Ultrasonic Fatigue Testing Historical Perspective Development of higher-frequency testing machines began early in the 20th century Prior to 1911, the highest fatigue testing frequency was on the order of 33 Hz, using mechanically driven systems Electrodynamic resonance systems appeared in 1911 when Hopkinson (Ref 1) introduced a machine capable of 116 Hz In 1925, Jenkin (Ref 2) tested wires of copper, iron, and steel at kHz, using similar techniques In 1929, Jenkin and Lehmann (Ref 3) were able to test materials up to 10 kHz using a pulsating air resonance system Mason (Ref 4) achieved ultrasonic frequency (20 kHz) in 1950 with the adaptation of magnetostrictive and piezoelectric-type transducers to fatigue testing This method translated 20 kHz electrical voltage signals into 20 kHz mechanical displacements A displacement-amplifying acoustical horn and the test specimen were driven into resonance by the transducer This concept has remained basically unchanged and is the foundation of the practices used in modern ultrasonic fatigue test technology In the early 1960s, frequencies as high as 92 and 199 kHz were employed for fatigue tests using Mason's techniques (Ref 5, 6) These extremely high frequencies surpass the upper limits of practicality because of the constraints of specimen size (frequency is inversely proportional to specimen length), machining tolerances, strain amplitude measurements, and energy considerations A review of the ultrasonic fatigue testing in the 1970s and 1980s shows that the majority of test stands operate at frequencies between 17 and 25 kHz This unofficial standard is primarily dictated by the availability of commercial high-power ultrasonic transducers and power supplies These frequencies are also desirable from a safety viewpoint because they are above the range of normal human hearing Fatigue testing at 20 kHz proceeds quietly in comparison to testing at to 10 kHz References cited in this section B Hopkinson, Proc R Soc (London) A, Vol 86, 1911, p 101 C.F Jenkin, Proc R Soc (London) A, Vol 109, 1925, p 119 C.F Jenkin and G.D Lehmann, Proc R Soc (London) A, Vol 125, 1929, p 83 W.P Mason, Piezoelectric Crystals and Their Application in Ultrasonics, Van Nostrand, New York, 1950, p 161 F Girard and G Vidal, Rev Metall., Vol 56, 1959, p 25 M Kikukawa, K Ohji, and K Ogura, J Basic Eng (Trans ASME D), Vol 87, 1965, p 857 Ultrasonic Fatigue Testing Strain Rates, Frequency, and Time Compression Ultrasonic fatigue testing increases the frequency of stress cycling to reduce the time necessary to accumulate a large number of cycles Consequently, the strain rate at these frequencies for a given strain amplitude is also increased In Table 1, strain rate is calculated as a function of frequency and strain amplitude For typical fatigue strain amplitudes in the range of 10-4 to 10-3, the strain rate at 20 kHz ranges from to 20 s-1 Table Strain rate as a function of test frequency and strain range Strain rate ( ), s-1, at strain (ε) of: ε = 10-2, m/m ε = 10-5, m/m ε = 10-4, m/m ε = 10-3, m/m 10 10-4 10-3 10-2 10-1 100 10-3 10-2 10-1 -2 -1 1,000 10 10 10 10,000 10-1 10 102 100,000 10 102 103 Ultrasonic fatigue techniques are particularly useful for providing fatigue data in applications where strains are being applied and removed at kilohertz frequencies; (e.g., high-frequency loading of turbine blades) In fact, ultrasonic fatigue testing may provide a better simulation of the higher frequency vibrations encountered in service than conventional testing does in these cases The test method is most applicable when the test material ultimately will be applied in service at frequencies at or near the test frequency For applications with lower frequency vibrations, the effect of frequency and strain rate on test results must be interpreted The time compression per cycle obtained with ultrasonic fatigue is pronounced For example, a conventional fatigue test at Hz would take 320 years for a 1010 cycle test At 100 Hz, the test would take 3.2 years At an ultrasonic frequency of 20 kHz, this test would be completed in less than days The time required to complete fatigue tests at different frequencies is shown in Fig This time compression is extremely attractive for situations that require high-cycle data Frequency, Hz Fig Testing time versus number of cycles to complete test as a function of frequency In comparison to conventional frequency testing, more test conditions and/or replicate tests can be performed in a given period of time at ultrasonic frequency This provides results and conclusions that are statistically more meaningful for planning and design On the other hand, the minimum number of cycles that can be measured practically is limited by kilohertz cycling This limit is 105 cycles for open-loop testing, with a testing time of s Shorter times (~1 s) are possible with closed-loop computer control of the test and data acquisition systems Similar time compression is possible in fatigue crack growth rate testing using ultrasonic fatigue Figure is a schematic of a typical crack growth rate, da/dN, versus stress intensity curve The time necessary to measure a crack advance of 0.1 mm (0.004 in.) while testing at Hz or 20 kHz is compared on the right side of the figure It is obvious that ultrasonic testing is the only practical approach to observe the extremely slow crack growth rates that are characteristic of the threshold regime Crack growth rate measurements as low as 10-11 mm (4 × 10-13 in.) have been reported Again, the practical upper bound of measurable fatigue crack growth rate at 20 kHz is on the order of 10-5 mm (4 × 10-7 in.) per cycle due to the rapid cycle accumulation Fig Typical crack growth rate versus stress intensity curve Difference in time to observe a finite crack growth increment at ultrasonic (20 kHz) and conventional (1 Hz) frequencies is shown The testing time compression possible with ultrasonic fatigue is an incentive for applying the