ournal Am,Ceam.Sox.,8s161350-65(2002) Stress Rupture in Ceramic-Matrix Composites: Theory and Experiment Howard g, halverson Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University. lacksburg. virginia 24061 William A. Curtin* Division of Engineering, Brown University, Providence, Rhode Island 02912 A micromechanically based model for the deformation the lifetimes at 950C are greatly overpredicted. Thus, the strength, and stress-rupture life of a ceramic-matrix composit micromechanical model can be successful quantitatively but developed for materials that do not degrade by oxidative clearly shows that the rupture life of the composite is ex attack, The rupture model for a unidirectional composite nsitive to the detailed mechanisms of fiber degrada incorporates fiber-strength statistics, fiber degradation with odel has practical applications for extrapolating time at temperature and load, the state of matrix damage, and lifetime data and predicting life in components with the effects of fiber pullout, within a global load sharing model. evolving spatial stresses. The constituent material parameters that are required to predict the deformation and lifetime can all be obtained independent of stress-rupture testing through quasi-static ten L. Introduction sion tests and tests on the individual composite constituents. The model predicts the tertiary creep, the remaining composite trength, and the rupture life, all of which are dependent C ERAMIC-MATRIX COMPOSITES (CMCs) are attractive materials for use in high-temperature applicati critically on the underlying fiber-strength degradation Sensi tivity of the rupture life to various micromechanical parame- engineers must be able to predict the material response to applied ters is studied parametrically. To complement the model, an loads and in various environments. The quasi-static deformation extensive experimental study of stress rupture in a Nextel and tensile strength of many CMCs are well understood in terms of 610/alumina-yttria composite at temperatures of 950 and the evolution of matrix cracking and fiber failure.l-s however,the 1050.C is reported. The Larson-Miller and Monkman-Grant time-dependent properties, such as creep deformation and strength life-prediction methods are inadequate to explain the current are not as well understood at the micromechanical level, despite a derived from quasi-static tests and literature data, and the designers the confidence to use CMCs in structural applications micromechanical model predictions are compared with mea- lies in obtaining a basic understanding of key damage mechanisn sured behavior. For a slow-crack-growth model of fiber and their effects on stress-rupture lifetime and deformation trength degradation, the lifetime predictions are shorter by Many researchers have used traditional engineering methods, two orders of magnitude. When the rupture life is fitted with such as the Larson-Miller (LM) and Monkman-Grant (MG) one parameter, however, the model prediction of the tertiary approaches, to predict stress rupture in ceramics and composites creep and residual strength at 1050 C agrees well with the under constant load. The LM approach relates the applied stress to experimental results. For a more complex degradation model, a failure parameter, @. given by the rupture life and tertiary creep at 1050 C can be predicted quite well; however, the spread in residual strength is not, and Q-T(log t,+ C) where T is the temperature, I, the rupture time, and C a constant. Predictions for fiber composites are made by first obtaining the LM parameter Q versus stress for single fibers via single-fiber test R, Kerans-contributins editor at various loads and temperatures. Then, basic mechanics is used to estimate the stress carried by the fibers in the composite and the composite failure time is assumed to be equal to that of the 88.72 Received May 11. 2001: approved December 18. 2001 individual fibers at the established stress level. This technique was used by Morscher and co-workers"to examine the stress rupture 4 suppor from the U S. Air Force O压和m的 of precracked Hi-NicalonTM/SiC minicomposites with BN inter faces. The predictions were accurate at low and high values of 2: however, at intermediate values, removal of the bn interface an Feature
