Effects of interfacial evolutions on the mechanical behaviour of ceramic matrix composites during cyclic fatigue

Scripta Metallurgica et Materialia, Vol. 31, No. 8, pp. 1061-1066, 1994 Copyright © 1994 Elsevier Science Ltd Printed in the USA. All rights re.served 0956-716X/94 $6.00 + 00

Pergamon

CONFERENCE SET No. 2

EFFECTS OF INTERFACIAL EVOLUTIONS ON THE MECHANICAL BEHAVIOUR OF CERAMIC MATRIX COMPOSITES DURING CYCLIC FATIGUE

P. Reynaud,

D. Rouby & G. Fantozzi

Groupe d'Etudes de M ~ t a l l u r g i e Physique et de Physique des Mat~riaux URA 341 - Institut National des Sciences Appliqu~es de Lyon 69621, V i l l e u r b a n n e cedex, France.

(Received May 6, 1994)

Introduction Under periodic loading Ceramic Matrix Composites (CMC) exhibit at room temperature cyclic fatigue effects (6,7,10). These phenomena lead to a variation of the macroscopic mechanical behaviour with the number of applied cycles, and to a delayed failure of the samples as shown by the life-time diagrams . In the case of cross-weave composites subjected to repeated tensile loading in the direction of the fibres, we have already proposed a micromechanical model (8) to describe the mechanical behaviour at room temperature of a standard SiC-SiC composite during a fatigue test. The composite used for the experimental studies was a bi-directional SiCSiC composite (2D SiC-SiC GS4C) supplied by the Soci~t~ Europ~enne de Propulsion (Etablissement de Bordeaux). This composite is characterised by a failure strain of 0.2% (3) and was unprotected against oxidation. This model assumes that cyclic fatigue in this composite comes from a progressive degradation of the interfacial zone due to the repeated slidings between the fibres and the matrix during each loading-unloading cycle. This implies an evolution of the mechanical behaviour which is independent of time ; this fact has been experimentally confirmed by the laws of decrease of the mean stiffness during a fatigue test, which are independent of frequency (7). With this approach, the theoretical lifetime diagrams and the evolutions of the stress-strain loops during a fatigue test on a ceramic matrix composite have been calculated (8). At high temperatures, very few studies of cyclic fatigue effects have been published yet (2,6,9) and no theoretical analysis of these phenomena have been developed. However, for temperatures up to 2000oc, two cases should be differentiated. When temperatures are low enough to inhibit any physical and chemical change in both fibres, matrix and interface (i.e. for temperatures lower than I100°C) the elastic characteristics of the constituents remain constant. Unless stabilisations of heat transfers between the sample and the testing system, no specific time dependent phenomenon is introduced by a change in the temperature of the test. The changes in the composite concern only the thermal stresses and their consequences on the fibre-matrix interfacial shear stress, due to the thermal expansion mismatch between the fibres and the matrix (1,5). When the temperature becomes high enough to enable some physico-chemical mechanisms (oxidation, decomposition of the fibres or of the matrix, 1061

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creep), time dependent contributions are added to the previous effects. In that case the characteristical parameters of each constituent (elastic modulus, interfacial shear stress, distributions of matrix defects and individual failure stresses of fibres) are affected and become both time and temperature dependent. The purpose of this paper is to present a simple extension of our micromechanical analysis (developped p r e v i o u s l y for behaviours at room temperature), to the case of low temperatures where only the thermal stresses are changed. This analysis shows that an increase of the temperature leads to a widening of the sliding areas, and induces an opening of the stress-strain loops, experimentally confirmed (fig. 3 & 4). Cyclic