technology in a more generic sense, that is, to extend fatigue information obtained at conventional frequencies and lower numbers of cycles to higher-cycle fatigue limits and threshold fatigue crack growth rates Because this accelerated test method alters testing conditions to produce fatigue in a shorter period of time, the influence of frequency and strain rate on cyclic material behavior must be well understood General acceptance of ultrasonic fatigue testing also requires an understanding of how to obtain data free of testing-induced artifacts Improper execution can have a marked effect on the property data obtained Much of the skepticism that endures about the use of ultrasonic fatigue stems from earlier testing where questionable techniques were used to measure cyclic strain amplitude and provide adequate cooling of the specimen Accordingly, the effects of strain rate, frequency, and test technique are the subject of most research on ultrasonic fatigue (Ref 7, 8) In general, testing by ultrasonic fatigue produces fatigue data that differ only slightly from those observed at more conventional frequencies Some data reveal a shift in the ultrasonic fatigue stress-life data (S-N) for a given stress level toward increased lifetimes relative to conventional-frequency results (Ref 9, 10, and 11) Other reports indicate no shift in the S-N behavior (Ref 12, 13) Most reports indicate that fatigue degradation at ultrasonic frequency occurs by the same sequence of events as at conventional frequencies, namely, saturation of rapid hardening, formation of persistent slip bands, formation and growth of intrusions, and crack propagation Materials that exhibit clearly defined endurance limits at conventional frequencies usually exhibit endurance limits at similar cyclic stress amplitudes at ultrasonic frequencies Similarly, materials that exhibit threshold stress intensities for fatigue crack growth at conventional frequencies also exhibit this behavior at ultrasonic frequencies Shifts in S-N fatigue behavior to higher stress levels and longer lifetimes or da/dN behavior to slower crack growth rates not occur for all materials tested at high frequency Recent testing shows that the effect of frequency on S-N and da/dN performance is primarily a function of the microplasticity and slip character of the material system under test It might also be inferred that corrosion fatigue interactions should be negligible at ultrasonic frequency due to the short cyclic period Again, experimental results illustrate that corrosion fatigue interactions are indeed observed at ultrasonic frequencies Recent testing shows that ultrasonic fatigue is an effective method for the evaluation of the degradation of fatigue properties produced by environmental interactions Ultrasonic fatigue testing is applicable to most situations in which conventional-frequency fatigue testing has been employed Examples of a variety of results from ultrasonic fatigue are presented later in this article As the technique continues to develop, the precise limits of applicability will become more clearly defined References cited in this section L.E Willertz, Int Met Rev., No 2, 1980, p 65, rev 250 J.M Wells, O Buck, L.D Roth, and J.K Tien, Ed., Ultrasonic Fatigue, TMS-AIME, Warrendale, PA, 1982 B.S Hockenhull, in Physics and Non Destructive Testing, Gordon Breach, New York, 1967, p 195 10 H Koganei, S Tanaka, and T Sakurai, Trans Iron Steel Inst Jpn., Vol 17, 1977, p 1979 11 J Awatani and K Katagiri, Bull Jpn Soc Mech Eng., Vol 12, 1969, p 10 12 W Hoffelner, in High Temperature Alloys for Gas Turbines: 1982, R Brunetaud, D Coutsouradis, T.B Gibbons, Y Lindblum, D.B Meadowcraft, and R Stickler, Ed., R Reidal Publishing, Boston, 1982, p 645 13 L.D Roth and L.E Willertz, in Environment Sensitive Fracture: Evaluation and Comparison of Test Methods, ASTM STP 821, E.N Pugh and G.M Ugiansky, Ed., ASTM, Philadelphia, 1984, p 497 Ultrasonic Fatigue Testing Testing Principles The principles of ultrasonic fatigue testing are quite simple Ultrasonic fatigue is a resonant test method, in which a large-amplitude displacement wave must be established in a resonant specimen This wave is generated by a relatively small periodic stimulus at the same frequency as the natural frequency of the test specimen Resonance is required to achieve the strain amplitude needed to produce fatigue in materials Displacement and strain are developed in a bar of material subjected to resonant acoustic loading Consider a straight bar of material having a uniform diameter and length L (Fig 3) A sound wave injected longitudinally into one end of the bar travels at a certain velocity through the bar, is reflected from the opposite end, and returns to the point of entrance The wave velocity, C, is determined by the material properties, the Young's modulus, E, and the density (mass/volume), ρ, by: (Eq 1) Fig Distribution of oscillatory displacement amplitude and strain amplitude over the length of a resonant bar of uniform cross section This velocity is the speed of sound through the material The time required to travel the length of the bar and return is 2L/C If this time is equal to the period of the injected sound wave, the reflected wave will be exactly in phase with the injected wave, standing wave conditions will be established, and the bar will be in resonance The length, L, of the bar is then exactly equal to the half wavelength of the sound wave The variation of displacement amplitude of oscillation at a point x along the length of the bar will be: A(x) = Ao cos(kx) (Eq 2) where Ao is the displacement amplitude at the end of the bar, k is 2π/λ, and λ is the wavelength of sound at the resonant frequency The strain distribution along the bar will be the derivative of the displacement amplitude with respect to distance or: (Eq 3) Thus, the maximum strain occurs when sin(kx) = 1, or x = λ/4 The maximum strain varies between ±kAo during each cycle Figure shows the distribution