June 200 Stress Rupture in Ceramic-Matrix Composites: Theory and Experiment 1351 its replacement with strongly bonded borosilicate glass resulted in showed the basic dependencies of the rupture time on parameters much shorter rupture lives than expected. In cases where the uch as the Weibull modulus of the fiber and the slow -crack atrix is not cracked, use of the MG approach has been propose The MG approach relates the steady-state strain rate (e)to the The Coleman model is an alternative to the slow-crack rupture time via two constants, k and D growth model for fiber rupture; in this method, the probability of fiber failure is a function of time and stress and no attempt is made Et=D (2 to determine fiber strength. Ibnabdeljalil and Phoenixdeveloped a composite stress-rupture model for the case where the fibers DiCarlo and Yun demonstrated that MG plots of steady-state carry all the applied loads; a Coleman model was used for the tiber-rupture behavior. Lamouroux et al.developed a model for 610 fibers successfully match lifetimes obtained by Zuiker on a of the fiber, a simple bundle model for fiber failure that neglected woven Nextel 610/aluminosilicate composites Although the accuracy of engineering methods can be good fiber pullout, and the Coleman fiber-rupture model. These models they are basically correlations between macroscopic measures of to account for a e life and tertiary creep, and they can be extended can predict rupt behavior and do not contain much information about the state of matrix damage, but this step has not yet been he material during the stress-rupture process. Therefore, they attempted. However, in the Coleman model. the fibers have an annot be used to (i) predict behavior a priori; (i)connect infinite fast-fracture strength; hence, the rupture is not related to different but related aspects of the deformation, such as the tertiary predicted at all timer th and the remaining strength cannot be creep and the remaining strength, to the rupture life: and (iii) If the matrix is sufficiently stiff and/or not fully cracked. it rovide insight into the optimization of composites, because ne direct connection to underlying constituent properties and/or the fiber-stress profile that can decrease the rate of fiber degrada a carries some axial stress, which leads to a spatially vary internal state of damage in the material exists. These factors also and increase composite lifetime. Many CMC materials are in- clearly limit the use of LM and MG approaches in the development tended for use at moderate stresses where the matrix cracking(i)is of new composites, where changes in constituents occur regularly ot saturated, (ii) is dependent on the applied stress level, or (iii) as improved materials become available. Micromechanically based can evolve during constant-load testing: thus, the details of the methods to predict deformation and failure under stress-rupture matrix damage state can have a significant role in determination of onditions. as a function of the underlying behavior of the the composite lifetime constituent materials, should be extremely useful for the design If the matrix does carry some significant portion of the applied and optimization of existing materials, for the development of new load, at least initially, then its response to applied stresses must composite systems, and to complement mechanical testing and, also be considered. At low stresses, most ceramic matrixes will hus, reduce development and design costs. remain uncracked. and the stresses carried by each constituent will The failure of most CMCs is concurrent with the failure of the en be controlled by the constituent creep response. The creep rate reinforcing fibers; therefore, a lifetime-prediction method should of a CMC can become a limiting factor in component design and is, thus, an area of considerable investigation. Holmes and co- general, fiber failure is a function of temperature, stress, and any workers2. 2 studied the creep rate of silicon carbide/calcium chemical interactions that occur (e.g, oxidation). For silicon arbide (SiC) fiber materials, where oxidation is a primary SiaN.) composites extensively. For SiC/Si N composites, the oncern, modeling has focused on the growth of an oxide scale on creep rate exhibited short primary and tertiary creep regions and an the fiber surface, which behaves similar to a surface flaw and leads extensive secondary(steady-state)region. In the SiC/CAS com- to a time-dependent decrease in fiber strength. Lara-Curzioo posites at 1200C, at which temperature the matrix carries only a analyzed this mechanism for a matrix-cracked composite, includ- fraction of the applied stress. the stress exponent of the compos g the statistics of fiber strength, and produced predictions for composite lifetime. Evans and co-workers- considered a sim 1.9 for Nicalon fibers:"). Composite creep due to combined fiber ilar process within growing matrix cracks wherein weakening by nd matrix creep, but without damage, was first modeled by McLean" and can rationalize some of this creep data. Stress oxide scale and subsequent failure of the exposed fibers in the redistribution during creep can be influenced by the damage state occurs when the remaining uncracked composite cross section cannot sustain the applied load. Other mechanisms, such as the co-workers2529 on SiC/Si, N, composites. They found that, when relaxation of crack-bridging stresses, because of fiber creep and the matrix was undamaged (at low applied stresses), the initial subsequent crack growth, have been discussed by Begley and composite creep rate was controlled by the transfer of stress from