fatiuue at room temperature

Schematic description of 2D composites Modelling the mechanical behaviour of a material by a micromechanical approach implies an idealized description of its microstructure, in order to separate all the individual mechanisms. The first hypothesis assumes that the longitudinal and the transversal yarns are independent (fig. 2), and that the bidirectional composite (2D) acts like a parallel association of two elements, each one corresponding respectively to the transversal and the longitudinal yarn. In the transversal yarns, the load is applied perpendicular to the direction of the fibres. As observed by optical microscopy, the fatigue damage in these yarns consists in a multiple cracking of the matrix plus a debonding of the fibres (fig. i). To simplify, the mechanical behaviour of the tranversal yarns is assumed to be elastic. But, to take into account the presence of the debonding and of the cracking, the elastic modulus can be assumed different under tension and compression load. In the longitudinal yarns, the load is applied parallel to the direction of the fibres. Since the variation of the tensile stress along the waved fibres is about 20%, the fibres can be assumed straight. Hence, the mechanical behaviour of the longitudinal yarns is equivalent to an unidirectional (ID) composite with parallel fibres. In a SiC-SiC composite the ultimate stress of the matrix is lower than the individual failure stress of the fibres. Hence, the multicracking of the matrix occurs in the longitudinal yarns, and the bridging fibres control the failure and the dissipative mechanisms of a 2D composite. Cyclic fatigue m e c h a n i s m During a f~tigue test, if the maximum stress applied is higher than the level needed to create the first crack, multicracking of the matrix is assumed totally achieved at the end of the first cycle. All the fatigue damage appearing further will affect only the fraction of broken fibres and the stress overload profile of the surviving fibres. But due to the repeated slips between fibres and matrix at each fatigue cycle, a wear mechanism in the interracial zone may lead to a progressive decrease of the interfacial shear stress (ISS) from an initial value (~0) to a non zero lower bound (~). This can be described by a power law such as : • (N) = max(Z.,~0 N-t)

(i)

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where the exponent (t) characterizes the rate of the interfacial wear. The calculation of the stress/strain loops (8) for a given ISS, and the introduction of eq. (I) gives us the evolution of the loops during a fatigue test, characterized by a widening of the loops, an increase of residual stresses and a decrease of the mean stiffness (8). Contributions of the fibre-matrix interactions on the ISS The analysis of the fatigue behaviour of ceramic matrix composites points out the essential role of the ISS, which controls the sliding between the fibres and the matrix. Since the composite is undamaged, the critical interfacial shear stress (~0) is the result of all the interactions which act to increase the friction between the fibres and the matrix. These interactions can be classified in two families : i) the short range interactions, and ii) the long range interactions. The short range interactions correspond to the phenomena which are associated to the roughness of the surfaces in contact for the fibres and the matrix. These interactions are both dependent on the morphology of fibres and matrix surfaces, and on the structure of the interphase layers. In the modelling of cyclic fatigue at room temperature, we assume that all the short range interactions are progressively removed by a wear of the interface during a cyclic fatigue test (see eq. i). Hence, the initial interracial shear stress (~0) is given by : ~0 = ~ S R

+ ~

(2)

where AESR represents the contribution of the friction due to the short range interactions, and %~ is the limit value of ISS which corresponds to the long range interactions alone. In the studied 2D SiC-SiC the value of A%SR is of about 60% of ~0 (8). Because of its dependence on the morphologies of the fibres, the n~trix and the interphases, the quantity A~SR will change at high temperatures when the chemical evolutions of the constituents are going on. On the other hand, the long range interactions are due to overall phenomena like: variations of the fibres diameter, fibres undulations and misalignment, Poisson's effects, thermal stresses, etc. Hence, all the long range interactions are assumed independent of the number of cycles during a cyclic fatigue (unless eventually Poisson's effects), and only the thermal stresses are affected by a change in the temperature of the test. Theoretical

effects of temperature on the ISS

According to the temperature range, in the case where the chemical reactions are inhibited only the thermal stresses change, i.e. the value of ~ . Assuming that the friction between fibres and m a t r i x is described by a law of Coulomb, the contribution of long range interactions on the ISS is given by : A ~ AT ~

= ~LR + ~

A

(3)

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where TLR is the contribution of the long range interactions other than the thermal stresses, ~ is the coefficient of friction , A S = l~rf - ~rml is the radial thermal expansion mismatch between the fibres and the matrix, AT = IT - ~I is the temperature difference between the testing temperature (T) and the processing temperature (To), and A is a constant characteristic of the