of longitudinal displacement amplitude and strain amplitude along the length of a bar in resonance The minimum displacement (displacement node) and maximum strain (strain antinode) occur at the center of the bar Similarly, the maximum displacement (displacement antinode) and minimum strain (strain node) occur at the ends of the bar The stress distribution for each point along the bar is obtained by an elastic conversion of the strain distribution: σ(x) = E · ε(x) (Eq 4) where E is the dynamic Young's modulus of the material The dynamic modulus of elasticity must be determined for the appropriate test frequency Because of the elastic conversion, the stress maximum physically coincides with the strain maximum Stresses cannot be obtained independent of strains in ultrasonic fatigue testing Therefore, strict stress-controlled tests cannot be performed Without independent per-cycle stress and strain information, plastic strain-controlled tests also are not possible at this time For more information on plastic strain-controlled ultrasonic fatigue testing, see Ref 14 The example of the uniform resonant bar embodies the basic concepts of ultrasonic fatigue testing With appropriate geometric modification, these concepts can be used to design the mechanical portion of the converter, the acoustic horns, and the test specimen The major difference between a conventional fatigue test specimen and a high-frequency resonant specimen is that the cyclic strain amplitude varies from zero at the ends to a maximum at the center, rather than being constant over its entire length This confines fatigue damage and, hence, fatigue crack initiation and propagation to the center of the specimen Because there is minimal strain at the ends of a resonant bar, the requirements for attachment of one resonant bar to another and for gripping the specimen also are minimal To produce strain in a bar, only one end of a resonant bar specimen must be in acoustic contact with the source of the sound waves This permits the testing of thin materials under reversed tension-compression loading without risk of buckling the specimen Consequently, sheet, tubing, and wire specimens may be subjected to fully reversed loading during ultrasonic fatigue, whereas more complex gripping and alignment techniques are required to accomplish similar tests at conventional frequencies The large and cumbersome arrangements for gripping the specimen that often are required in conventional fatigue testing are not needed in ultrasonic fatigue A specimen with a free end also provides the ultrasonic fatigue system with a degree of portability that is not easily obtained with conventional-frequency test methods Fatigue testing can be performed with the specimen in an operating environment by feeding the free end of the wave train through an access port to the environment Similarly, testing can be performed under the view of an optical or electron microscope without the need of complex load-transmitting stages Cyclic straining can be achieved in a bar at any desired resonance frequency by appropriately choosing (tuning) the length of the bar For a bar with a uniform cross section, the required length for fatigue testing will be λ/2 at the resonance frequency For bars with variable cross sections or dumbbell specimen geometries, the resonant length generally is shorter than the resonant length of a uniform bar at the given test frequency Thus, each component in a resonant testing system must be designed (tuned) to the resonance frequency to transmit the acoustic energy efficiently into the test specimen The equations developed by Neppiras (Ref 15) are helpful in calculating the appropriate resonant lengths for variable specimen section geometries These equations are presented later in this article in a section on specimen design References cited in this section 14 P Bajons, in Ultrasonic Fatigue, J.M Wells, O Buck, L.D Roth, and J.K Tien, Ed., TMS-AIME, Warrendale, PA, 1982, p 15 15 E.A Neppiras, Proc ASTM, Vol 59, 1959, p 691 Ultrasonic Fatigue Testing Testing Equipment and Methods Packaged ultrasonic fatigue test systems, with one exception, are not commercially available However, an ultrasonic fatigue test system may be constructed easily from commercially available parts Tien et al (Ref 16) describe the construction of a test machine using ultrasonic components normally used in ultrasonic joining processes This machine, an open-loop test stand, contains the basic equipment needed for testing Information on test stands with additional capabilities—including double converters, mean loading, electrochemical cells, and computerized control systems—can be found in Ref 17, 18, and 19, and 20 A portable test machine including ultrasonics, external loading frame, environmental system, and test chamber is shown in Fig Fig Portable 20 kHz corrosion-fatigue machine with mean load capability Figure is a schematic of a typical ultrasonic fatigue test machine The machine is centered around an acoustic wave train composed of a sonic energy converter, a series of acoustic amplifying horns, and the test specimen A typical wave train is shown in Fig The acoustic energy is supplied by a high-frequency power supply An amplitude-measuring device and a means of dissipating the heat generated by the deformation process are also necessary This basic equipment is appropriate for stress-life (S-N) or fatigue-crack-growth rate (da/dN) testing A frequency display, cycle counter, and temperature-measuring equipment are used to monitor the test Additional monitoring equipment is necessary to measure crack length in da/dN testing Fig Schematic of an ultrasonic fatigue test system Fig Typical 20 kHz acoustic wave train Power supplies for ultrasonic fatigue testing typically range from 500 to 4000 W of electrical power The actual output to the specimen is lower than this during normal resonant operation Most power supplies have built-in feedback circuits, which