J.Am.cerm.Soc.836]1469-75(200 urna Rate of Strength Decrease of Fiber- Reinforced Ceramic-Matrix Composites during Fatigu Bent f. sorensen Materials Research Department, Riso National Laboratory, DK-4000 Roskilde, Denmark John W. holmes Ceramic Composites Research Laboratory, Depart Mechanical Engineering and Applied Mechanics, of Michigan, Ann Arbor, Michigan 48109-2125 Eddy L. Vanswijgenhoven Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, De Croy laan 2, B-3001 Heverlee E An experimental investigation ormed to study the rate resistance must be sufficiently low, such that interfacial sliding can at which strength-controlling amage evolves in a readily take place ceramic-matrix composite Te pecimens of a unidirec- The stress-strain behavior of CMCs at high temperature may tional Sic-fiber-reinforced calcium aluminosilicate matrix differ from the behavior observed at room temperature since creep omposite were cycled to failure or to a preselected number of and oxidation damage may occur.9-lI If oxidation occurs at the cycles under similar loading histories. The residual strength of per/matrix interface, an interphase with strong bonding may he precycled specimens was found to be similar to that of form. 10, 12, 13 This hinders interfacial sliding, resulting in a loss of virgin specimens. Microstructural investigations showed that damage-tolerant behavior, the composite then fails in a brittle the fracture surfaces of the specimens cycled to failure had a manner central region where fiber pullout was negligible. It is pro- Most experimental studies of CMCs subjected to cyclic loading posed that frictional heating (due to interfacial sliding) is the have been conducted at room temperature. 2, 14-19 Typically, the ause of fatigue failure. High interfacial temperatures are assumed to cause the formation of a strong interface bond, composite stiffness decreases rapidly in the early cycles, reaching leading to internal embrittlement minimum within 10-10 cycles. ,The number of cycles to failure may be significantly higher than the number of cycles at which the modulus reaches a minimum. 7 Damage evolution L. Introduction during cyclic loading has been found to be similar to that found for monotonic tension(multiple matrix cracking, fiber/matrix debond- emperature load-carrying components, such as turbine blades or Macroscopically, this slip results in hysteresis in the stress-strain heat exchangers. Before CMCs can be used in such applications, behavior and a temperature rise of the specimens( frictional temperatures, and environments must be understoauons of loads, heating, 17,20). At the microscale, cyclic slip may result in their long-term behavior under complex combinati interfacial wear wering the interfacial frictional slid The monotonic stress-strain behavior of unidirectional compos- shear stress, T. It has been proposed that a decrease in the tes has been studied extensively at room temperature nterfacial shear stress may decrease the composite strength and underlying damage mechanisms have been identified as the initi cause fatigue failure. For instance, for 2D SiC/SiC, Rouby and ation and growth of multiple matrix cracks. The matrix cracks are Reynaud found a fatigue limit( maximum allowable stress, o bridged by intact fibers, with debonding and sliding occurring at giving run-out) at 2.5 x 10 cycles, which corresponded nicely the fiber/matrix interface. Composite failure occurs when the with predictions based on a decrease in T. In their study, fatigue fibers fail. This distinction between matrix cracking and composite failures all occurred within 2 x 10 cycles. This is consistent with fracture provides damage-tolerant behavior, that is attractive from the decrease in T, which occurs within a low number of cycles desensineering point of view. Models have been developed to Thus, for high stresses, a mechanism for low cycle fatigue failure these mechanisms. The models predict that in order to appears to be the cyclic-induced decrease in T. However, for other have a damage-tolerant behavior, the interface bonding and sliding CMCs, the number of cycles to failure can exceed by orders of magnitude the number of cycles at which the interfacial shear itional fatigue damage mechanisms exist. F. W. Zok-contributing editor Experimental fatigue studies conducted at high temperature have shown that embrittlement due to oxidation damage of the nterphase layer may be the most severe problem. 023-26Holmes found that the life of cyclically loaded SCS-6 SiC/Si, speci- 999nuscrip No. 189843. Received septemder u, 98, approved Decem mens at 1200C was shorter than the creep life. The fatigue life Support for B. F. Sorensen was decreased with decreasing stress ratio. This provides clear evi- o551 support was dence of a high-temperature fatigue-life controlling mechanism orce Office of Scientific Research( Grant No. F49620-95-1-0206) Thus, fatigue interactions with oxidation and creep are damage Member, American Ceramic Society mechanisms that must be understood 1469
Rate of Strength Decrease of Fiber-Reinforced Ceramic-Matrix Composites during Fatigue Bent F. Sørensen Materials Research Department, Risø National Laboratory, DK-4000 Roskilde, Denmark John W. Holmes Ceramic Composites Research Laboratory, Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, Michigan 48109-2125 Eddy L. Vanswijgenhoven Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, De Croylaan 2, B-3001 Heverlee, Belgium An experimental investigation was performed to study the rate at which strength-controlling fatigue damage evolves in a ceramic-matrix composite. Tensile specimens of a unidirectional SiC-fiber-reinforced calcium aluminosilicate matrix composite were cycled to failure or to a preselected number of cycles under similar loading histories. The residual strength of the precycled specimens was found to be similar to that of virgin specimens. Microstructural investigations showed that the fracture surfaces of the specimens cycled to failure had a central region where fiber pullout was negligible. It is proposed that frictional heating (due to interfacial sliding) is the cause of fatigue failure. High interfacial temperatures are assumed to cause the formation of a strong interface bond, leading to internal embrittlement. I. Introduction BECAUSE of their damage-tolerant behavior, ceramic-matrix composites (CMCs) have the potential for use in hightemperature load-carrying components, such as turbine blades or heat exchangers. Before CMCs can be used in such applications, their long-term behavior under complex combinations of loads, temperatures, and environments must be understood.1 The monotonic stress–strain behavior of unidirectional composites has been studied extensively at room temperature.2–4 The underlying damage mechanisms have been identified as the initiation and growth of multiple matrix cracks. The matrix cracks are bridged by intact fibers, with debonding and sliding occurring at the fiber/matrix interface. Composite failure occurs when the fibers fail. This distinction between matrix cracking and composite fracture provides damage-tolerant behavior; that is attractive from an engineering point of view. Models have been developed to describe these mechanisms.5–8 The models predict that in order to have a damage-tolerant behavior, the interface bonding and sliding resistance must be sufficiently low, such that interfacial sliding can readily take place. The stress–strain behavior of CMCs at high temperature may differ from the behavior observed at room temperature, since creep and oxidation damage may occur.9–11 If oxidation occurs at the fiber/matrix interface, an interphase with strong bonding may form.10,12,13 This hinders interfacial sliding, resulting in a loss of damage-tolerant behavior; the composite then fails in a brittle manner. Most experimental studies of CMCs subjected to cyclic loading have been conducted at room temperature.2,14–19 Typically, the composite stiffness decreases rapidly in the early cycles, reaching a minimum within 103 –105 cycles.15,17 The number of cycles to failure may be significantly higher than the number of cycles at which the modulus reaches a minimum.17 Damage evolution during cyclic loading has been found to be similar to that found for monotonic tension (multiple matrix cracking, fiber/matrix debonding and sliding). In addition, during cyclic loading, repeated forward and reverse slip can occur at the fiber/matrix interface. Macroscopically, this slip results in hysteresis in the stress–strain behavior and a temperature rise of the specimens (frictional heating16,17,20). At the microscale, cyclic slip may result in interfacial wear,17,19,21 lowering the interfacial frictional sliding shear stress, t. It has been proposed that a decrease in the interfacial shear stress may decrease the composite strength and cause fatigue failure.19 For instance, for 2D SiC/SiC, Rouby and Reynaud19 found a fatigue limit (maximum allowable stress, smax giving run-out) at 2.5 3 105 cycles, which corresponded nicely with predictions based on a decrease in t. In their study, fatigue failures all occurred within 2 3 104 cycles. This is consistent with the decrease in t, which occurs within a low number of cycles. Thus, for high stresses, a mechanism for low cycle fatigue failure appears to be the cyclic-induced decrease in t. However, for other CMCs, the number of cycles to failure can exceed by orders of magnitude the number of cycles at which the interfacial shear stress reaches a minimum value.17,20,22 This disparity suggests that additional fatigue damage mechanisms exist. Experimental fatigue studies conducted at high temperature have shown that embrittlement due to oxidation damage of the interphase layer may be the most severe problem.10,23–26 Holmes27 found that the life of cyclically loaded SCS-6 SiCf /Si3N4 specimens at 1200°C was shorter than the creep life. The fatigue life decreased with decreasing stress ratio. This provides clear evidence of a high-temperature fatigue-life controlling mechanism. Thus, fatigue interactions with oxidation and creep are damage mechanisms that must be understood. F. W. Zok—contributing editor Manuscript No. 189843. Received September 30, 1998; approved December 14, 1999. Support for B. F. Sørensen was provided by the Risø Engineering Science Center for Structural Characterization and Modeling of Materials. Additional support was provided by the National Science Foundation (Grant No. DMR-9257557) and the Air Force Office of Scientific Research (Grant No. F49620-95-1-0206). *Member, American Ceramic Society. J. Am. Ceram. Soc., 83 [6] 1469–75 (2000) 1469 journal