co-workers.and Lewinsohn er al., i6 among others he creeping matrix to the noncreeping elastic fibers, as per the If environment effects can be eliminated through the use of model of McLean. At higher stresses, the initial loading rate coatings or oxidation-resistant constituents, fiber failure should be strongly influenced the creep behavior. At high rates of loading a function of stress and temperature only. CMCs with active matrix fracture was pronounced and composite lifetimes were oxidation have very limited lifetimes; therefore, we will focus on relatively short. At lower rates of loading, the matrix was able to lax in creep and did not fracture, resulting in much-longer absent. Specifically, we will use the slow-crack-growth model to and McMeeking 0 and Fabeny and Curtin" to incorporate statis- dict fiber-damage evolution and failure and envision the app cation of our models to all-oxide ceramic composites, Although ical fiber fracture and its influence on creep and rupture but not matrix damage. These works also emphasized that stress transfe evidence for any particular fiber- degradation mechanism in oxide- ceramic fibers is difficult to ascertain. 7-9 the general power-law solutions and provides a relationship between the initial fiber reep of the matrix and a subsequent increase in the ineffective form of the slow-crack-growth-rate equation lends itself to analytic length of broken fibers, resulting in time-dependent composite strength and the fiber strength after some arbitrary stress and failure temperature history. Failure of the fibers in a composite under slow Giv modeling back- crack growth is dependent on the actual stress history experienced ground cs and statistics by each fiber, which is dependent on the applied load, the state of and composite matrix damage, and the interfacial sliding between the fibers and as a function of the matrix damage state, using the slow- crack the matrix. lyengar and Curtin studied composite failure when growth model for fiber degradation. The resulting model includes the matrix was fully saturated with closely spaced cracks and fiber-strength statistics, fiber degradation with time at temperature
1352 Journal of the American Ceramic Society-Halverson and Curtin Vol. 85. No. 6 and load, and the effects of fiber pullout, within the well- prevent large-scale sintering of the materials at elevated tempera established framework of the global load sharing (GLS) model. ures but small enough to permit stress transfer between the The model predicts interrelated phenomena of tertiary cree constituents by frictional shear stress. The carbon also serves to dependent critically on the underlying fiber-strength degradation. processing of the AL,O,/Y,O, mall mical reactions during the remaining composite strength, and rupture life, all of which are The constituent material parameters required to predict the defor- To create the matrix, a slurry of Al,O, powder first was mation and lifetime predictions can be obtained independent of pressure-cast into the fiber preform. Next, a sol of Y2O, particles stress-rupture testing through quasi-static tension tests and tests on was infiltrated into the preform, and the preform was dried at the individual composite constituents. To complement and validate 700"C. After a few infiltration and drying steps, the part was fired the model, an experimental study of the stress-rupture life, creep at 1 100C for-I h. Then, the infiltration/drying/firing cycle was deformation, and the associated damage modes for a unidirectional repeated until the desired density was attained. For these materials, Nextel 610 fiber/alumina-yttria matrix CMC(manufactured by processing was halted when the composite porosity was% McDermott Technologies, Inc (MTD), Lynchburg. VA) with a which typically required 4-6 cycles. The Y,O, reacts with the fugitive carbon interface has been conducted, This oxide/oxide Al, O, during the firing cycle to create AlYO, and Y,Al,O,: CMC system should be unaffected by the oxidation, and the hence, the exact composition of the matrix was not determined unidirectional configuration permits direct comparison with the model. Using literature data for the fiber-strength degradation, the (2)Mechanical Testing model predicts lifetimes that are two orders of magnitude shorter than that measured. When one parameter, the fiber-degradation The unidirectional material was used for quasi-static and stress- rate constant, is fit to the experimental results, the trends in rupture testing at three temperatures:23°,950°,and1050°C composite lifetime with stress and temperature are well-matched Then, the model also predicts tertiary creep rates and remaining MTS Systems, Eden Prairie, MN) with a controller(Model 458, data. The measured star ery good agreement with the experimental MTS Systems ). Specimens were tabbed with 0.020 in. fully annealed aluminum tabs, to prevent damage from gripping. The be correlated with the scatter in the initial