Extraction of interface properties from a fiber push-out test

Scripta METALLURGICA et MATERIALIA

Vol. 25, pp. 2457-2462, 1991 Printed in the U.S.A.

EXTRACTION FROM

OF A

INTERFACE

FIBER

Pergamon Press plc

PROPERTIES

PUSH-OUT TEST

T.A.Parthasarathy*, P.D.Jero # and R.J.Kerans # *- UES Inc., 4401 Dayton-Xenia Rd, Dayton, OH-45432 #- Wright Laboratory, WL/MLLM, WPAFB, OH 45433-6533 (Received July 22, 1991) (Revised August 23, 1991)

Introduction

The properties of the fiber/matrix interface are believed to play a key role in determining the mechanical behavior of ceramic composites (for reviews see [1,2]). This has led to the development of techniques that attempt to measure the interface mechanical properties (e.g.,ref.[3]). Among them the indentation technique developed by Marshall [4] has been the most popular. Recent investigators [5,6,7,8] have modified it into a flat-probe push-out technique. However, the analyses of the data generated from these techniques have been interpreted in a variety of ways, some of which are clearly inadequate (see ref.[9]). Recent theoretical works by Gao et al. [10], Hutchinson and Jenson [11], Kerans and Parthasarathy [9] and Cox [12] have relaxed many of the assumptions of the earlier treatments resulting in a new basis for analyzing push-out test data. Butler et al. [13] have attempted to use the analysis of Gao et al. to extract interface parameters from pull-out tests. However the work of Gao et al. neglects the residual axial strain in the fiber which is now believed to have important effects [9,11,12]. In this work, data generated from flat-probe push-out tests on a composite of SCS6/borosilicate glass is used to examine the possibility of extracting more detailed and useful interface properties using the analysis of Kerans and Parthasarathy [9], which includes the effect of the residual axial strain in the fiber. Push-out Tests

The composite used in this work was prepared using ~-SiC monofilaments (SCS-6@) and a potassium borosilicate glass*. The glass used was measured to have a CTE of 3.96x10-6/°C in the 25-500°C temperature range. The fiber, fabricated by chemical vapor deposition, has a diameter of 142 p.m with a 33 p.m diameter carbon core and a 3 p.m double coating which is rich in carbon. Unidirectional composites were fabricated by vacuum hot pressing at 850°C for 20 minutes at 500 psi. The specimens were prepared by cutting the hot-pressed composite plates into thin slices and polishing the surfaces to a ll~m surface finish. The specimen used in this work was 1.87 mm thick. The push-out apparatus used is described in detail elsewhere [6,7]. Briefly, a flat-end probe 125 I~m in diameter, made of tungsten carbide, was used to push a selected fiber out of the specimen. The bottom of the specimen was supported on a block of steel with a slot roughly three times the fiber diameter into which the fiber was pushed. The fibers were pushed typically through a distance of 100300 I~m before the specimen was flipped and the fibers pushed back. The push-back tests, which result in the seating drop [6,7], are useful in obtaining information about the contribution of surface roughness to the friction. @ SCS-6, TextronSpecialtyMaterials,Lowell, MA " Customcomposition, ComingGlassWorks,Coming, NY 2457 0036-9748/91 $3.00 + .00

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FIBER PUSH-OUT TEST

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The load was measured using a 101b (44.5N) load cell and measurement was fed directly into a datalogging computer which was used to measure and record the data every 100 milliseconds. The test was done under a constant displacement rate of 127 I~m per minute. The test data reported here were all acquired from the same specimen by pushing on different fibers. The load-displacement trace obtained in one of the tests is shown in Fig.l. As normally observed, the peak load is followed by a sudden drop in load; the load then decreases steadily until it reaches a steady state. During pushback, the load is approximately constant until passing through a pronounced minimum when the fiber is pushed through the origin. The bottom of this "seating drop" gives the contribution to friction from residual stresses alone, while the magnitude of the drop gives the contribution from surface roughness.