produce a constant-amplitude oscillation in the converter Some power supplies have circuits for automatic shutoff when the specimen or any part of the wave train goes out of resonance This is useful for S-N testing The fatigue crack at failure will be some fraction of the cross-sectional area when the power supply shuts off This fraction can range from a few percent to 50% of the cross-sectional area, depending on the automatic shut-off controls Sonic Converters Acoustic resonance is developed in the converter by application of the electrical excitation provided by the power supply The converter generates a standing acoustic wave that produces a cyclic displacement at the end of the converter The acoustic wave proceeds down the rest of the resonant wave train to the specimen Variation of the displacement and strain amplitudes along the wave train is shown in Fig Fig Variation of the displacement and strain amplitudes along the acoustic wave train Several cycles of application of the electronic stimulus of the power supply are required to achieve the maximum resonant amplitude in the converter and the rest of the wave train The rise time of the converter should be know when considering a pulsed mode versus continuous-cycling mode of an ultrasonic fatigue system In a pulsed-mode operation, the specimen is subjected to a series of pulses (~1 s) of high-amplitude cycles followed by a cooling period without cycling Rise time of ultrasonic equipment varies among manufacturers If rise time is longer than pulse time, variable-amplitude test conditions exist Pulsed-mode operation has been suggested by some investigators to overcome the rapid heating manifested by high-damping materials upon cycling Ultrasonic fatigue systems take several cycles for the maximum resonant amplitude to be developed Hence the tendency to overshoot the desired amplitude setpoint on the first cycle is small Converters for generating ultrasonic displacement waves generally are magnetostrictive or piezoelectric devices Most modern converters use piezoelectric materials for conversion efficiency Magnetostrictive devices have a low (20%) conversion efficiency Piezoelectric converters with efficiencies greater than 90% are readily available Converter types and designs vary among manufacturers Some piezoelectric devices use lead-zirconium-titanate (PZT) for the converter material The end displacement amplitude developed by a 20 kHz PZT converter ranges from 0.010 to 0.020 mm (0.0004 to 0.0008 in.) Piezoelectric plastic materials are being considered for higheramplitude ultrasonic converters A single- or double-converter arrangement can be used to drive the specimen into resonance In a singletransducer system, one end of the specimen is coupled to the converter and the other end remains free In a double-converter system, both ends of the specimen are coupled to two coaxial antiphase-driven ultrasonic converters (Ref 17) The advantage of a double-converter system is its symmetry A comparison of the displacement, strain, and specific energy parameters for a high-damping perspex (Lucite) test specimen tested with a single- and double-converter system is shown in Fig (Ref 21) The symmetry of the converters is reflected in the greater symmetry of the displacement and strain distributions produced in a resonant specimen While equivalent testing conditions can be produced with either single- or double-converter systems through precise design of the acoustic elements, the double converter is less sensitive to small differences between the resonance frequency of the specimen and the driving frequency of the converter Data also show that the double-converter arrangement is less sensitive to detuning of the specimen due to changes in elastic properties or the growth of a fatigue crack Fatigue crack growth testing benefits from the longer crack length attainable with a double-converter system before significant frequency degradation occurs Fig Round-robin results comparing fatigue parameters of various ceramics determined by using dynamic loading SSN, sintered silicon nitride; RBSN, reaction-bonded silicon nitride; ZTA, zirconiatoughened alumina; HPSN, hot pressed silicon nitride Source: Ref 66 A second round-robin tested alumina flexure specimens in distilled water (Ref 66, 67) The participants were instructed to test 15 specimens in the as-received condition and 15 specimens with a kg indentation Most participants covered less than two orders of magnitude in the stress rate, and the combined participant data covered nearly five orders of magnitude Figure summarizes the fatigue parameters generated by the participants for the as-received condition Generally, the results improve as the number of specimens increases from 15 to 33 However, even 33 test specimens can be inadequate Most troublesome is the fact that the fatigue parameter has been overestimated two out of three times If the data points that appear to be outliers are removed, a slight improvement results, as shown in Fig Although the final recommendations from the round-robin were not published, the initial recommendations were that at least three orders of magnitude be covered Also, for testing at rates greater than 100 MPa/s, a piezoelectric load cell was recommended Fig Round-robin results comparing estimated fatigue parameters measured by dynamic loading of an alumina in distilled water Fig Round-robin results comparing estimated fatigue parameters for an alumina in distilled water Outlying data were censored The effect of the range of the stress rate can be seen in Fig If three orders of magnitude are covered, the estimated value of n improves somewhat; however, more data are needed It is not effective to increase the number of tests without increasing the stress range For example, one data set consisting of 33 tests measured over 2.4 orders of magnitude still resulted in an estimated fatigue parameter three times greater than that for all the data Based on