composite strength predicting several different features that are associated with the ps s placed in the MrS test-frame grip. The pressure of the grip using the model. The success of the model in simultaneously ically deformed the aluminum to"fit"the specimen, and no adhesive was used. Grip pressures were maintained at -0.7 MPa deformation and failure, despite the need for a fitting parameter. The tests were run under load control. at a rate of 180 N/s Strain demonstrates the power of such a micromechanically based ap- proach. An alternative assumption for the fiber-degradation mech- 63211B. MTS Systems). Specimen alignment was maintained lifetime predictions at high temperature but poorer residual rough a fixture at the grips. strength and tertiary creep predictions. The implications of A compact oven was used for the tests that were conducted at extreme sensitivity of the rupture life to the precise mechanisms elevated temperature. The oven had four SiC resistance elements fiber-strength degradation, and/or the inadequacy of the ex sittt (Norton Advanced Ceramics, Worcester, MA) that heated the specimen. The oven shell was stainless steel and had nominal fiber-strength degradation to the in situ behavior, is an important dimensions of 3.5 in. x 3 in.X 3 in. Fused-silica insulation issue of discussion The remainder of this paper is organized as follows. We Cotronics Corp, Brooklyn, NY) lined the inside of the oven in Section Il, with a description of the experimental techniques and which reduced the nominal interior dimensions to 2.5 in, x 2 in results and a comparison of the measured rupture lives to the LM X 2 in. Two temperature controllers (Model 818S, Eurotherm d MG models; their inadequacy motivates the subsequent model Reston, VA)controlled the SiC heating elements: one for the two development. In Section Ill, the analytic model for the fiber upper elements, and one for the two lower elements. Each dominated stress rupture of composites is developed. In Section controller received input from a type R(platinum/platinum IV, the experimental data are analyzed and compared with the predictions of the modeL. In Section V, we discuss our results by alumina-fabric insulation, for efficient heating and to help further, address important issues that this work raises, and outline maintain a constant temperature. A heat shield that was attached to how the present model can be used with structural design model the oven held an extensometer(Model 621-5IE. MTS Systems) for CMC components The extensometer measured strain according to the deflection of two 5 in. Al,O, rods that pass through the oven shell and contact the specimen. The entire assembly was attached to the test frame Il. Experimental Details, Results, and Predictions of at one of the posts. The extensometer, the heat shield, and the MTs Engineering models We begin our discussion with the experimental results and temperature. Then, the temperature was held constant for 10 min omparisons to the Larson-Miller (LM)and Monkman-Grant before the test began, to ensure thermal equilibrium. (MG) engineering models to demonstrate that such approaches to The stress-rupture testing proceeded similarly to the quasi-static life predictions are generally inadequate. This provides significant testing. However, the load rate for the stres motivation for the extensive theoretical developments of Section to 660 N/s, to minimize creep effects during the initial loading III ramp. When the desired load was attained. it was held constant until failure occurred. Strain data were collected throughout the (1) Material System test. Some tests were stopped after specified times to determine the The material system examined here is an oxide/oxide CMC that remaining strengths. As a test of remaining strength, the load was vas produced by MTl. This material consists of Nextel 610 first returned to zero and then the specimen was ramp fibers(>99% Al,O,)aligned in a unidirectional configuration and at 180 N/s embedded in an alumina-yttria (AL,O,Y, O,) matrix with a fugitive carbon interface. The nominal fiber volume fraction is (3) Experimental Results and Discussion 51%, and the overall composite porosity is 19. These materials (A) Virgin Specimens: Polished sections of several unidirec have no fiber/matrix bond; this is accomplished by first coating the tional panels were examined using scanning electron microscopy fibers with a thin(80-100 nm) layer of carbon through an (SEM), and matrix cracks with a mean spacing of-40 um were immiscible-liquid coating process and then, after the matrix has visible, as shown in Fig. I(a). The cracks likely formed to relieve been added, oxidizing the carbon to leave a small gap between the the stresses caused by the volume changes that occurred during the fibers and the matrix. This gap is intended to be large enough to sol-gel process and any thermal expansion mismatch