Analysis of Results and Discussion Kerans and Parthasarathy [9] have analyzed the push-out test using a progressive debonding model, in which the debond crack begins to propagate at a critical fiber stress and then propagates stably as the load increases. The stability of the interface crack propagation comes from the frictional resistance of the debonded interface and the increasing compliance of the specimen. At the peak load the debond crack is nearly through the specimen; the crack then propagates spontaneously through the remaining interface with a resultant load drop. The load required for further sliding is determined purely by the frictional resistance at the interface and decreases as the fiber is pushed out. During the rising part of the load-displacement trace (after the debond starts propagating but before the peak load is reached), the external load, Pa, is related to the external displacement, & in terms of the interface toughness, Gi, the residual clamping stress at the interface, (rN, the residual axial stress, Pr/~r2, and the friction coefficient, I~, as follows: 1-2vfk 8 = CmPa + 211k/l;rEf

[Pa'Pd'Pr + (P*'Pr)In(

P'-Pa

P'-Pd'Pr

)]

...

(1)

for Pa -< Pd + Pr where Em Vf Pd = k = Ef (l+Vrn)+ Em (1-Vf) ;

( G i 4 ~ r3 E~ )o.s ( 1 - 2 V~k )

;

P" =

"

~11/~r2 k

In Eqn.1, Cm is the machine (load train) compliance, r is the fiber radius, and Pd/~r2 is the critical fiber stress for interface debonding and is related to the interfacial toughness as shown above. El, Em, vf, and v m are the elastic moduli and Poisson's ratios of the fiber and the matrix, respectively. Pa and Pd, being compressive, are negative and Pr is taken to be negative when the fiber is in residual axial compression. The clamping stress, aN, is negative when the interface is under compression; it consists of the residual stress arising from the CTE mismatch between the fiber and the matrix plus the clamping stress arising from the interface roughness. The clamping stress from interface roughness makes a significant contribution only when the relative displacement between the fiber and the matrix is of the order of half the period of the roughness or greater (see [9]). The period of roughness assessed from seating drop studies [6,7] is about 10 I~m. During the rising part of the loaddisplacement curve, when progressive debonding occurs, the relative fiber/matrix displacement at the loaded end is about one micron in these specimens. Thus, the contribution of interface roughness to the clamping stress will not be significant during debonding. From the rising part of the load-displacement trace (i.e., before peak load) where Eqn 1 is applicable, it must be possible to extract the interface toughness, the residual axial stress, the residual clamping stress at the interface, and the friction coefficient. If the contribution of roughness during debonding is neglected and the CTE of the fiber taken to be isotropic, then the clamping stress at the interface and the residual axial stress in the fiber are related. This reduces the number of unknowns to three. Since