can Ceramic SocietSoren Vol. 83. No 6 Fatigue failure occurs when the residual strength of the com-(3) Microstructural Characterization posite, O, has decreased to the maximum applied cyclic stress, gmax. It is the aim of the present study to investigate t After the tensile or fatigue tests, the average matrix crack the rate at which the strength-controlling damage evolves in a CMC during spacing was measured at the ished face by optical microscopy prior work had shown that well-developed surface cracks typi he experimental ap- cally span the entire cross section of a specimen), as follows:The proach is straightforward. The tensile strength of virgin and number of cracks was counted along 20-30 mm long lines parallel refatigued specimens is determined experimentally. Other speci- with the fiber direction. Usually more than 300 cracks were nens are cycled under similar conditions until fatigue failure counted. All measurements were taken away from the localized ccurs. Then, a diagram of composite strength as a function of region associated with the fracture surface Fracture surfaces were number of load cycles can be constructed inspected with optical and environmental sca electron micro- scopes(Model E-3, ElectroScan Corp, Wilmington, MA). In order to observe debris at the fracture surfaces, the specimens were II. Experimental Methods neither cleaned nor coated before being investigated. Finally, using (I Specimen Preparation a conventional scanning electron microscope, overview pictures The material used in this study was an 8-ply unidirectional were taken of gold-coated fracture surfaces Nicalon SiC-fiber-reinforced calcium aluminosilicate composit denoted SiC/CAS II, from Corning Inc. The nominal fiber volume Il. Results and discussion fraction was 35-40%. The composite was processed by hot pressing. During processing, an approximately 0 I um thick (I Monotonic Tensile Tests of virgin Specimens arbon-rich interphase layer developed around the SiC fibers, Typical stress-strain curves for the virgin material are shown in (The thickness of the carbon layer, which depends on processing Fig. I. The shape of the stress-strain curves is typical of damage conditions, was not measured in the present study. )The carbon- tolerant CMCs, , The shape reflects elastic response at low interphase layer is known to enable debonding and frictional strain(stage D), multiple matrix cracking(stage ID), large-scale sliding along the interfaces. The fiber diameters were in the range interfacial slip along the interfaces of intact fibers(stage II),and distributed fiber failures(stage IV) prior to localization of damage Edge-loaded tensile specimens, with the Some characteristic parameters of the virgin composite are sum parallel with the fiber direction, were cut from rec marized in Table I. E. is the elastic modulus within the first linear portion of the stress-strain curve, Uo.oz is the stress level where the crack spacing to be measured. The polishing was performed using axial strain, e, deviates 0.02% from linear elasticity(note that a 38 mm mandrel rotating at 1500 rpm. The following polishing matrix cracks develop below oo.o? T. and E. are the failure procedure was used: (1)600-grit SiC paper for 5 min, (2)45 um stress and strain, respectively, and s is the average matrix crack in(nylon cloth), (4)1. 0 um diamond paste for 10 min(nylon s was calculated by the rule of mixtures, utilizing a Young's modulus of 200 and 98 GPa, respectively, for the fibers and matrix.",A similar value of v was found by the area fraction method (i. e, by using micrographs to estimate the cross-sectional (2) Mechanical Testing area fraction of fibers For all specimens, the fracture was located within the gage Four specimens were loaded in monotonic uniaxial tension(the section. The fracture surface was macroscopically flat, but dis ading rate was 100 MPa/s)to establish the stiffness and strength of the virgin material. Four other specimens were cycled under played considerable fiber pull-out(Fig. 2). In the region near the identical conditions(o 240 MPa, omin 10 MPa, 200 Hz) fracture surface, the matrix cracks were opened significantly more until fatigue failure occurred. Four additional specimens were opening is assumed to have occurred by fibers that had broken and cycled under the same conditions, but for only 10 cycles, which subsequently pulled out. Thus, the length of this localization zone, vas slightly lower than the number of cycles to failure found for L(Table I), is an indirect measure of the interfacial slid the previous samples. These specimens were then loaded in stress monotonic tension(100 MPa/s) in order to measure the residual strength of the composite after 10 cycles nts were conducted on a mTS servohydrau- (2) Specimens Cycled to Failure ic test frame(Model No 331, MTS Systems Corp, Minneapolis, The shape of the cyclic stress-strain curves changed during MN). The fatigue tests were performed inside a 0. 1 m'water ycling. These changes were accompanied by the development of cooled chamber, where the temperature of the walls and grips was a permanent offset strain, e", and an increase in the surface kept constant at 22.0+0. 1C(see Holmes and Cho for details) The temperature rise of the specimen surface(caused by frictional ating)was measured with an infrared pyrometer(Model No 5402, Everest Interscience Inc, Fullerton, CA), focused at a 5 mm 600 [o] SiC/CAS pot size within the specimen gauge section. In order to achieve 100 PAls table temperature conditions, the chamber temperature was al lowed to stabilize for at least 2 h before the fatigue tests were arted. The axial strain data were measured with an extensometer (Model 632.27B-20, MTS System Corp )with a 33 mm gauge length. For the cyclic tests, the extensometer was mounted along a specimen edge by O-rings and fixed to the specimen with Super-Glue. Stress-strain data were recorded at regular intervals, and from these data the hysteresis modulus(averaged over one cycle) was calculated as a function of the number of load cycles The specimens were cycled between omin= 10 MPa an omax= 240 MPa with a sinusoidal waveform at a frequency of 200 02040.60.811.21.4 Hz. In order to prevent overshooting during the first few load Strain cycles, the load span was increased (linearly with time) from zero Fig. 1. Two typical monotonic stress-strain curves obtained from vi to the maximum stress within o8s
Fatigue failure occurs when the residual strength of the composite, su, has decreased to the maximum applied cyclic stress, smax. It is the aim of the present study to investigate the rate at which the strength-controlling damage evolves in a CMC during high cycle fatigue at room temperature. The experimental approach is straightforward. The tensile strength of virgin and prefatigued specimens is determined experimentally. Other specimens are cycled under similar conditions until fatigue failure occurs. Then, a diagram of composite strength as a function of number of load cycles can be constructed. II. Experimental Methods (1) Specimen Preparation The material used in this study was an 8-ply unidirectional Nicalon SiC-fiber-reinforced calcium aluminosilicate composite, denoted SiCf /CAS II, from Corning Inc. The nominal fiber volume fraction was 35–40%. The composite was processed by hot pressing. During processing, an approximately 0.1 mm thick carbon-rich interphase layer developed around the SiC fibers12,13 (The thickness of the carbon layer, which depends on processing conditions, was not measured in the present study.) The carboninterphase layer is known to enable debonding and frictional sliding along the interfaces. The fiber diameters were in the range of 10–20 mm. Edge-loaded tensile specimens,28 with the tensile direction parallel with the fiber direction, were cut from rectangular plates. A minor face of each specimen was polished to allow the matrix crack spacing to be measured. The polishing was performed using a 38 mm mandrel rotating at 1500 rpm. The following polishing procedure was used: (1) 600-grit SiC paper for 5 min, (2) 45 mm diamond paste for 5 min (nylon cloth), (3) 6 mm diamond paste for 5 min (nylon cloth), (4) 1.0 mm diamond paste for 10 min (nylon cloth). (2) Mechanical Testing Four specimens were loaded in monotonic uniaxial tension (the loading rate was 100 MPa/s) to establish the stiffness and strength of the virgin material. Four other specimens were cycled under identical conditions (smax 5 240 MPa, smin 5 10 MPa, 200 Hz) until fatigue failure occurred. Four additional specimens were cycled under the same conditions, but for only 105 cycles, which was slightly lower than the number of cycles to failure found for the previous samples. These specimens were then loaded in monotonic tension (100 MPa/s) in order to measure the residual strength of the composite after 105 cycles. All fatigue experiments were conducted on a MTS servohydraulic test frame (Model No. 331, MTS Systems Corp., Minneapolis, MN). The fatigue tests were performed inside a 0.1 m3 watercooled chamber, where the temperature of the walls and grips was kept constant at 22.0 6 0.1°C (see Holmes and Cho17 for details). The temperature rise of the