June 2002 Stress Rupture in Ceramic-Matrir Composite teory and Experiment Fig. I. Matrix cracking in (a) a virgin specimen and (b) a specimen tested in stress rupture (B) Quasistatic and Stress-Rupture Results: Stress-strain shown in Fig. I(b), unchanged from the virgin material.The curves for the quasi-static tension tests are shown in Fig. 2, and tiber-failure surfaces did not differ significantly in appearance their characteristic features are listed in Table I. There is a general from those tested in quasi-static tension. The stress-rupture life trend toward decreasing strength and modulus and increasing time and strain-rate data will be presented below, within the failure strain with increasing temperature. The nonmonotonic context of traditional engineering models for rupture, and again in trends are believed to be a result of specimen-to-specimen var Section Iv bility, most likely a consequence of the experimental nature of the manufacturing process. Unload/reload tests have been performed at various applied loads to obtain hysteresis loops. (4) Predictions of Rupture Using Engineering Models examine whether two engineering approaches that g During quasi-static testing, longitudinal splits were observed have been used in recent literature-the Larson-Miller(LM)and Iso,failure was accompanied by disintegration of the matrix near Monkman-Grant(MG the(presumed) failure plane, probably as a result of the high matrix porosity. Hence, fiber-pullout measurements could not b used to assess the behavior of the composite from the behavior of performed. However, observation of the failure surface indicated he constituent fibers accurately that fiber fractures were not confined to one plane of the compos In regard to fiber composites, it has been suggested that the LM plot of applied stress versus @(see Eq.())for the composite ite, so that cracks were deflected at the fiber/matrix interface. should be identical to that for the fibers at an appropriate stress Examination of the polished edges of tested specimens demon- strated that the matrix-crack spacing on completion of a tensile test This method is thought to be applicable when the matrix has been was identical to that in virgin specimens(40 um). Typical fiber fully cracked, so that the fibers can be assumed to carry the entire failure surfaces were smooth, with no discernable fracture origin applied stress along their entire length. The LM data for the Some fiber-fracture surfaces at room temperature demonstrated Nextel"fibers, as determined by Yun et al., and the LM plots derived fro evidence of fracture mirrors: however, the proportion of such a range of loads and temperatures are shown in Fig. 3. The fiber-fracture surfaces of specimens tested at higher temperatures agreement is poor, particularly considering that the plot has a were similar in appearance to those tested at low temperature logarithmic time scale. Under stress-rupture loading conditions, the matrix-crack spac The MG approach envisions that rupture damage is driven by gs observed on the specimen edge were, again, 40 um, as creep deformation. The MG relationship between the steady-state strain rate t and the rupture lifetime f, is, from Eq (2) logt+klog∈=D where k and D again are constants(k= 1). Use of the measured 1050°C composite e value to predict the composite lifetime, with the constants k and D obtained from single fibers, has been proposed for composites wherein the matrix has not cracked and does carry load. For similar reasons, it should also apply when the matrix is fully cracked and does not carry any load, so that both creep and rupture are strongly fiber-dominated. Figure 4 shows a log-log plot of the rupture lifetime versus the steady-state creep rate obtained for the single Nextel 610 fibers and for the composites studied here. At a given te ure, the composite data do show 100 a linear relationship that is consistent with Eq (3), but the slope is substantially different from that for the individual fibers, further. more, at different temperatures. the single-fiber data almost fall 00.050 0.1502 030.3504 long a common line, which indicates that Eq. (3)applies, with k and D independent of temperatur where data are shifted by substantial fa hich suggests that k is indep Fig. 2. Measured quasi-static stress-strain curves at several temperatures of temperature but D is strongly dependent on temperature. Such black lines) and fits at elevated behavior has been observed previously in monolithic ceramics such as silicon nitride(see, for example, Ferber and Jenkins, S 0.=1060 MPa at 950 C and 1000 MPa at 1050 C (curves offset by 0.1% Luecke et al.,and Menon et al. "). At a fixed temperature, the for cla MG corre n creep and rupture do to t