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FIBER PUSH-OUT

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2459

Eqn.1 was arrived at assuming progressive debonding, the raw push-out data must first be analyzed to determine if the debond was progressive or catastrophic. The analysis [9] predicts that the loaddisplacement trace must deviate from linearity at the point where the debond begins to propagate. Thus it is possible to determine if the debond was progressive and to identify the progressive debond regime in the load-displacement trace. As seen in Fig.l, there was no apparent non-linearity in the rising part of the load-displacement trace; however, when the machine compliance was removed and the load-displacement trace converted to an "effective displacement'-Ioad plot, Fig. 2(a), the non-linearity was obvious. The effective displacement was calculated by subtracting the steady state machine compliance (-41~m/N) from the data. The plot shows an initial region where the compliance decreases with increasing load, as is normal for any compliant load train. At about 4 N, the compliance saturates to zero (i.e., the actual compliance equals the steady state machine compliance) before increasing beyond about 10 N. This increase amounts to a departure from linearity as predicted to occur due to progressive debonding. Fig. 2(b) shows the data of seven push-out tests taken from the same specimen superposed on top of each other. It is seen that the data is reproducible without significant scatter. The data from these seven tests were individually fit to Eqn.1 and the set of interface parameters (1~,ON and Gi) that gave the best fit was obtained for each data set. The fitting was done using a non-linear least squares fitting routine that uses the downhill Simplex method. The initial "guess" for the iteration was varied to ensure that the solution was a global minimum. The quality of fit obtained for the data in Fig. 1, is shown in Fig. 3(a). The interface parameters extracted from the seven data sets are compared in Fig. 3(b,c,d). Using the extracted parameters the model can be used to predict the peak load. This was done assuming that the debond crack becomes unstable (propagates to failure) when it is within a fiber diameter of the specimen end. Similarly the load corresponding to friction was calculated using the specimen thickness as the embedded length. The predicted peak loads and friction loads are compared with the corresponding measured loads in Fig. 3(e) and 3(f). The mean value of 0.13 obtained for the friction coefficient compares well with an independent measurement of IZ (as -0.15) for graphite on glass by Gupta [14]; and the scatter in the data is fair. The low interfacial toughness (0.18 Jim 2) also is consistent with what is known about the carbon-rich fiber coating preventing significant bonding between the fiber and the matrix. The larger scatter in the interfacial toughness may be due to the exceptionally low toughness of the interface and/or the inherent scatter in the fracture behavior of glass. The residual stress shows very little scatter; however the mean value of -53 MPa is significantly larger than that estimated from the CTE of the glass matrix and the fiber. Taking the processing temperature (850°C) to be the stress-free temperature, a residual stress of -53 MPa translates to a CTE mismatch of 1.5xl0-6pC. The measured CTE oflhe glass in the 25-500°C range is about 4xl0-6pC, while the widely quoted value for the fiber in the axial direction is 3.6x10-6/°C [15] for a mismatch of 0.4xl0-6pC. This discrepancy is unexplained, although it may be due to an anisotropy in the CTE of the fiber between the radial and axial directions. The predicted peak loads agree very well with the measured values. The friction loads predicted using the parameters extracted from the rising part of the load-displacement trace are found to be close to the loads at the bottom of the seating drop and far from the load measured immediately following the peak load. This is consistent with the suggestion that the interface roughness contributes significantly to the friction load immediately following the peak load but makes a much smaller contribution before the debond is complete, i.e., before the peak load is reached. Summerv

Recent theoretical works [9-12] have relaxed assumptions of earlier treatments providing a new basis for extracting interface properties from fiber push-out/pull-out test data. The feasibility of extracting useful information from fiber push-out tests was examined. The push-out data generated using a SCS6/borosilicate glass composite system and a fiat-probe push-out test, was analyzed to extract the fiber/matrix interface properties. The load-displacement traces were fit to the expressions of Kerans

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FIBERPUSH-OUT

TEST

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and Parthasarathy [9] using a non-linear least squares fitting routine. The load-displacement behavior was qualitatively consistent with the predictions of progressive debonding. The best fit of the data showed that the interface friction coefficient and the residual stress thus extracted exhibited low scatter while the interface toughness exhibited a larger scatter. The friction coefficient compared well with independent measurements [14], but the residual stresses were higher than what were calculated using existing data on the CTE (longitudinal) of the fiber. This discrepancy is unexplained, although anisotropy in the CTE of the fiber may be a possible cause. The predicted peak load was found to be in reasonable agreement with the measured value, if the debond crack was taken to be unstable one fiber diameter from the end of the specimen. The predicted friction load was closer to the load measured at the bottom of the seating drop rather than the load immediately following the peak load. This implies that the interface roughness contributes significantly to the friction load immediately following the peak load. Acknowledoements

This work was funded by the U.S.Air Force in part under on-site contract # F33615-89-C-5604 (UES, Inc.). Referen ces