specimen surface (caused by frictional heating) was measured with an infrared pyrometer (Model No. 5402, Everest Interscience Inc., Fullerton, CA), focused at a 5 mm spot size within the specimen gauge section. In order to achieve stable temperature conditions, the chamber temperature was allowed to stabilize for at least 2 h before the fatigue tests were started. The axial strain data were measured with an extensometer (Model 632.27B-20, MTS System Corp.) with a 33 mm gauge length. For the cyclic tests, the extensometer was mounted along a specimen edge by O-rings and fixed to the specimen with Super-Glue. Stress–strain data were recorded at regular intervals, and from these data the hysteresis modulus (averaged over one cycle) was calculated as a function of the number of load cycles. The specimens were cycled between smin 5 10 MPa and smax 5 240 MPa with a sinusoidal waveform at a frequency of 200 Hz. In order to prevent overshooting during the first few load cycles, the load span was increased (linearly with time) from zero to the maximum stress within 0.8 s. (3) Microstructural Characterization After the tensile or fatigue tests, the average matrix crack spacing was measured at the polished face by optical microscopy (prior work had shown that well-developed surface cracks typically span the entire cross section of a specimen), as follows: The number of cracks was counted along 20–30 mm long lines parallel with the fiber direction. Usually more than 300 cracks were counted. All measurements were taken away from the localized region associated with the fracture surface. Fracture surfaces were inspected with optical and environmental scanning electron microscopes (Model E-3, ElectroScan Corp., Wilmington, MA). In order to observe debris at the fracture surfaces, the specimens were neither cleaned nor coated before being investigated. Finally, using a conventional scanning electron microscope, overview pictures were taken of gold-coated fracture surfaces. III. Results and Discussion (1) Monotonic Tensile Tests of Virgin Specimens Typical stress–strain curves for the virgin material are shown in Fig. 1. The shape of the stress–strain curves is typical of damagetolerant CMCs.3,4,17 The shape reflects elastic response at low strain (stage I), multiple matrix cracking (stage II), large-scale interfacial slip along the interfaces of intact fibers (stage III), and distributed fiber failures (stage IV) prior to localization of damage. Some characteristic parameters of the virgin composite are summarized in Table I. Ec is the elastic modulus within the first linear portion of the stress–strain curve, s0.02 is the stress level where the axial strain, ε, deviates 0.02% from linear elasticity (note that matrix cracks develop below s0.02 3,4), su and εu are the failure stress and strain, respectively, and s is the average matrix crack spacing measured after the tensile test. The fiber volume fraction, vf , was calculated by the rule of mixtures, utilizing a Young’s modulus of 200 and 98 GPa, respectively, for the fibers and matrix.3,4 A similar value of vf was found by the area fraction method (i.e., by using micrographs to estimate the cross-sectional area fraction of fibers). For all specimens, the fracture was located within the gage section. The fracture surface was macroscopically flat, but displayed considerable fiber pull-out (Fig. 2). In the region near the fracture surface, the matrix cracks were opened significantly more than at locations distant to the fracture site. This enhanced crack opening is assumed to have occurred by fibers that had broken and subsequently pulled out. Thus, the length of this localization zone, L (Table I), is an indirect measure of the interfacial sliding shear stress. (2) Specimens Cycled to Failure The shape of the cyclic stress–strain curves changed during cycling. These changes were accompanied by the development of a permanent offset strain, ε*, and an increase in the surface Fig. 1. Two typical monotonic stress–strain curves obtained from virgin specimens. 1470 Journal of the American Ceramic Society—Sørensen et al. Vol. 83, No. 6
June2000ateofSmenghDecreaseofFiberReinorcedceramic-MarixComposiesdhuringanigue 1471 Table Summary of Monotonic Tensile 140 Test Results 133.7±3.4GPa 51±8MPa 08±31MPa 1.05±0.17% 154±17m gn3°0 0.35±003 100 F [oJ] SIC/CAS ≈04mm g =240 MPa 200 Hz. RT 03 0= 240 MPa 60200Hz,RT Imm W025 Fig. 2. SEM micrograph showing the fracture surface of a spe Cycles tested in monotonic tension Fig. 3. Recorded damage indicators for two typical specimens cycle evolution of the hysteresis modulus as a function of the number of load temperature, AT, of the specimen(due to frictional cycles N;(b)temperature rise, AT, as a function of the number of cycles. The hysteresis modulus, E, was calculated from the stress-strain data. Figure 3(a)shows how E changes as a function of the number Table l characteristies of of cycles N for specimens that were cycled to failure. The Specimens Cycled to Failure evolution of E for all four specimens follows the same trend: The 87 7GPa modulus decreases significantly, to about 87 GPa within approx- lately 2 x 10 cycles. Thereafter E remains nearly constant(a 0.08±0.01% slight modulus recovery, about I GPa, was found for two of the l44±33pm specimens) L Values for the characteristic parameters are listed in Table Il 1.3×105-3.5×105 Note that the values of e and e are the values that were measured 69±14K just before localization occurred; s was measured away from the calized region after fatigue failure. These parameters can thus be used in micromechanical models. which are based on intact fibers Figure 3(b)shows the temperature rise curves recorded for the( Fig. 4(a)suggests that the center region failed before final specimens cycled to failure. For these specimens fatigue failure overload of the remainder cross section. At some locations(within occurred outside the 5 mm spot size of the infrared pyrometer. The the core region with no fiber pull-out)significant debris was heating curves follow the same trend; they increased slowly within present(Fig. 4(b)) the first 10 cycles, but increased rapidly during additional cycling Like the fracture surface, the broad faces of the specimens were This rapid increase is attributed to an increasing number of matrix found to have an inhomogeneous appearance. Along the sides of cracks and accompanying slip zones. The peak temperatures of the the specimens there were zones with larger matrix crack openings fact that the specimens fail at different numbers of cycles, while L, was about 6-10 times the matrix crack spacing. This the temperature is increasing. If they had failed at the same number considerably larger than the localized zone found after monoton- of cycles, the maximum temperature rise of each specimen likel ically loading virgin specimens to failure(see Table I). The larger would have been roughly the same. For specimens that failed L of the cyclically loaded specimens indicates a lower value of T within the spot size of the pyrometer a very rapid temperature rise In contrast, in the middle of the broad face( where the core region occurred within the last few seconds before failure was close to the surface), there was no such localized zone, the The fracture surfaces of the specimens cycled to failure had two matrix crack opening was similar to that remote from the fracture distinctively different regions. One part of the fracture surface site. This indicates that no global load sharing and no fiber pull-out displayed fiber pull-out, while the other area had no fiber pull-out had taken place near the core region during specimen failure (Fig. 4). The area without fiber pull-ou ocated in the core of the specimen cross section; fiber pull always present in region near the specimen edges. This ap nce is opposite to 1 (3) Specimens Cycled to 10 Cycles found at the fracture surfaces of specimens that have been exp The evolution of hysteresis modulus and the temperature rise of to external oxidation. The appearance of the fracture su specimens cycled to 10. cycles are included in Fig. 3. After
temperature, DT, of the specimen (due to frictional energy dissipation). The hysteresis modulus, E#, was calculated from the stress–strain data. Figure 3(a) shows how E# changes as a function of the number of cycles N for specimens that were cycled to failure. The evolution of E# for all four specimens follows the same trend: The modulus decreases significantly, to about 87 GPa within approximately 2 3 105 cycles. Thereafter E# remains nearly constant (a slight modulus recovery, about 1 GPa, was found for two of the specimens). Values for the characteristic parameters are listed in Table II. Note that the values of E# and ε* are the values that were measured just before localization occurred; s was measured away from the localized region after fatigue failure. These parameters can thus be used in micromechanical models, which are based on intact fibers. Figure 3(b) shows the temperature rise curves recorded for the specimens cycled to failure. For these specimens fatigue failure occurred outside the 5 mm spot size of the infrared pyrometer. The heating curves follow the same trend; they increased slowly within the first 104 cycles, but increased rapidly during additional cycling. This rapid increase is attributed to an increasing number of matrix cracks and accompanying slip zones. The peak temperatures of the four specimens differ somewhat. This difference is attributed to the fact that the specimens fail at different numbers of cycles, while the temperature is increasing. If they had failed at the same number of cycles, the maximum temperature rise of each specimen likely would have been roughly the same. For specimens that failed within the spot size of the pyrometer a very rapid temperature rise occurred within the last few seconds before failure. The fracture surfaces of the specimens