers.[34,35,36] Thus, theC layer appears to be a weak link in both the MMC andCMC interfaces. In the current material, failure in the carbonlayer occurred in a number of locations, indicating similarstrength throughout the carbon layer. However, the chemicalmakeup of the carbon layer may be important, and both pureturbostratic carbon layers and varying C and SiC concentra-tions have been observed from the innermost C layer (i.e.,closest to the SiC) to the outermost C layer.[37,38] This may beone reason why other MMC systems have exhibited greaterinterfacial strengths, and failure within the C layer has not

Fig. 13—SEM image illustrating normal interface separation in the vicinity been observed. For example, the measured interfacialof a radial matrix crack in a high fiber volume fraction Sigma-1240/7040 strengths of SCS-6/Ti-6Al-4V (wt pct) and Trimarc-1/Ti-glass composite; the interface crack is located within the carbon layer close

6Al-4V (wt pct) are 115 to 160 and 70 6 30 MPa, respec-to the SiC interface.tively.[3,5,28,39] It is useful to note that in the current system,no failure occurred at the TiB2/carbon interface. Thus, this

indication of this is represented by the noticeably different coating appears to be a good one for bonding to carbona-stress-strain responses at different locations within the cruci- ceous coatings.form and rectangular specimens. For the cruciform speci-mens, the onset of nonlinearity for the uniform section of

VI. CONCLUSIONSthe vertical arm occurred at significantly lower stresses thanthose in the center section of the horizontal arm. For the Using a cruciform test-specimen geometry demonstratedwide-uniform rectangular specimens, the stress at the onset previously on single-fiber composites, this work was theof nonlinearity for edge locations was lower than that in the first to verify the combined experimental and computationalcenter, whereas edges always experienced strains greater methodology to determine the relevant average interfacialthan or equal to those at interior locations. These results strength and residual-stress parameters in a manufactured,confirm that debonding initiates at the free edges and propa- high–fiber-volume-fraction multiply MMC. The methodol-gates inward. The stress-strain response of the narrow-uni- ogy incorporated the following: (1) nonlinearity of the stress-form rectangular specimen more closely resembled that of strain curve to identify the onset of debonding, (2) simplethe wide-uniform edge locations and was also similar to that analytical and computational procedures to determine theof transverse tests of other SiC fiber/Ti matrix composite local stress at the fiber-matrix interface at debond initiation,specimens containing fibers exposed to the free sur- (3) etching experiments to determine residual stress at thefaces.[10,11,32] It may be noted that the center strain gage in the fiber-matrix interface, and (4) metallography to identify thewide-uniform rectangular specimens did indicate interface interfacial separation location. Together, they provided adebonding at strains that were comparable to the center of benchmark for the applicability of this technique to othercruciform specimens. However, there was data scatter, and manufactured multiply composites intended for practicalthere is always the possibility that the free edges might engineering applications. Such a methodology will be essen-influence the bond-strength results. Hence, the cruciform tial for validation of advanced cohesive-zone models in com-specimen appears to be the only dependable geometry for plex composite systems.extracting the bond strength from composite samples. The experiments performed on rectangular specimens,

The geometrical factor associated with the cruciform containing both narrow and wide widths, filled a gap thatgeometry was very close to unity, indicating the small effect existed in the previous literature on transverse interface prop-on local stresses within the cross of the cruciform. By sub- erties. The tests confirmed that debond initiation occurs attracting the measured radial residual stress from the meas- the free edges and propagates inward for all such specimens,ured value of the local applied stress at the onset of and, therefore, that the rectangular geometry is not reliablenonlinearity within the cross of the cruciform, an interfacial for obtaining accurate fiber-matrix bond-strength data. Fordebond strength of 22 MPa was determined. This value the current six-ply Sigma-1240/Ti-6Al-2Sz-4Zr-2Mo (wtagrees well with that measured for the interfacial strength pct) plasma-processed composite, the fiber-matrix bondof a Sigma-1240/7040 glass CMC,[31] where the strength strength was 22 MPa and debonding failure was observedwas estimated to be approximately 5 MPa. Similar to the to occur within the C-rich interfacial layer. Although nocurrent material, in that case, too, failure was observed in interfacial-strength data exist for this MMC system in eitherthe carbon layer, but very close to the SiC surface. Figure single- or multiply form, these results are consistent with13 shows fracture in the carbon layer for that system. The some previous observations on CMC systems containingfailure was caused by a nearby radial crack, but the location both Sigma and SCS-6 fibers.of failure is clearly visible. In another CMC, SCS-6/Si3N4,the interfacial strength was between 5 and 18 MPa, and the

ACKNOWLEDGMENTS100-nm-thick pure turbostratic carbon layer between the twooutermost carbon layers was the preferred failure site.[33] The experimental work was performed at the Wright-

Patterson Air Force Research Laboratory (AFRL) MaterialsFailure within the C layer has also been observed for a


16. G.P. Tandon, R.Y. Kim, S.G. Warrier, and B.S. Majumdar: Composites,and Manufacturing Directorate under Air Force Contract1999, vol. 30B, pp. 115-34.Nos. F33615-91-C-5663 and F33615-C-96-5258 to UES,

17. A. Needleman: Int. J. Fract., 1990, vol. 42, pp. 21-40.Inc. The authors thank Dr. Kevin Kendig (Air Force 18. P.H. Guebelle: Int. J. Solids Struct., 1995, vol. 32, pp. 1003-16.Research Laboratory) for helpful discussions and Mr. 19. S. Ghosh, Y. Ling, B.S. Majumdar, and R. Kim: Mech. Mater., 2000,

vol. 32, pp. 561-91.Nicolas Wolfe (New Mexico Tech) for assistance with20. R. Shatwell: DERA, Farnbrough, United Kingdom, private communi-metallography. One author (CB) acknowledges the support

cation, 1998.received from Los Alamos National Laboratory (Contract 21. E.W. Collings: The Physical Metallurgy of Titanium Alloys, ASM,No. W-7405-ENG-36) and another author (BM) acknowl- Materials Park, OH, 1984, p. 16.

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24. J.C. Halpin and S.W. Tsai: U.S. Air Force Materials Laboratory ReportNo. AFML-TR-67, Wright-Patterson Airforce Base, OH, 1967, p. 423.

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