these results, it appears that at least 30 specimens and three orders-of-magnitude separation are required Better results from a statistical viewpoint could be attained by testing of the specimens at the lowest rate and at the highest rate (Ref 63) Fig Round-robin results comparing estimated fatigue parameters for an alumina tested in distilled water Numbers in parentheses represent the number of specimens tested The round-robin results prompted the National Physical Laboratory to sponsor a follow-up, United Kingdom only, round-robin (Ref 68) This led to another testing standard, ENV 843-3 “Determination of Subcritical Crack Growth Parameters from Constant Stressing Rate Flexural Strength Tests” (Ref 15) Cyclic Loading Cyclic loading of ceramics and glasses has been performed for quite some time (e.g., Ref 1) Initial results on glasses and materials with glass boundaries indicated little synergy of cycling on the life Thus, simpler test methods such as static and dynamic loading have generally been used, and the analysis adjusted to account for load variation (Ref 45) However, as ceramics materials have been made less glasslike by devitrification treatments and have been toughened by elongating the grain structure, transformation toughening, or adding second phase particles, cyclic loading has been recognized as a significant issue (Ref 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, and 32), and fatigue effects independent of the environment have been measured Two testing methods have been standardized for the determination of cyclic fatigue strength of ceramics (Ref 16, 19) The standards focus on the method of data generation and give no guidance on how the data are to be used The two standards are somewhat complementary because one uses flexure of rectangular beam (Ref 16), while the other uses uniaxial tension (Ref 19) Test method JIS R 1621 “Testing Method for Bending Fatigue of Fine Ceramics” (Ref 16) recommends applying a 20 Hz sinusoidal wave with an R-ratio of 0.1 to standard three- or four-point flexure configurations (Ref 56) Other waveforms and frequencies are allowed Three tests at three different maximum stress levels that result in specimen fracture before 107 cycles are recommended If three tests in a row result in lives greater than 107 cycles, the remaining tests are conducted at a higher stress The initial stress level is based on the monotonic strength of the materials as measured with the same specimen and testing configuration Testing can be halted after 107 cycles An example of failure stress data as a function of the applied cycles is shown in Fig 10 Fig 10 Example of the cycles to fracture for a ceramic material subjected to cyclic loading Adapted from Ref 16 Axial cyclic tensile fatigue testing can be performed with ASTM C 1361 “Standard Practice for ConstantAmplitude, Axial Tension-Tension Cyclic Fatigue of Advanced Ceramics at Ambient Temperatures” (Ref 19) Any of the tensile test specimens specified in ASTM C 1273 “Standard Test Method for Tensile Strength of Monolithic Advanced Ceramics at Ambient Temperatures” (Ref 69) are allowed These include a variety of cylindrical button-head specimens, pin-loaded dog-bone specimens, and shoulder-loaded dog-bone specimens The standard allows any frequency, waveform, and R ratio as needed for a particular application A test may be terminated for any of four reasons: specimen fracture, reaching a predetermined number of run-out cycles, reaching a predetermined specimen compliance or material elastic modulus, or reaching a predetermined phase lag between control mode and response Tension-compression cyclic fatigue has been attained by use of the button-head tensile specimen and a clamping and alignment fixture (Ref 39) Fully reversed bending fatigue can also be attained with flexure specimens by use of two symmetric sets of load and support pins (Ref 70) Another cyclic fatigue test method that has been applied to ceramics is rotary bending (Ref 71, 72) This approach is particularly relevant to applications involving shafts, such as ceramic turbocharger rotors The method avoids problems associated with edge finish by using cylindrical specimens, and a wide range of frequencies is easily attained Tests run on alumina and silicon nitride at 57 Hz indicate a linear S-N curve to 107 cycles at which an indistinct knee occurs, implying a fatigue limit at ~108 cycles The endurance stress corresponded to about ¼ of the strength of the alumina and about ½ that of the silicon nitride The fatigue parameter n was 13 for the alumina and 25 for the silicon nitride, respectively, which is lower than those typically determined for aluminas and silicon nitrides by static or dynamic techniques The differences in the fatigue parameters were attributed to the effect of reversed bending Cyclic fatigue of ceramics has also been performed by using cantilever bending of rectangular, dog-bone, and tapered-beam test specimens at a variety of frequencies Tapered beams and dog-bone specimens reduce the probability that failure will occur at the support where the stress is a maximum Figure 11 illustrates a taperedcantilever beam used to obtain 3000 Hz accelerated fatigue data on silicon nitride (Ref 39) Fig 11 Schematic of a high-frequency, tapered-cantilever beam test apparatus Source: Ref 39 Testing of silicon nitride using tapered-cantilever beams at frequencies as high as 3000 Hz indicated a fatigue limit at 40% of the monotonic strength (Ref 39) Interestingly, the life depended on the number of cycles rather than the time and was well described by the modified Goodman diagram used to describe metallic fatigue The probability of failure was well described by the Weibull model Axial tension-compression testing of the same sintered silicon nitride indicated a fatigue limit around 107 cycles at a stress of 60% of the strength and an increase in fatigue strength with increasing R ratio The implication for this particular silicon