cycled to failure had two distinctively different regions. One part of the fracture surface displayed fiber pull-out, while the other area had no fiber pull-out (Fig. 4). The area without fiber pull-out was located in the core of the specimen cross section; fiber pull-out was always present in a region near the specimen edges. This appearance is opposite to that found at the fracture surfaces of specimens that have been exposed to external oxidation.11 The appearance of the fracture surface (Fig. 4(a)) suggests that the center region failed before final overload of the remainder cross section. At some locations (within the core region with no fiber pull-out) significant debris was present (Fig. 4(b)). Like the fracture surface, the broad faces of the specimens were found to have an inhomogeneous appearance. Along the sides of the specimens there were zones with larger matrix crack openings (Fig. 5). The length (in the fiber direction) of this localized zone, L, was about 6–10 times the matrix crack spacing. This is considerably larger than the localized zone found after monotonically loading virgin specimens to failure (see Table I). The larger L of the cyclically loaded specimens indicates a lower value of t. In contrast, in the middle of the broad face (where the core region was close to the surface), there was no such localized zone; the matrix crack opening was similar to that remote from the fracture site. This indicates that no global load sharing and no fiber pull-out had taken place near the core region during specimen failure. (3) Specimens Cycled to 105 Cycles The evolution of hysteresis modulus and the temperature rise of specimens cycled to 105 cycles are included in Fig. 3. After Table I. Summary of Monotonic Tensile Test Results Ec 133.7 6 3.4 GPa s0.02 351 6 8 MPa su 508 6 31 MPa εu 1.05 6 0.17% s 154 6 17 mm vf 0.35 6 0.03 L '0.4 mm Fig. 2. SEM micrograph showing the fracture surface of a specimen tested in monotonic tension. Fig. 3. Recorded damage indicators for two typical specimens cycled to failure (solid lines) and specimens cycled to 105 cycles (dashed lines): (a) evolution of the hysteresis modulus as a function of the number of load cycles N; (b) temperature rise, DT, as a function of the number of cycles. Table II. Characteristics of Specimens Cycled to Failure E# 87 6 7 GPa ε* 0.08 6 0.01% s 144 6 33 mm L '1.0 mm Nf 1.3 3 105 –3.5 3 105 (DT)max 69 6 14 K June 2000 Rate of Strength Decrease of Fiber-Reinforced Ceramic-Matrix Composites during Fatigue 1471
1472 can ceramic soc Vol. 83. No 6 Fig. 4. Micrographs showing part of the fracture surface of a typical specimen cycled to fatigue failure: (a)overview(conventional SEM), showing the core region without fiber pull-out and the external region with extensive pull-out; (b) ESEM micrograph of the core region with no fiber pull-out, but debris at the fibers and matrix Virgin Specimen 15KV 1 mm WD43 Fig. 6. Comparison between the ain behavior of a virgin Fig. 5. Micrograph of the broad face of a specimen cycled to failure. Near nd the tensile curve of a precycled specimen. The stress-strain the edge there is a zone where the fiber pull-out has caused larger crack curve of the precycled specimen is offset by the permanent strain, E, that penings. The length of this zone, L, is about 8-10 crack spacings. In the was recorded at zero load after cycling. The two curves are very similar for center of the specimens(close to the core region) such a zone is absent. stresses above the matrix crack saturation of the virgin specimen material. In order to obtain a true comparison, the strain value of cycling, the specimens had a permanent strain, e*. The average the prefatigued specimen is offset by a value e*, which is the matrix crack spacing was measured after cycling and after the tensile tests (Table Ill). E was measured from the stress-strain data permanent strain that was recorded at the unloaded state after cycling. While the monotonic tensile curve of the virgin specim (0-0.2% axial strain)obtained from the residual strength test, and exhibits linear elastic behavior at low applied stress, the tensile the interfacial shear stress T was calculated from models- usin the approach described in the Appendix. The value of T at 10 curve of the prefatigued specimen is nonlinear even at low loads cycles(6 MPa) is roughly similar to the value derived from This nonlinearity is attributed to the fact that the precycled frictional heating experiments, 2 but significantly lower than the specimens possess significant damage(distributed matrix cracking and interfacial debonding) prior to the tensile test, while the virgi material is free of damage Beyond 400 MPa(assumed to be the MPa. 17, 32-34 This confirms the hypothesis that t decreases during stress level corresponding to matrix crack saturation) the two cycling(note, however, that T may be velocity dependent4, 35) A typical tensile curve for a specimen cycled to 10 cycles is curves follow each other closely. This indicates that the damage states of the virgin and precycled specimens are very similar at plotted in Fig. 6, together with a stress-strain curve for the virgin these stress levels. Indeed, the average matrix crack spacing was 154 10 um for the virgin specimens(after the tension test)and 156+ 10 um for the specimens cycled to 10 cycles(after Table Ill. Characteristics of Specimens cycling), and 112 10 um after the residual strength tests. The Cycled to 10 Cycles residual strength of the prefatigued specimens was 491+ 13 MPa 91.3±1.5GP (Table Ill). Thus, both the matrix crack spacing and the composite 0.07±0.01% strength of the prefatigued specimens were fairly similar to those 156±10m(1±10pm) of the virgin specimens The fracture surface of the prefatigued specimens had a large amount of fiber pull-out(see Fig. 7). Unlike the specimens cycled 491±13MPa to failure, the prefatigued specimens showed fiber pull-out over the 60±07MPa entire fracture surface. The pull-out length of the precycled ax63±3K specimens is significantly longer than for the virgin specimens f s in parentheses refers to the value measured (compare Figs. 2 and 7). The length of the localized also longer than for the virgin specimens. Both of e esults
cycling, the specimens had a permanent strain, ε*. The average matrix crack spacing was measured after cycling and after the tensile tests (Table III). E# was measured from the stress–strain data (0–0.2% axial strain) obtained from the residual strength test, and the interfacial shear stress t was calculated from models29–31 using the approach described in the Appendix. The value of t at 105 cycles (6 MPa) is roughly similar to the value derived from frictional heating experiments,17,22 but significantly lower than the value for the virgin composite, which is typically about 20–30 MPa.17,32–34 This confirms the hypothesis that t decreases during cycling (note, however, that t may be velocity dependent34,35). A typical tensile curve for a specimen cycled to 105 cycles is plotted in Fig. 6, together with a stress–strain curve for the virgin material. In order to obtain a true comparison, the strain value of the prefatigued specimen is offset by a value ε*, which is the permanent strain that was recorded at the unloaded state after cycling. While the monotonic tensile curve of the virgin specimen exhibits linear elastic behavior at low applied stress, the tensile curve of the prefatigued specimen is nonlinear even at low loads. This nonlinearity is attributed to the fact that the precycled specimens possess significant damage (distributed matrix cracking and interfacial debonding) prior to the tensile test, while the virgin material is free of damage. Beyond 400 MPa (assumed to be the stress level corresponding to matrix crack saturation) the two curves follow each other closely. This indicates that the damage states of the virgin and precycled specimens are very similar at these stress levels. Indeed, the average matrix crack spacing was 154 6 10 mm for the virgin specimens (after the tension test) and 156 6 10 mm for the specimens cycled to 105 cycles (after cycling), and 112 6 10 mm after the residual strength tests. The residual strength of the prefatigued specimens was 491 6 13 MPa (Table III). Thus, both the matrix crack spacing and the composite strength of the prefatigued specimens were fairly similar to those of the virgin specimens. The fracture surface of the prefatigued specimens had a large amount of fiber pull-out (see Fig. 7). Unlike the specimens cycled to failure, the prefatigued specimens showed fiber pull-out over the entire fracture surface. The pull-out length of the precycled specimens is significantly longer than for the virgin specimens (compare Figs. 2 and 7). The length of the localized zone, L, was also longer than for the virgin specimens. Both of these results Fig. 4. Micrographs showing part of the fracture surface of a typical specimen cycled to fatigue failure: (a) overview (conventional SEM), showing the core region without fiber pull-out and the external region with extensive pull-out; (b) ESEM micrograph of the core region with no fiber pull-out, but debris at the fibers and matrix. Fig. 5. Micrograph of the broad face of a specimen cycled to failure. Near the edge there is a zone where the fiber pull-out has caused larger crack openings. The length of this zone, L, is about 8–10 crack spacings. In the center of the specimens (close to the core region) such a zone is absent. Table III. Characteristics of Specimens Cycled to 105 Cycles E# 91.3 6 1.5 GPa ε* 0.07 6 0.01% s 156 6 10 mm (112 6 10 mm)† L '0.8 mm su 491 6 13 MPa t 6.0 6 0.7 MPa (DT)max 63 6 3 K † Value of s in parentheses refers to the value measured after the tensile test. Fig. 6. Comparison between the stress–strain behavior of a virgin specimen and the tensile curve of a precycled specimen. The stress–strain curve of the precycled specimen is offset by the permanent strain, ε*, that was recorded at zero load after cycling. The two curves are very similar for stresses above the matrix crack saturation of the virgin specimen. 1472 Journal of the American Ceramic Society—Sørensen et al. Vol. 83, No. 6