Journal of the American Ceramic Society-Halverson and Curtin Vol. 85. No 6 Table L. Quasi-static Tension Test Results Modulus(GPa) Strength(MPa Failure strain (5) Number of tests 245± 392±63 0.177±0.034 4 189±6 0.194±0.037 1050 191±16 370±54 0.214±0.018 1093 197±14 305+28 0.206±0.240 composite system: a measurement of creep can be used to accurate. A lack of correlation "predict"the failure time(although Fig. 4 shows that order-of- between the composi fiber data also exists: therefore magnitude fluctuations in life exist at a fixed creep rate). However, we do not advocate th e of these approaches to describe the shift in the MG plot with temperature limits such"predictions the high-temperature ind failure of ceramic compos to each temperature of interest. Furthermore, the behavior does not ites. These facts further motivate the consideration of microme relate with the single-fiber data, so that fiber data alone are chanical models for rupture insufficient to predict composite life. The MG approach suggests a coupling of creep and rut However, a relationship that follows Eq. (3)is obtained when IlL. Micromechanical Model of Composite Stress Rupture reep and rupture have independent power-law dependencies on the applied stress. Specifically, if the creep rate follows the relation The composite degradation and stress-rupture model proposed e=Ao while the rupture lifetime follows the relation t,= Bo cre are based on an analysis of the stochastic accumulation of then one can obtain the MG form precisely, as fiber failure in the material. The matrix and the fiber/matrix interface determine, through micromechanical models, the stress log∈=lg(BA") state in the fibers, which governs the rate of fiber degradation, as (4) shown schematically in Fig. 5. Here, we begin with an analysis of independent of any physical relationship between the two. mecha associated fiber degradation without considering the effects of nisms. If the two mechanisms are physically different, then th previously damaged fibers on the stress state. Subsequently, the "constant"log(BA")=D should be strongly dependent on temper behavior of the collection of interacting fibers in the composite is ature, despite the fact that the slope rc is independent of temperature considered, which leads to the full model for composite damage but the rate prefactors A and B should be Arrhenius-like with evolution and failure. The general approach encompasses both completely different activation energies: this dependence has been quasi-static and stress-rupture behavior quite naturally; therefore. observed with our te data. Thus. the existence of an MG 1G we begin with the quasi-static problem, because it sets the stage for correlation"at a single temperature has no implications for the the subsequent time evolution interdependence of creep and rupture in this composite system Neither the LM approach nor the MG approach contain under- (1) Fiber Strength, Stress, and degradation ying information about damage state, nor do they provide infor- (A) Quasi-static Behavior: Ceramic fibers are brittle materials remaining strength or any other phenomena that whose strengths must be described statistically. This description is occur in the composite. Moreover, the general idea of applying single-fiber rupture data directly to explain composite rupture has commonly accomplished by assuming a single flaw population and using a tw eter Weibull model, for which the probability of several incorrect implications for composite failure and rupture. failure occurring in an increment of a fiber element of length 8z within The concept implies that composite rupture occurs at the average failure time of a single fiber at the(arbitrary)ex situt-tested gauge incremental stress range of o to o 8o is given by length Lo and, thus, because fiber strength is dependent on gauge length, that rupture life is dependent on the lo value used in the P(,b0,82) single-fiber experiments. This concept also implies that failure occurs when every fiber is typically broken once within a length lo Here, oo is the characteristic fiber strength at gauge length lo and in the composite and that the tensile strength is simply the volume m is the Weibull modulus, which describes the statistical distribu fraction of fibers multiplied by the typical fiber strength at lengt tion of the strength around o. Following previ ses 3. 38 the cumulative probability of fiber failure in a length 21, loaded at pplied stress Uno, where U nn and matrix damage cause a 10000 longitudinal-fiber stress profile o(z), is given by q(0=,D)=1 1000 叫 do(z) do'dz do(6) When o(z) is a constant value app), Eq.(6) reduces to the well-known Weibull expression (m,D)=1 n a unidirection a single matrix crack and a 25 33 debonded, sliding fiber/matrix interface described by an interfacial Q=T( t,+F) shear stress T, the fiber stress is dependent on position and Eq (6) must be used to determine failure. The stress on a fiber near an Fig. 3. Larso - rupture data and/unn versus parameter @) for isolated matrix crack located at the longitudinal position z =0 plot(applied stress (- single-fibe measured composite stress- under a remote applied stress app is accurately modeled by a rupture data. shear-lag model as follows. At the matrix- crack plane. the entire