elastic

properties

of

the

fibres

and

the

matrix

(A = i , + i_i + v~) Ef E m 1 - vf for a fibre in a limited matrix subjected to the radial and the longitudinal thermal stresses (5) ; E i and v i are respectively the Young's modulus, and the volume fraction of the phase i (i = m for the matrix and f for the fibres), Poisson's effects being neglected here. According to eq. (3) ~ decreases when the temperature increases, leading theoretically to an increase of the dissipation during a fatigue cycle. To confirm this result we have done some cyclic loadings at various ranges of temperature on a specimen previously subjected to periodic loadings at room temperature. The fatigue ageing at room temperature was realised under tension-compression with an amplitude of 130 MPa (just beyond the fatigue limit). Then, for temperatures raising up to 1300°C, 1000 cycles with 120 MPa of amplitude where applied under a inert atmosphere. For temperatures up to 1000oc the shape of the loops is independent of the number of applied cycles: no fatigue effect occurs. The opening of the loops with the temperature range indicates an increase of the dissipation due to the decrease of the thermal stresses, i.e. a decrease of ~ . For higher temperatures (from II00°C to 1300°C) the shape of the loops hardly changes during fatigue, indicating that physico-chemical instabilities began to be activated. The opening of the loops in that case is not only due to thermal stresses relaxation. Moreover, the dissymetry observed on the behaviour under tension and compression at very high temperature shows that creep is not predominant and that the dissipation should be mainly attributed to irreversible interfacial evolutions. Conclusions The extension at the high temperatures (where the thermal stresses are modified) of a micromechanical model describing already the fatigue behaviour of ceramic matrix composites at room temperature implies that at low temperature dissipation increases with the relaxation of thermal stresses. The calculation of the opening of the stress/strain loops with this micromechanical model is compatible with experimental results, but the dissipation in the transversal yarns have to be quantified for more accurate quantitative predictions. At higher temperatures, the evolution of the behaviour is mainly due to physico-chemical instabilities which have to be indentified and quantified to describe cyclic fatigue at very high temperatures. Acknowledaements This work was supported by CNRS, MESR, DRET, A~rospatiale, SEP and CNES who sponsored two scientific associations: the Groupement Scientifique "Comportements Thermom4caniques des Composites C4ramique-C~ramique Fibres" and the Groupement Scientifique "Composites Thermostructuraux". Thanks are particularly due to Dr M. Bourgeon, Dr F. Abbe and Dr J.Ph. Richard from SEP for numerous fruitful discussions and for providing the materials.

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References i. 2. 3. 4.

M.K. Brun & R.N. Singh, A d v a n c e d C e r a m i c Materials, 3, 506 (1988) J.W. Holmes, J. Am. Ceram. Soc., 74, 1639 (1991) A. Lacombe, M a t 4 r i a u x et Techniques, Juin, 3 (1989) G. Morscher, P. Pirouz & A.H. Heuer, J. Am. Ceram. Soc., 73, 713 (1990) 5. H.J. Oel & V.D. Frechette, J. Am. Ceram. Soc., 69, 342 (1986) 6. K.M. Prewo, J. Mater. Sci., 22, 2695 (1987) 7. P. Reynaud, D. Rouby, G. Fantozzi, Revue des C o m p o s i t e s et des M a t ~ r i a u x Avanc~s, I, 9 (1993) 8. D. Rouby & P. Reynaud, Composites Science and Technology, 48, 109 (1993) 9. Z.G. Wang, C. Laird, Z. Hashin, W. Rosen, C.F. Yen, J. Mater. Sci., 26, 5335 (1991) i0. L.P. Zawada, L.M. Butkus, G.A. Hartman, J. Am. Ceram. Soc., 74, 2851 (1991)

Fig.

1 Cyclic fatigue damage on 2D SiC/SiC at room temperature (S = 135 MPa, just b e y o n d the limit fatigue).

Transversal

Longitudinal

yarns

yarns

(matrix crack and b r i d g i n g Fig.

2 Schematic

description

fibres)

of fatigue damage in 2D SiC/SiC GS4C.

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Stress (MPa) 150

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200°C 400°(3 600°C 8000C 1000°(3 100oc 3000c 500=c 700oc 900oc

OOo ////'ii +o //////// 0 :

I

I

I

-100

-150

Strain (%) -0,2

0

0,2

0,4

0,6

0,8

Fig. 3 Theoretical stress/strain loops under tension/compression for a 2D Ceramic Matrix Composite at different temperatures - Calculation of low temperature effects, (the shift of the loops is due to the thermal expansion of the specimen).

Stress (MPa) 150 100 50 0 = -50 -100

100°C 300°C 500°C 5( 700°C 900°C 1100"(3 600°C 800oc 1000°C 1200o13 RT° 200°C 400°C

I////'//, / ?////

/

1300°C

I

Strain(%)

-150 -0,2

0

0,2

0,4

0,6

0,8

1

Fig. 4 Experimental stress/strain loops at various temperatures (from i00 to 1300oc under Argon) of a 2D SiC/SiC GS4C previously damaged by cyclic fatigue at room temperature (the spacing of the loops is really observed, and is due to the longitudinal thermal expansion).