Rate of strength Decrease of Fiber-Reinforced Ceramic-Matrix Composites during Fatigue 0=240 MPa [og] SiC/CAS ll 200 Hz, RT 15K 1静028 0210310′ 0510° Number of cycles, N Fig 8. Residual co ngth as a function of the number of cycled to 10 cycles and tested in monotonic tension thereafter cycles. The residual strength is fully retained at approximately 500 MPa until 10 cycles, but decreases to 240 MPa within a short number of cycle suggest that T was lower for the precycled specimens than for the virgin material IV. A Possible High Cycle Fatigue Damage Mechanism (1 Summary of Observed Behavior (4) Model Prediction of Residual Strength There are several characteristic features of the high-frequency Existing models for composite strength predict that a decrease fatigue process in T should result in a decrease in the residual strength. These (1)The temperature of the specimen increases during the models are valid only if global load sharing(GLS)takes place; this initial stages of fatigue. Next, it levels off and, for long-duration requirement is fulfilled for specimens where fiber pull-out occurs atigue at moderate stress levels. decreases. If failure is avoided across the entire fracture surface and the fiber pull-out length the shape of the temperature rise curve is often bell shaped. If varies from one fiber to the next. These assumptions are fulfilled failure occurs, a sharp rise in temperature occurs within the for the virgin specimens and the specimens cycled to 10 cycles localized zone immediately prior to fracture(typically of the order GLS models predict that the residual strength after N cycles, of several seconds ). o (N), is related to the initial composite strength, ou,as (2) The density of matrix rapidly during the itial stages of fatigue. For o(N)/(N)\/m+l) density quickly stabilizes and for the duration of (1) the fatigue life. The development of matrix cracks is assumed to be influenced by stress corrosion crackingand decrease in T due to where T is the initial value of T, M is the value attained after M interfacial wea cycles, and m is the Weibull modulus describing the strength ( The hysteresis modulus decreases rapidly during the initial tages of fatigue, reaches an approximate plateau, and, if failure is ariation of the fibers(in Eq (1)the fiber strength is assumed to avoided, may show a gradual increase. The initial modulus remain unchanged during cycling). Equation(1)predicts that if T decreases during cycling(aN)<T), then the residual strength of decrease is attributed to the formation of matrix cracks and a posite decreases as well. U =20MPa,N=105) decrease in T, the later modulus recovery is likely to be caused by 6 MPa, m=3(value taken from Curtin), ou= 508 MPa (Table an increase in T. The increase in T may be caused by various D), Eq (1) predicts o (N=10 )=376 MPa. This prediction mechanisms, such as accumulation of debris along the interface ol significantly lower than the experimental results(491 MPa, Tabl a chemical reaction, increasing the interfacial sliding resistance or bondin II). This inconsistency indicates that a decrease in the interfacial shear stress, acting alone, may not have the effect predicted by the formation of a central zone where the fiber pull-out lengths are GLS models, and that the models do not adequately describe the negligible. Surrounding this zone, which consumes roughly half of the fracture surface, is a zone of extensive fiber pull-out. Speci- mens that were prefatigued at the same stress level, followed by (5) Residnal Strength as a Function of cycles monotonic loading to failure, exhibited extensive fiber pull-out From the measured strength values a graph that shows the throughout the entire fracture surface. Virgin specimens tested residual strength of the composite as a function of the number of cles can be constructed. The four specimens that were cycled to pull-out across the entire fracture surface. failure are also included in this graph, since the residual strength of these specimens must have been equal to omax(i.e, 240 MPa) (2) Interpretation of Fracture Surface and Failure Mode when they failed. The results are presented in Fig. 8. As already Since the fracture surface of the prefatigued specimens exhib- mentioned the residual strength of the specimens cycled for 10 ited extensive fiber pull-out, the central core(in specimens cycled les was almost the same as that measured for th to failure) must have formed very rapidly just prior to specimen specimens. From Fig 8, we conclude that the loss of composite fracture( between 10 cycles and the occurrence of fatigue failure) strength does not occur gradually over the fatigue life, rather, for To understand the development of the core region, we must this unidirectional composite, the loss of residual strength of th identify a mechanism that can form a region with no fiber pull-out composite occurs within the last 20% of the specimen lifetime within a short number of cycles. Apparently the final stage It should be noted that although the present results are obtained (localization) is not cycle count dependent but damage and at specific test conditions, similar results have been found under temperature rise dependent different conditions. Therefore, the trends of the results are likely The lack of fiber pull-out in the core region indicates that the to be of a general nature usual composite behavior (interfacial slip) has been hindered
suggest that t was lower for the precycled specimens than for the virgin material. (4) Model Prediction of Residual Strength Existing models for composite strength predict that a decrease in t should result in a decrease in the residual strength.8,19 These models are valid only if global load sharing (GLS) takes place; this requirement is fulfilled for specimens where fiber pull-out occurs across the entire fracture surface and the fiber pull-out length varies from one fiber to the next. These assumptions are fulfilled for the virgin specimens and the specimens cycled to 105 cycles. GLS models predict that the residual strength after N cycles, su(N), is related to the initial composite strength, su 0 , as19 su~N! su 0 5 S t~N! t0 D 1/~m11! (1) where t0 is the initial value of t, t(N) is the value attained after N cycles, and m is the Weibull modulus describing the strength variation of the fibers (in Eq. (1) the fiber strength is assumed to remain unchanged during cycling). Equation (1) predicts that if t decreases during cycling (t(N) , t0 ), then the residual strength of the composite decreases as well. Using t 5 20 MPa, t(N5105 ) 5 6 MPa, m 5 3 (value taken from Curtin8 ), su 0 5 508 MPa (Table I), Eq. (1) predicts su(N5105 ) 5 376 MPa. This prediction is significantly lower than the experimental results (491 MPa, Table II). This inconsistency indicates that a decrease in the interfacial shear stress, acting alone, may not have the effect predicted by the GLS models, and that the models do not adequately describe the high cycle fatigue failure of CMCs. (5) Residual Strength as a Function of Cycles From the measured strength values a graph that shows the residual strength of the composite as a function of the number of cycles can be constructed. The four specimens that were cycled to failure are also included in this graph, since the residual strength of these specimens must have been equal to smax (i.e., 240 MPa) when they failed. The results are presented in Fig. 8. As already mentioned the residual strength of the specimens cycled for 105 cycles was almost the same as that measured for the virgin specimens. From Fig. 8, we conclude that the loss of composite strength does not occur gradually over the fatigue life; rather, for this unidirectional composite, the loss of residual strength of the composite occurs within the last 20% of the specimen lifetime. It should be noted that although the present results are obtained at specific test conditions, similar results have been found under different conditions.36 Therefore, the trends of the results are likely to be of a general nature. IV. A Possible High Cycle Fatigue Damage Mechanism (1) Summary of Observed Behavior There are several characteristic features of the high-frequency fatigue process: (1) The temperature of the specimen increases during the initial stages of fatigue. Next, it levels off and, for long-duration fatigue at moderate stress levels, decreases. If failure is avoided, the shape of the temperature rise curve is often bell shaped. If failure occurs, a sharp rise in temperature occurs within the localized zone immediately prior to fracture (typically of the order of several seconds). (2) The density of matrix cracks increases rapidly during the initial stages of fatigue. For a fixed maximum stress, this crack density quickly stabilizes and remains constant for the duration of the fatigue life. The development of matrix cracks is assumed to be influenced by stress corrosion cracking37 and decrease in t due to interfacial wear.17 (3) The hysteresis modulus decreases rapidly during the initial stages of fatigue, reaches an approximate plateau, and, if failure is avoided, may show a gradual increase. The initial modulus decrease is attributed to the formation of matrix cracks and a decrease in t; the later modulus recovery is likely to be caused by an increase in t. The increase in t may be caused by various mechanisms, such as accumulation of debris along the interface or a chemical reaction, increasing the interfacial sliding resistance or bonding. (4) A unique feature of high cycle fatigue failure is the formation of a central zone where the fiber pull-out lengths are negligible. Surrounding this zone, which consumes roughly half