nitride is that a cyclic effect, rather than environmentally induced stress corrosion, dominated crack growth Tests using dog-bone specimens at 30 Hz (Ref 73) indicated no effect of cycling on the strength of two different silicon nitrides for less than 107 cycles; however, relatively few specimens were tested At temperatures of 1200 and 1300 °C (2190 and 2370 °F), the effects of fatigue were more pronounced In contrast to the reversed fatigue results, tension-tension flexure fatigue of reaction-bonded, hot pressed, and sintered silicon nitrides indicated environmentally related crack growth to be the failure-controlling mechanism (Ref 74) Fatigue testing of magnesia-partially-stabilized zirconia by using straight cantilever beams indicated a fatigue limit around 108 cycles at a stress of 50% of the tensile strength (Ref 40) Reversed loading significantly shortened the life of the material as compared with tension-tension loading Generally, servohydraulic actuators are used to generate cyclic fatigue loading of test specimens However, piezoelectric actuators in the form of stacks and cantilever spring plates also have been used (Ref 75, 76) These systems allow relatively high frequencies (30 to 550 Hz) and compact test frames that not require a hydraulic pressure source Figure 12 illustrates the test apparatuses Fig 12 Schematics of test apparatuses using piezo-electric ceramics to generate fatigue loading of ceramic beam specimens Source: Ref 75, 76 Cyclic fatigue test results indicate substantial changes in the mechanism controlling crack growth (i.e., cyclically induced versus environmentally induced) for different materials Fatigue behavior for a given ceramic (e.g., silicon nitride) depends on factors such as the grain boundary phase, grain size, and the fracture mode (transgranular versus intergranular) Thus, fatigue testing needs to consider both environmentally induced and cyclically induced crack growth References cited in this section C Gurney and S Pearson, Fatigue of Mineral Glass under Static and Cyclic Loading, Proc R Soc A., Vol 192, 1948, p 537–543 15 DD ENV 843-3 Advanced Technical Ceramics—Monolithic Ceramics—Mechanical Properties at Room Temperature, Part 3: Determination of Subcritical Crack Growth Parameters from Constant Stressing Rate Flexural Strength Tests, British Standards Institution, London, 1997 16 “Testing Method for Bending Fatigue of Fine Ceramics,” JIS R 1621, Japanese Standards Association, Tokyo, Japan, 1996 17 “Standard Test Method for Determination of Slow Crack Growth Parameters of Advanced Ceramics by Constant Stress-Rate Flexural Testing at Ambient Temperature,” C 1368, Annual Book of ASTM Standards, ASTM, Vol 15.01, 1999, p 706–714 18 “Test Methods for Static Bending Fatigue of Fine Ceramics,” JIS R 1632, Japanese Standards Association, Tokyo, Japan, Dec 1998 19 Standard Practice for Constant-Amplitude, Axial Tension-Tension Cyclic Fatigue of Advanced Ceramics at Ambient Temperatures,” C1361, Annual Book of ASTM Standards, ASTM 22 F Gigu, Cyclic Fatigue of Polycrystalline Alumina in Direct Push-Pull, J Mater Sci Lett., Vol 13 (No 6), 1978, p 1357–1361 23 M.V Swain, Lifetime Prediction of Ceramic Materials, Mater Forum, Vol (No 1–2), 1st and 2nd Quarter 1986, p 34–44 24 H Kawakubo and K Komeya, Static and Cyclic Fatigue Behavior of a Sintered Silicon Nitride at Room Temperature, J Am Ceram Soc., Vol 70 (No 6), 1987, p 400–405 25 R.H Dauskardt, W Yu, and R.O Ritchie, Fatigue Crack Propagation in Transformation Toughened Zirconia, J Am Ceram Soc., Vol 70 (No 10), 1987, p C-248–C-252 26 G Grathwohl, Fatigue of Ceramics under Cyclic Loading, Mater Sci Technol., Vol 19 (No 4), April 1988, p 113–124 (in German) 27 M.J Reece, F Guiu, and M.F.R Sammur, Cyclic Fatigue Crack Propagation in Alumina under Direct Tension-compression Loading, J Am Ceram Soc., Vol 72 (No 2), 1989, p 348–352 28 Y Mutoh, M Takahashi, T Oikawa, and H Okamoto, Fatigue Crack Growth of Long and Short Cracks in Silicon Nitride, Fatigue of Advanced Materials, R.O Ritchie, R.H Dauskardt, and B.N Cox, Ed., Material and Component Engineering Publications, Ltd., Edgbaston, U.K., 1991, p 211–225 29 S Horibe and H Hirahara, Cyclic Fatigue of Ceramics Materials: Influence of Crack Path and Fatigue Mechanisms, Acta Metall Mater., Vol 39 (No 6), 1991, p 1309–1317 30 M Okazaki, A.J McEvily, and T Tanaka, On the Mechanism of Fatigue Crack Growth in Silicon Nitride, Metall Trans A, Vol 22A, 1991, p 1425–1434 31 T Tanaka, N Okabe, H Nakayama, and Y Ishimaru, Fatigue Crack Growth of Silicon Nitride with Crack Wedging by Fine Fragments, Fatigue Fract Eng Mater Struct., Vol 17 (No 7), 1992, p 643– 653 32 R.O Ritchie, C.J Gilbert, and J.M McNaney, Mechanics and Mechanisms of Fatigue Damage and Crack Growth in Advanced Materials, Int J Solids Struct., Vol 37, 2000, p 311–329 39 M Masuda, T Soma, M Matsui, and I Oda, Fatigue of Ceramics, Part 1: Fatigue Behavior of Sintered Silicon Nitride under Tension-Compression Cyclic Stress, J Ceram Soc Jpn Int Ed., Vol 96, 1988, p 275–280 40 A Steffen, R.H Dauskardt, and R.O Ritchie, Cyclic Fatigue Life and Crack Growth Behavior of Microstructural Small Cracks in Magnesia-Partially-Stabilized Zirconia Ceramics, J Am Ceram Soc., Vol 74 (No 6), 1991, p 1259–1268 43 S.M Weiderhorn, Prevention of Failure in Glass by Proof-Testing, J Am Ceram Soc., Vol 56 (No 4), 1973, p 227–228 45 A.G Evans and E.R Fuller, Crack Propagation in Ceramic Materials under Cyclic Loading Conditions, Metall Trans A, Vol (No 1), 1974, p 27–33 56 “Test Method for Flexural Strength (Modulus of Rupture) of Fine Ceramics,” JIS R 1601, Japanese Standards Association, Tokyo, Japan, 1995 57 J.E Ritter, Jr., Assessment of Reliability of Ceramic Materials, Fracture Mechanics of Ceramics, Vol 6, R.C Bradt et al., Ed., Plenum Press, 1983, p 227–251 58 J.E Ritter, Jr., Engineering Design and Fatigue Failure of Brittle Materials, Fracture Mechanics of Ceramics, Vol 4, R.C Bradt et al., Ed., Plenum