1) A.G.Evans and D.B.Marshall, "The Mechanical Behavior of Ceramic Matrix Composites', Acta Metall., v37, No.10, pp2567-2583 (1989). 2) R.J.Kerans, R.S.Jay, N.J.Pagano and T.A.Parthaserathy, "The Role of the Fiber Matdx Interface in Ceramic Composites', Amer. Ceram. Soc. Bull., v68, No.2, pp429-442 (1989). 3) R.J.Kerans, P.D.Jero and T.A.Parthasarathy, A.Chatterjee, "Determination of Fiber/Matrix Interface Mechanical Properties in Brittle Matdx Composites', MRS Symposium Proc., vt 94, pp263-270 (1990). 4) D.B.Marshall, "An Indentation Method for Measuring Matrix/Fiber Frictional Stresses in Ceramic Composites', JI of Amer. Ceram. Soc., v67, No.12, ppc259-c260 (1984). 5) J.D.Bright, D.K.Shetty, C.W.Griffin and S.Y.Umaye, "Interface Bonding and Friction in SiC(filament) Reinforced Ceramic and Glass Matrix Composites', JI of Amer. Ceram. Soc., v72, No.10, pp1892-1898 (1989). 6) P.D.Jero and R.J.KeranS, "The Contribution of Interfadal Roughness to Sliding Friction of Ceramic Fibers in a Glass Matdx=, Scripta Metall. & Mater., v24, pp2315-2318 (1990). 7) P.D.Jero, R.J.Kerans, and T.A.Parthaserathy, "Effect of Interracial Roughnesson the Frictional Stress Measured Using Push-out Tests', JI of Arner. Ceram. Soc., in press. 8) J.l.Eldddge andP.K.Brindley, "Investigation of Interracial Shear Strength in a sic fibre/Ti-24Al-11Nb Composite by a Fiber Push-out Technique', JI of Mater. Sci. letters, v8, pp1451-1454 (1989). 9) R.J.Kerans and T.A.Parthaserathy, "Theoretical Analysis of the Fiber Pull-out and Push-out Tests', JI of the Amer. C,eram. Soc., v74 [7] pp1585-1596 (1991). 10) Y.C.Gao, Y-W Mal and B.Cotterell, "Fracture of Fiber Reinforced Materials', JI of App. Math. & Phys., v39, pp550-572 (1988). 11) J.W.Hutchinson and H.M.Jensen," Models of Fiber Debonding and Pull-out in Brittle Composites with Friction', Mech. of Mater.,vg, pp139-163 (1990). 12) B.N.COx, "lnterfacial Sliding Near a Free Surface in a Fibrous or Layered Composite During Thermal Cycling', Acta Metall. & Mater., v38, No.12, pp2411-2424 (1990). 13) E.P.Butler, E.R.Fuller and H.M.Chan, "Interface Properties for Ceramic Composites from a Single Fiber Pull-out Test', in Interfaces in Composites edited by C.P.Panatano & E.J.H.Chen, Mater. Res. Soc. Sympos. Proc., v170, pp17-24 (1990). 14) P.K.Gupta, "Simple Method for Measuring the Friction Coefficient of Thin Fibers', JI. of the Amer. Ceram. So<:., v74 [7], pp1692-1694 (1991). 15) J.A.DiCado, "Creep of Chemically Vapor Deposited SiC Fibers', JI of Mater. Sci., v21, pp217-224 (1986).

Vol.

25, No.

FIBER PUSH-OUT

ii

TEST

2461

20

Push-back

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DISPLACEMENT (micrometers)

EJggr.Lt; The load-displacement trace obtained during a fiber push-out test and during fiber push-back.

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EFFECTIVE DISPLACEMENT(micrometers)

(A) The data in Fig.1 is replotted after subtracting the load-train compliance. (B) Seven sets of data superposed on top of each other showing that the data does not exhibit significant scatter.

2462

FIBER PUSH-OUT TEST

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AI I Q.

25, No. ii

.(B)

(A)

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Vol.

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.(F)

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Loadat bottomof seating dropI LoadImmediatelyAfterPeak J

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l=iaure 3: (A) The quality of fit to the data in Fig.2(A) is shown graphically. The extracted parameters for the seven sets of data are shown in (B),(C) and (D). The predicted and measured peak loads are compared in (E). The predicted friction load is compared with the load at the bottom of the seating drop and the load immediately after the peak in (F).