of the fracture surface, is a zone of extensive fiber pull-out. Specimens that were prefatigued at the same stress level, followed by monotonic loading to failure, exhibited extensive fiber pull-out throughout the entire fracture surface. Virgin specimens tested under monotonic tension also exhibited nearly uniform fiber pull-out across the entire fracture surface. (2) Interpretation of Fracture Surface and Failure Mode Since the fracture surface of the prefatigued specimens exhibited extensive fiber pull-out, the central core (in specimens cycled to failure) must have formed very rapidly just prior to specimen fracture (between 105 cycles and the occurrence of fatigue failure). To understand the development of the core region, we must identify a mechanism that can form a region with no fiber pull-out within a short number of cycles. Apparently the final stage (localization) is not cycle count dependent but damage and temperature rise dependent. The lack of fiber pull-out in the core region indicates that the usual composite behavior (interfacial slip) has been hindered, Fig. 7. SEM micrographs of a typical fracture surface of a specimen cycled to 105 cycles and tested in monotonic tension thereafter. Fig. 8. Residual composite strength as a function of the number of load cycles. The residual strength is fully retained at approximately 500 MPa until 105 cycles, but decreases to 240 MPa within a short number of cycles thereafter. June 2000 Rate of Strength Decrease of Fiber-Reinforced Ceramic-Matrix Composites during Fatigue 1473
can ceramic either by an increase in the interfacial shear stress"). The predicted appearance of the fracture sur formation of strong interface bonding. If globa sharing consistent with the observations in Figs 4 and 5 cannot occur, the composite behaves like a brittle material in the It is plausible that it may take a certain temperature and time core; matrix cracking can penetrate the fibers before the interface damage reaches the critical state, where fiber But why has the damage developed differently in the center of slip can no longer occur. Thus, in the initial stages, fatigue damage the cross section than at the edges? The answer is not obvious, may increase slowly, without causing fiber failures ince for ID composites the macroscopic stress state(uniaxial The fatigue mechanism postulated above may in principle oncentration,and temperature field. The latter may vary across the specimen cross section, since energy is lost at the surface by may be understood in terms of the local temperature at the fiber/matrix interface, which may scale roughly with the energy dissipation. Both a larger stress range and a higher loading frequency increase the frictional energy dissipation(per unit time), (3) A Fatigue Damage Mechanism: Embrittlement Due to resulting in a higher temperature rise. This may accelerate the Internal Heating increase in T, and shorten the fatigue life Assume that the interfacial shear stress can increase or a strong (2)It has been found that thicker (32 ply) test specimens bonding can form with increasing temperature and time. Next, possess a lower fatigue life than thinner(8-ply) specimens. The imagine a situation where composite cross section (in the localized proposed fatigue mechanism indicates that the occurrence of region) consists of three domains(see Fig. 9): The core area atigue failure will depend on geometry and the thermal boundary (domain D), in which the fibers are broken(initially, there may be conditions. It is likely that, for identical loading conditions, thicker no broken fibers in domain I; it may start from a crack in a specimens possess a higher temperature rise in the center of the matrix-rich region). Outside the core area is a transition zone cross section than thinner specimens; temperature-induced damage (domain In) where the stresses at the fibers are now higher than the is likely to progress at a faster rate nominal value, since there is local load sharing(stress concentra- tion), and domain Ill, where intact fibers experience global load sharing due to a lower value of T Fatigue damage may evolve as follows. During cyclic loading (4 Temperature-Driven Interface Changes the energy dissipation is highest in domain Il, near the fibers The scenario described above is based on the assumption that located at the edge of domain I(at this location the fibers the interfacial shear stress or bond decreases initially but then perience the highest stress concentration). If the resulting increases with increasing temperature and time. There may be temperature rise is sufficiently high, then after some time interfa- several causes for changes in interfacial properties as the tempe cial slip may be hindered and the fibers in the vicinity of domain ature increases. The test environment, such as humidity and I fail, transferring more stress on the surviving fibers in domain ll. oxygen, affects the sliding behavior of a CMC possessing a carbon These fibers are now subjected to the highest stresses and interphase. 40. Obviously, such phenomena may depend on tem- temperature. In this manner, domain I can extend across the cross perature. Probably the most documented phenomenon for em- section of the specimen; the mechanism is self-sustaining. The composite fails when the remaining cross section cannot carry the brittlement of CMCs is oxidation damage. If the temperature at the nterface rises above approximately 200C, the C-interphase layer applied load. Then the fracture surface will show an to co CO interior region with no fiber pull-out(corresponding to domain D), Thomas and Sanches 2). If the temperature at the interface exceeds and an exterior region displaying usual fiber pull-out(note that bout 700C, the Sic fibers may decompose and form SiO, at the shorter fiber pull-out lengths reflect a higher interfacial shear interface. Since burn-off of the C-layer would reduce the mismatch between the fibers and matrix, it is likely that the interfacial shear stress T decreases. On the other hand. the formation of Sio, results in strong bonding It is well known that strong interfacial bonding results in brittle behavior of CMCs. 423,25,42 It cannot be ruled out that fatigue failure may be caused by the formation of a strong SiO, bond ( note that locally at contact points along the fiber/matrix interface, where the frictional energy dissipation takes place, the temperature may be much higher than the surrounding bulk temperature) IAFT Broken Fibers No Slip For the particular material system examined( 8-ply unidirec- tional SiC/CAs II)and test conditions(room-temperature cycling between g 240 MPa and omin 10 MPa at 200 Hz) the following were found DomainI Domain l Domain Ill (1) The residual strength of specimens cycled to 10 cycle was similar to the tensile strength of virgin specimens. Conse- quently, measurements of residual strength(e.g, after 10 cycles) cannot be used as a predictor of fatigue failure, since the strength decrease seems to take place only shortly before the occurrence of fatigue failure. Also, the retained strength raises doubts about the X alidity of GLs models, which predict a significant Fig 9. Schematic drawing of the pr reduction if the interfacial shear stress decreases Fibers fail when the interfacial shear becomes so high that fiber/ (2) The results suggest that frictional interface ng was matrix slip is hindered. The assumed va of the interfacial shear stress hindered within the specimen core, causing brittle fracture in the center of cross sections of the specimens
either by an increase in the interfacial shear stress or by the formation of strong interface bonding. If global load sharing cannot occur, the composite behaves like a brittle material in the core; matrix cracking can penetrate the fibers. But why has the damage developed differently in the center of the cross section than at the edges? The answer is not obvious, since for 1D composites the macroscopic stress state (uniaxial tension) does not vary across the cross section. Other parameters may vary across the cross section, such as humidity, oxygen concentration, and temperature field. The latter may vary across the specimen cross section, since energy is lost at the surface by radiation and convection. (3) A Fatigue Damage Mechanism: Embrittlement Due to Internal Heating Assume that the interfacial shear stress can increase or a strong bonding can form with increasing temperature and time. Next, imagine a situation where composite cross section (in the localized region) consists of three domains (see Fig. 9): The core area (domain I), in which the fibers are broken (initially, there may be no broken fibers in domain I; it may start from a crack in a matrix-rich region). Outside the core area is a transition zone (domain II) where the stresses at the fibers are now higher than the nominal value, since there is local load sharing (stress concentration), and domain III, where intact fibers experience global load sharing due to a lower value of t. Fatigue damage may evolve as follows. During cyclic loading the energy dissipation is highest in domain II, near the fibers located at the edge of domain I (at this location the fibers experience the highest stress concentration). If the resulting temperature rise is sufficiently high, then after some time interfacial slip may be hindered and the fibers in the vicinity of domain I fail, transferring more stress on the surviving fibers in domain II. These fibers are now subjected to the highest stresses and temperature. In this manner, domain I can extend across the cross section of the specimen; the mechanism is self-sustaining. The composite fails when the remaining cross section cannot carry the maximum applied load. Then the fracture surface will show an interior region with no fiber pull-out (corresponding to domain I), a transition region with short fiber pull-out lengths (domain II), and an exterior