Press, 1978, p 667–685 59 E.B Haugen, Probabilistic Mechanical Design, John Wiley & Sons, 1980 60 N.N Nemeth, L.M Powers, L.A Janosik, and J.P Gyekenyesi, “Durability Evaluation of Ceramic Components Using CARES/LIFE,” ASME Paper 94-GT-362 and NASA-TM 106475, ASME/IGTI Gas Turbine Conference, June 1994 61 A.D Peralta, D.C Wu, P.J Brehm, J.C Cuccio, and M.N Menon, Strength Prediction of Ceramic Components under Complex Stress States, Proceedings of the International Gas Turbine and Aeroengine Congress and Exposition, 5–8 June 1995 (Houston, TX), American Society of Mechanical Engineers, 1995; Allied Signal Document 31-12637, 1995 62 “Fatigue Crack Growth Program NASA/Flagro 2.0,” JSC 22267A, NASA Johnson Space Flight Center, May 1994 63 J.E Ritter, N Bandyopadhyay, and K Jakus, Am Ceram Soc Bull., Vol 60, 1981, p 798 64 “Standard Test method for Flexural Strength of Advanced Ceramics at Ambient Temperature,” C 1161, Annual Book of ASTM Standards, ASTM, Vol 15.01, 1999, p 309–315 65 H.A Linders and B Caspers, Method for Determining Life Diagrams of Mechanoceramic Materials DKG/DKM-Joint Experiment, Ceramics in Science and Practice, Mechanical Properties of Ceramic Construction Materials, G Grathwohl, Ed., DGM Information Association, Verlag, Germany, 1993, p 191–195 (in German) 66 S Freiman, “Pre-Standardization and Standardization Activities in the USA in Mechanical Property Testing of Advanced Structural Ceramics,” presentation at the 7th CIMTEC World Ceramics Congress, Montecatini Terme, Italy, 23 June 1990 67 S.W Freiman and E.R Fuller, Versailles Project on Advanced Materials and Standards, VAMAS TWA Bulletin 8, July 1988 68 W.P Byrn and R Morrell, “Results of the UK Interlaboratory Strength Test Exercise,” NPL Report DMM (D) 72, National Physical Laboratory, Teddington, Middelsex, U.K., Crown Copyright, Dec 1990 69 “Standard Test Method for Tensile Strength of Monolithic Advanced Ceramics at Ambient Temperatures,” C 1273, Annual Book of ASTM Standards, Vol 15.01, ASTM, 1999, p 671–678 70 Cyclic Fatigue Testing of Silicon Nitride, Ceramics (newsletter), Ceramics Division of IIT Research Institute, Chicago, IL, 42, March 1978; Ceram Eng and Sci Proc of the 18th Annual Conference on Composites and Advanced Ceram Mater.-A, Part of 2, 9–14 Jan 1994, Vol 15 (No 4), July–Aug 1994 (Cocoa Beach, FL), Am Ceram Soc., Westerville, OH, 1994, p 32–39 71 H.N Ko, Cyclic Fatigue Behavior of Ceramics under Rotary Bending, Materials Research Society International Meeting on Advanced Materials, Materials Research Society, Vol 5, 1989, p 43–48 72 H.N Ko, Cyclic Fatigue Behavior of Sintered Al2O3 under Rotary Bending, J Mater Sci Lett., Vol 6, 1987, p 801–805 73 R Kossowsky, “Cyclic Fatigue of Hot Pressed Silicon Nitride,” J Am Ceram Soc., Vol 56, 1973, p 10, 531–535 74 Y Matsuo, Y Hattori, Y Katayama, and I Fukuura, Cyclic Fatigue Behavior of Ceramics, Progress in Nitrogen Ceramics, F.L Riley, Ed., Martinus Nijhoff, 1983, p 515–522 75 K Ohya, K Ogur, and M Takatsu, Effect of Loading Waveform on Cyclic Fatigue Behavior of PSZ, J Soc Mater Sci., Jpn., Vol 38 (No 425), 1989, p 144–148 76 K Ohya, K Ogura, and M Takatsu, Cyclic Fatigue Testing Device for Fine Ceramics by Using PiezoElectric Bimorph Actuator, J Soc Mater Sci., Jpn., Vol 38 (No 424), 1989, p 44–48 Fatigue Testing of Brittle Solids J.A Salem, Glenn Research Center at Lewis Field; M.G Jenkins, University of Washington Fracture Mechanics Methods Fracture mechanics methods or “direct” methods generally employ test specimens with relatively large, induced cracks Crack growth data is typically determined directly by observation of the crack or by devices that monitor test specimen compliance, such as clip gages and strain gages (Ref 77, 78) One exception to this is the double torsion specimen, which has a relatively constant stress-intensity factor, KI, over a wide range of crack length Thus, the KI can be calculated without observation of the crack length When used in this fashion, the method is effectively an indirect, long crack method Two general types of fracture mechanics specimen are employed: line loaded or flexural specimens Lineloaded specimens such as the double torsion (DT), double-cantilever beam (DCB), or compact tension (CT) allow cracks to be extended over large distances Flexural specimens such as notched and precracked beams can be scaled so that crack length is comparatively small or large The main advantage of fracture mechanics specimens is that large amounts of data can be derived from a single test specimen, and the results are not subject to the scatter associated with the natural flaw distribution that is sampled by strength techniques However, as the cracks are large in comparison with those developed naturally in smooth specimens, the fatigue behavior may be different In particular, for materials that exhibit transformation toughening or for materials with a coarse or elongated grain structure, a strong effect of crack length on crack growth resistance is exhibited Figure 13 shows the effect of crack growth resistance on the stress-intensity factor for both long and short crack lengths Although the same range of stress-intensity factors is measured, the rates at which resistance develops, and possibly the rate at which fatigue damages the resistance, are very different Thus, techniques that use different crack length scales may result in different fatigue parameters Fig 13 Crack growth resistance as a function of crack extension for alumina The Double Torsion Method The double torsion method, which was developed by Outwater and Gerry (Ref 79, 80) and developed further by other researchers (Ref 81, 82, 83, 84, 85, 86, 87, 88, and 89) is illustrated in Fig 14 Detailed experimental and analytical analyses of the specimen have been given by Fuller (Ref 88) and Pletka et al (Ref 89) Tests can be performed with or without a guide groove on one or both sides of the specimen However, the use of a guide groove