region displaying usual fiber pull-out (note that shorter fiber pull-out lengths reflect a higher interfacial shear stress8 ). The predicted appearance of the fracture surface is consistent with the observations in Figs. 4 and 5. It is plausible that it may take a certain temperature and time before the interface damage reaches the critical state, where fiber slip can no longer occur. Thus, in the initial stages, fatigue damage may increase slowly, without causing fiber failures. The fatigue mechanism postulated above may in principle explain the following experimental observations: (1) A larger stress range and higher loading frequency shorten the fatigue life of CMCs with weakly bonded interfaces.20,38 This may be understood in terms of the local temperature at the fiber/matrix interface, which may scale roughly with the energy dissipation.22 Both a larger stress range and a higher loading frequency increase the frictional energy dissipation (per unit time), resulting in a higher temperature rise. This may accelerate the increase in t, and shorten the fatigue life. (2) It has been found that thicker (32 ply) test specimens possess a lower fatigue life than thinner (8-ply) specimens.39 The proposed fatigue mechanism indicates that the occurrence of fatigue failure will depend on geometry and the thermal boundary conditions. It is likely that, for identical loading conditions, thicker specimens possess a higher temperature rise in the center of the cross section than thinner specimens; temperature-induced damage is likely to progress at a faster rate. (4) Temperature-Driven Interface Changes The scenario described above is based on the assumption that the interfacial shear stress or bond decreases initially but then increases with increasing temperature and time. There may be several causes for changes in interfacial properties as the temperature increases. The test environment, such as humidity and oxygen, affects the sliding behavior of a CMC possessing a carbon interphase.40,41 Obviously, such phenomena may depend on temperature. Probably the most documented phenomenon for embrittlement of CMCs is oxidation damage. If the temperature at the interface rises above approximately 200°C, the C-interphase layer may begin to disappear by oxidation to CO or CO2 (see, e.g., Thomas and Sanches42). If the temperature at the interface exceeds about 700°C, the SiC fibers may decompose and form SiO2 at the interface.42 Since burn-off of the C-layer would reduce the mismatch between the fibers and matrix, it is likely that the interfacial shear stress t decreases. On the other hand, the formation of SiO2 results in strong bonding.10,11,42 It is well known that strong interfacial bonding results in brittle behavior of CMCs.14,23,25,42 It cannot be ruled out that fatigue failure may be caused by the formation of a strong SiO2 bond (note that locally at contact points along the fiber/matrix interface, where the frictional energy dissipation takes place, the temperature may be much higher than the surrounding bulk temperature). V. Conclusions For the particular material system examined (8-ply unidirectional SiCf /CAS II) and test conditions (room-temperature cycling between smax 5 240 MPa and smin 5 10 MPa at 200 Hz) the following were found: (1) The residual strength of specimens cycled to 105 cycles was similar to the tensile strength of virgin specimens. Consequently, measurements of residual strength (e.g., after 105 cycles) cannot be used as a predictor of fatigue failure, since the strength decrease seems to take place only shortly before the occurrence of fatigue failure. Also, the retained strength raises doubts about the validity of GLS models, which predict a significant strength reduction if the interfacial shear stress decreases. (2) The results suggest that frictional interface sliding was hindered within the specimen core, causing brittle fracture in the center of cross sections of the specimens. Fig. 9. Schematic drawing of the proposed fatigue damage mechanism. Fibers fail when the interfacial shear stress becomes so high that fiber/ matrix slip is hindered. The assumed variation of the interfacial shear stress is indicated. 1474 Journal of the American Ceramic Society—Sørensen et al. Vol. 83, No. 6
June 2000 Rate of strength Decrease of Fiber-Reinforced Ceramic-Matrix Composites during Fatigue APPENDIX AR. F. Cooper and K. Chyung, "Structure and Chemistry of Fiber-Matrix Interfaces in Silicon Carbide Fiber-Reinforced Glass-Ceramic Composites: An By the of a simple micromechanical model T can be muted from the hysteresis modulus, E, or the stress-strain data Reinforced Glass-Ceramics: A High-Resolution Scanning Transmission Electron ter, the following procedure is used. For a given strain incre ure of Silicon Carbide Fiber-Reinforced rom the unloaded state, Ae, the corresponding stress increment Glass-Ceramics, J. Mater. Sci., 22, 2695-701(1987) is determined. The hysteresis modulus at that stress level is 'L M. Butkus, L. P Zawada, and G. A Hartman, "Room Temperature Tensile then e= Ao/. this value is then used in the model. however and Fatigue Properties of Silicon Carbide Fiber-Reinforced Ceramic Matrix Com- different equations are valid for different states of interfacial slip If the slip length is smaller than s/2 the composite experiences J. w. Holmes and S. F. Shuler, Temperature Rise During Fatigue of Fiber- artial slip. Else, the composite experiences full slip. The transition Reinforced Ceramics, J. Mater. Sci. Lett, 9, 1290-91(1990) tween partial and full slip occurs when the hysteresis modul J. w. Holmes and C. Cho,"Experimental Observations of Frictional Heating in Fiber-Reinforced Ceramics, J. Am. Ceram. Soc., 75, 929-38(1992)- L P. Zawada, L M. Butkus, and G. A. Hartman, "Room Temperature Tensile E (A-1) Ceram. Eng. Sci. Proc., 11, 1592-606(1990) D. Rouby and P. Reynaud, "Fatigue Behavior Related to the Interface Modifi- E where Em is the Youngs modulus of the matrix If E>Eps-s 2J. W. Holmes, X. Wu, and B. F. Sorensen,"Frequency Dependency of Fatigue the composite is in partial slip, and T can be calculated from- Life and Internal Heating of a Fiber-Reinforced Ceramic Matrix Composite,J.Am Cera. Soc,7,3284-86(1994). Er△a/Em1 Zok, and R. M. MeMeeking, ""Fatigue of Ceramic Matrix Composites, Acta Metall. Mater, 43, 859-75(1995) EsEr(E。vr E 2808-18 (1990)5 es rom nictona Heating Measurements, 3. mt ceram 2E. Y. Luh and A. G. Evans, "High-Temperature Mechanical Properties of i where Er denotes the Young's modulus of the fiber and r is the Ceramic Matrix Composite,J. Am. Ceram Soc., 70, 466-69(1987). fiber radius. If full slip applies(E Ens-s, then T can be 24K. M. Prewo, B. Johnson, and S. Starrett, "Silicon Carbide Fibre-Reinforced calculated from Glass-Ceramic Composite Tensile Behaviour at Elevated Temperature, "J.Mater. Sa.,24,137y-79(1989 R. T, Bhatt, " Oxidation Effects on the Mechanical Properties of Sic-Fiber (A-3) 406-12(1992) 2J F. Mandell, D. H. Grande, and J. Jacobs, " Tensile Behaviour of Glass/Ceramic When E was determined from the stress-strain data of the residual Composite Materials at Elevated Temperatures,J. Eng Turbines Power: 109 strength test, the matrix J. W. Holmes, "Influence of Stress Ratio on the Elevated-Temperature Fatigue of (i. e, before the tensile tes Silicon Carbide Fiber-Reinforced Silicon Nitride Composite, J. Am. Ceram. Soc., 74, cracking is assumed to 639-45(1991) stress is below the maximum 2J. W. Holmes, "A Technique for Tensile Fatigue and Creep Testing of the cycling. 7 A. w. Pryce and P. A Smith, "Matrix Cracking i Ceramic matrix W. P Keith and K. T. Ke "The Stress-Strain Behavior of a porous The impetus for this study arose from discussions with Dr. Xin Wu. Unidirectional Ceramic matrix s,"Model of the Mechanical behavior o Continuous Fiber Reinforced Ceramic Matrix Composites During Cyclic Loading, "J. References Eur Ceran Soc. submitted T. Mackin and F. W. Zok,"Fiber Bundle Pushout: A Technique for the J. W. Holmes and B. F. Sorensen, "Fatigue Behavior of Continuous-Fiber- Measurement of Interfacial Sliding Properties, J. Am. Ceram. Soc., 75, 3169-71 (1992) havior of Ceramic Matrix Composites. Edited by S. V. Nair and K. Jakus. E. Lara-Curzio and M. K, Feber, "Methodology for the Determination of the Butterworth Heineman, Newton, MA, 1995. Interfacial Properties of Brittle Matrix Composites, J. Mater. Sci, 29, 6152-58 Karandikar and T -w. Chou, "Damage Development and Moduli Reduction (1994) icalon-Calcium Aluminosilicate Com under Static Fatigue and Cyclic B. F, Sorensen and J. w. Holmes,"Effect of Loading Rate on the Monotonic Fatigue, J. Am. Ceram. Soc 76, 1720-28(1993 S. Beyerle, S. M. Spearing, F. w. Zok, and A. G. Evans, "Damage and Failur Ceram. Soc., 79, 313-20(1996 Cracking of a Fiber-Reinforced Ceramic, "J.Am. Tensile behavior 3SR. W. Goettler and K. T. Faber. ""Interfacial Shear Stress in Fiber-Reinforced Glasses,Compos. Sci. TechnoL, 37, 129-47(1989) B. F. Sorensen and R. Talreja, "Analysis of Damage in Ceramic Matrix Holmes, "Fatigue of Continuous Fiber-Reinforced i IntJ. Damage M Ceramic Matrix Composites: Review of Mechanisms and Models": pp. 487-500 in B. Budiansky, J, W, Hutchinson, and A. G. Evans, "Matrix Fracture in Fiber- Reinforced Ceramics, J. Mech. Phys. Solids, 34, 167-78(1986) Proceedings of the International Symposium on Fatigue under Thermal and Mechan- rittle- MatrIx Fiber- ical Loading. Edited by J. Bressers and L. Remy, Kluwer Academic Publishers Reinforced Composites, Proc. R. Soc. London, A409, 329-50(1987 Dordrecht, Netherlands, 1996 man and H. Zhu, "Multi-fracture of Ceramic Composites, J. Mech. S. M. Spearing, F. M. Zok, and A. G. Evans, "Stress Corrosion Cr Sd,4.351-88199 w.A. Curtin, ""Theory of Mechanical Properties of Ceramic Matrix Composites, 3*B F. Sorensen and J.w. Holmes, "Influence of Stress oc, 77, 562- Unidirectional Ceramic-Matrix Composite, J. Am. Cera J.Am. Ceran.Soe,74,2837-45(1991) J. w. Holmes and x. Wu, "Elevated Temperature Creep Behavior of Continuous ated Temperature Behavior of J. I. Eldridge. "Environmental Effects on Fiber Debonding and Sliding in an amic Matrix Composites. Edited by S. V, Nair and K. Jakus. Butterworth SCS-6 SIC C Mater.,32,1085-89(1995) Camus, R. Naslain, and J. Thebault, "Oxidation Mechanisms and 41J dge, R. T. Bhatt, and N. P, Bansal, "Investigation of Fiber /Matrix Kinetics of ID-SiC/C/SiC Composite Materials: 1, An Experimental Approach," Interfacial Mechanical Behavior in Ceramic Matrix Composites by Cyclic Fiber Push-in Testin 266-78(1996 A. G. Evans, F. W. Zok, R. M. McMeeking, and Z. Z. Du, "Models of 2w. A. Thomas and J. M. Sanchez, "Influence of Inter facial Sliding Stress on High-Temperature, Environmentally Assisted Embrittlement in Ceramic Matrix Fatigue Behavior of Oxidized Nicalon/Calcium Aluminosilicate Composites, " J.Am Composites,J. Am. Ceram Soc., 79, 2345-52(1996). Ceram.Sor,79,2659-65(1996
APPENDIX By the use of a simple micromechanical model t can be computed from the hysteresis modulus, E#, or the stress–strain data from a monotonic tensile test of precycled specimens. For the latter, the following procedure is used. For a given strain increment from the unloaded state, Dε, the corresponding stress increment, Ds, is determined. The hysteresis modulus at that stress level is then E# 5 Ds/D«. This value is then used in the model. However, different equations are valid for different states of interfacial slip. If the slip length is smaller than s/2 the composite experiences partial slip. Else, the composite experiences full slip. The transition between partial and full slip occurs when the hysteresis modulus is31 E# ps2fs 5 Ec 1 1 1 2 vf vf Em Ec (A-1) where Em is the Young’s modulus of the matrix. If E# . E# ps2fs the composite is in partial slip, and t can be calculated from29–31 t 5 E# 1 2 E# Ec r s Ds Ef S Em Ec 1 2 vf vf D 2 (A-2) where Ef denotes the Young’s modulus of the fiber and r is the fiber radius. If full slip applies (E# , E# ps2fs), then t can be calculated from30,31 t 5 E# 2 vfEc vfE# r s Ds (A-3) When E# was determined from the stress–strain data of the residual strength test, the matrix crack spacing, s, recorded after cycling (i.e., before the tensile test) was used, since no additional matrix cracking is assumed to occur as long as the maximum applied stress is below the maximum stress level that was applied during the cycling.17 Acknowledgment The impetus for this study arose from discussions with Dr. Xin Wu. References 1 J. W. Holmes and B. F. Sørensen, “Fatigue Behavior of Continuous-FiberReinforced Ceramic Matrix Composites”; pp. 261–326 in Elevated Temperature Behavior of Ceramic Matrix Composites. Edited by S. V. Nair and K. Jakus. Butterworth Heineman, Newton, MA, 1995. 2 P. Karandikar and T.-W. Chou, “Damage Development and Moduli Reductions in Nicalon–Calcium Aluminosilicate Composites under Static Fatigue and Cyclic Fatigue,” J. Am. Ceram. Soc., 76, 1720–28 (1993). 3 D. S. Beyerle, S. M. Spearing, F. W. Zok, and A. G. Evans, “Damage and Failure in Unidirectional Ceramic-Matrix Composites,” J. Am. Ceram. Soc., 75, 2719–25 (1992). 4 B. F. Sørensen and R. Talreja, “Analysis of Damage in Ceramic Matrix Composites,” Int. J. Damage Mech., 2, 246–71 (1993). 5 B. Budiansky, J. W. Hutchinson, and A. G. Evans, “Matrix Fracture in FiberReinforced Ceramics,” J. Mech. Phys. Solids, 34, 167–78 (1986). 6 L. N. McCartney, “Mechanics of Matrix Cracking in Brittle-Matrix FiberReinforced Composites,” Proc. R. Soc. London, A409, 329–50 (1987). 7 Y. J. Weitsman and H. Zhu, “Multi-fracture of Ceramic Composites,” J. Mech. Phys. Solids, 41, 351–88 (1993). 8 W. A. Curtin, “Theory of Mechanical Properties of Ceramic Matrix Composites,” J. Am. Ceram. Soc., 74, 2837–45 (1991). 9 J. W. Holmes and X. Wu, “Elevated Temperature Creep Behavior of Continuous Fiber-Reinforced Ceramics”; pp. 193–260 in Elevated Temperature Behavior of Ceramic Matrix Composites. Edited by S. V. Nair and K. Jakus. Butterworth Heineman, Newton, MA, 1995. 10L. Filipuzzi, G. Camus, R. Naslain, and J. The´bault, “Oxidation Mechanisms and Kinetics of 1D-SiC/C/SiC Composite Materials: I, An Experimental Approach,” J. Am. Ceram. Soc., 70, 459–66 (1996). 11A. G. Evans, F. W. Zok, R. M. McMeeking, and Z. Z. Du, “Models of High-Temperature, Environmentally Assisted Embrittlement in Ceramic Matrix Composites,” J. Am. Ceram. Soc., 79, 2345–52 (1996). 12R. F. Cooper and K. Chyung, “Structure and Chemistry of Fiber-Matrix Interfaces in Silicon Carbide Fiber-Reinforced Glass-Ceramic Composites: An Electron Microscopy Study,” J. Mater. Sci., 22, 3148–69 (1987). 13L. A. Bonney and R. F. Cooper, “Reaction Layer Interfaces in SiC-FiberReinforced Glass-Ceramics: A High-Resolution Scanning Transmission Electron Microscopy Analysis,” J. Am. Ceram. Soc., 73, 2916–26 (1990). 14K. M. Prewo, “Fatigue and Stress Rupture of Silicon Carbide Fiber-Reinforced Glass-Ceramics,” J. Mater. Sci., 22, 2695–701 (1987). 15L. M. Butkus, L. P. Zawada, and G. A. Hartman, “Room Temperature Tensile and Fatigue Properties of Silicon Carbide Fiber-Reinforced Ceramic Matrix Composites”; in Aeromat’90, Advanced Aerospace Materials/Processes Conference (Long Beach, CA, May 21–24, 1990), 1990. 16J. W. Holmes and S. F. Shuler, “Temperature Rise During Fatigue of FiberReinforced Ceramics,” J. Mater. Sci. Lett., 9, 1290–91 (1990). 17J. W. Holmes and C. Cho, “Experimental Observations of Frictional Heating in Fiber-Reinforced Ceramics,” J. Am. Ceram. Soc., 75, 929–38 (1992). 18L. P. Zawada, L. M. Butkus, and G. A. Hartman, “Room Temperature Tensile and Fatigue Properties of Silicon Carbide Fiber-Reinforced Aluminosilicate Glass,” Ceram. Eng. Sci. Proc., 11, 1592–606 (1990). 19D. Rouby and P. Reynaud, “Fatigue Behavior Related to the Interface Modification during Load Cycling in Ceramic-Matrix Composites,” Compos. Sci. Technol., 48, 109–18 (1993). 20J. W. Holmes, X. Wu, and B. F. Sørensen, “Frequency Dependency of Fatigue Life and Internal Heating of a Fiber-Reinforced Ceramic Matrix Composite,” J. Am. Ceram. Soc., 77, 3284–86 (1994). 21A. G. Evans, F. W. Zok, and R. M. McMeeking, “Fatigue of Ceramic Matrix Composites,” Acta Metall. Mater., 43, 859–75 (1995). 22C. Cho, J. W. Holmes, and J. R. Barber, “Estimation of Interfacial Shear in Ceramic Composites from Frictional Heating Measurements,” J. Am. Ceram. Soc., 74, 2808–18 (1991). 23E. Y. Luh and A. G. Evans, “High-Temperature Mechanical Properties of a Ceramic Matrix Composite,” J. Am. Ceram. Soc., 70, 466–69 (1987). 24K. M. Prewo, B. Johnson, and S. Starrett, “Silicon Carbide Fibre-Reinforced Glass-Ceramic Composite Tensile Behaviour at Elevated Temperature,” J. Mater. Sci., 24, 1373–79 (1989). 25R. T. Bhatt, “Oxidation Effects on the Mechanical Properties of SiC-FiberReinforced Reaction-Bonded Si3N4-Matrix Composites,” J. Am. Ceram. Soc., 75, 406–12 (1992). 26J. F. Mandell, D. H. Grande, and J. Jacobs, “Tensile Behaviour of Glass/Ceramic Composite Materials at Elevated Temperatures,” J. Eng. Gas Turbines Power, 109, 267–73 (1987). 27J. W. Holmes, “Influence of Stress Ratio on the Elevated-Temperature Fatigue of Silicon Carbide Fiber-Reinforced Silicon Nitride Composite,” J. Am. Ceram. Soc., 74, 1639–45 (1991). 28J. W. Holmes, “A Technique for Tensile Fatigue and Creep Testing of Fiber-Reinforced Ceramics,” J. Compos. Mater., 26, 915–32 (1992). 29A. W. Pryce and P. A. Smith, “Matrix Cracking in Unidirectional Ceramic Matrix Composites under Quasi-Static and Cyclic Loading,” Acta Metall. Mater., 41, 1269–81 (1993). 30W. P. Keith and K. T. Kedward, “The Stress–Strain Behavior of a Porous Unidirectional Ceramic Matrix Composite,” Composites, 26, 163–74 (1995). 31B. F. Sørensen and J. W. Holmes, “Model of the Mechanical Behavior of Continuous Fiber Reinforced Ceramic Matrix Composites During Cyclic Loading,” J. Eur. Ceram. Soc., submitted. 32T. Mackin and F. W. Zok, “Fiber Bundle Pushout: A Technique for the Measurement of Interfacial Sliding Properties,” J. Am. Ceram. Soc., 75, 3169–71 (1992). 33E. Lara-Curzio and M. K. Feber, “Methodology for the Determination of the Interfacial Properties of Brittle Matrix Composites,” J. Mater. Sci., 29, 6152–58 (1994). 34B. F. Sørensen and J. W. Holmes, “Effect of Loading Rate on the Monotonic Tensile Behavior and Matrix Cracking of a Fiber-Reinforced Ceramic,” J. Am. Ceram. Soc., 79, 313–20 (1996). 35R. W. Goettler and K. T. Faber, “Interfacial Shear Stress in Fiber-Reinforced Glasses,” Compos. Sci. Technol., 37, 129–47 (1989). 36B. F. Sørensen and J. W. Holmes, “Fatigue of Continuous Fiber-Reinforced Ceramic Matrix Composites: Review of Mechanisms and Models”; pp. 487–500 in Proceedings of the International Symposium on Fatigue under Thermal and Mechanical Loading. Edited by J. Bressers and L. Remy. Kluwer Academic Publishers, Dordrecht, Netherlands, 1996. 37S. M. Spearing, F. M. Zok, and A. G. Evans, “Stress Corrosion Cracking in a Unidirectional Ceramic-Matrix Composite,” J. Am. Ceram. Soc., 77, 562–70 (1994). 38B. F. Sørensen and J. W. Holmes, “Influence of Stress Ratio on the Fatigue Life of a Continuous Fiber-Reinforced Ceramic Matrix Composite,” unpublished work. 39J. W. Holmes, unpublished research. 40J. I. Eldridge, “Environmental Effects on Fiber Debonding and Sliding in an SCS-6 SiC Fiber Reinforced Reaction-Bonded Si3Ni4 Composite,” Scr. Metall. Mater., 32, 1085–89 (1995). 41J. I. Eldridge, R. T. Bhatt, and N. P. Bansal, “Investigation of Fiber/Matrix Interfacial Mechanical Behavior in Ceramic Matrix Composites by Cyclic Fiber Push-in Testing,” Ceram. Eng. Sci. Proc., 17, 266–78 (1996). 42W. A. Thomas and J. M. Sanchez, “Influence of Interfacial Sliding Stress on Fatigue Behavior of Oxidized Nicalon/Calcium Aluminosilicate Composites,” J. Am. Ceram. Soc., 79, 2659–65 (1996). M June 2000 Rate of Strength Decrease of Fiber-Reinforced Ceramic-Matrix Composites during Fatigue 1475