can lead to errors (Ref 90, 91), and elimination of the groove can be achieved by using thin, carefully aligned specimens If side grooves must be used, wide grooves and thinner specimens help to avoid interaction between the groove wall and the crack Fig 14 Schematic of the double torsion test specimen Source: Ref 88 A variety of complications associated with the test specimen have been discussed and analyzed to varying degrees These include crack front curvature leading to a variation in the stress-intensity factor along the crack front; variation in the stress-intensity factor with crack length; and poor reproducibility of data for certain conditions, particularly for polycrystalline ceramics when multiple load relaxations are performed with the same specimens Most noteworthy is the last of the problems just noted, as opposite trends have been observed for different materials It seems that the crack-microstructure interactions, which are more prevalent for long cracks, may be the source of discrepancy Despite the complication associated with the DT, it does provide a simple geometry that is easy to load and crack Further, for testing of opaque materials or for hostile environments, the constant stress-intensity factor is advantageous The stress-intensity factor for the DT method is (Ref 89): (Eq 30) with: ξ = - 0.6302t + 1.20t exp (-π/t) where P is the applied force, Wm is half the test specimen width minus half the notch width, d is the total thickness, dn is the notch depth, W is the total width, ν is Poisson's ratio, and ξ is a correction factor for thick test specimens where t = 2d/W It has been recommended that the crack length be maintained between W < a < L - W, where a is the crack length and L is the length, to ensure that the crack is in the constant KI region (Ref 88) Three methods of loading DT specimens have been developed: constant load, constant displacement (Ref 83, 84) and load relaxation The load relaxation technique has the advantage that less crack extension is required to obtain an accurate measure of crack velocity and stress intensity factor (Ref 88) In the load relaxation technique, a precracked specimen is loaded rapidly in a displacement control mode (~0.2 to 0.5 mm/min, or ~0.01 to 0.02 in./min) to nearly the load required to cause specimen fracture If the crack begins to move rapidly, the displacement is halted and the load is recorded as a function of time Once the crack has stopped apparent movement, the test specimen is removed and the final crack length measured The stressintensity factor at any load is calculated from Eq 30, and the crack velocity from the slope of the load-time curve and either the specimen displacement or the crack length and load before or after the test (Ref 91): (Eq 31) (Eq 32) where E is Young's modulus, Pi and are the initial load and crack length values, respectively, and Pf and af are the values at the end of the relaxation The DCB Method The double-cantilever beam (DCB) specimen has been used to test glass, sapphire, magnesium fluoride, and various polycrystalline ceramics (Ref 8, 14, 91, 92, and 93) Also, a form of the DCB specimen referred to as the compact tension has been standardized for fracture toughness testing of metals (Ref 52) A variety of methods can be used to apply load to the DCB specimen These include wedge loading and the application of a constant moment (Ref 94) If a constant KI is desired, the specimen can be tapered (Ref 95) Often, side grooves are used to guide the crack longitudinally For the geometry shown in Fig 15, the stressintensity factor and fracture toughness can be determined from: (Eq 33) where P is the applied force, h is half height of the test specimen, B is the thickness of the test specimen, b is the Web thickness, and a is the crack length Some advantages of this geometry are the constant stress-intensity factor for some configurations (e.g., tapered DCB or applied moment DCB), simple test specimen preparation, efficient material usage, and the simple loading configuration The primary disadvantages are effects associated with the side groove and the difficulty of introducing a sharp crack Fig 15 Double-cantilever beam (DCB) test specimen (Ref 8) Slots on both sides of the specimen for restraining the crack to the midplane are not shown Generally, crack growth measurements are made by optical observation of the crack on the side of the specimens while a constant load is applied For glass, good agreement between DCB and strength measurements (Ref 8, 91) and between DCB and DT measurements have been obtained (Ref 86, 96) Cyclic Fatigue by Other Fracture Mechanics Methods Cyclic fatigue measurement using the direct or fracture mechanics approach can be classified into two crack-length regimes: long cracks made by using large specimens that are typically applied in metals testing (e.g., compact tension) or shorter cracks generated by indentation with Knoop or Vickers hardness indenters (Fig 16) Both the DT and DCB, however, can be loaded cyclically Fig 16 Flexure test specimen with a precrack formed by Vickers indentation Both crack-length regimes have advantages and disadvantages The core issue for both approaches is whether the behavior in real applications is represented For long cracks this is basically an issue of scale, while for the short, indentation cracks, the residual stress field about the indentation and its changes during fatigue are an issue Probably the simplest method of long crack testing is the use of the single-edge-precracked-beam (SEPB) specimen A precrack is formed by bridge indentation (Ref 97) and loaded in three- or four-point flexure The crack extension can be monitored directly on the specimen sides, or by compliance measurements via extensometers, clip gages, strain gages (Ref 77, 78), or electrical grids (Ref 98, 99) This method has been used to generate long crack fatigue data for silicon nitride in vacuum and air (Ref 30) The results indicate lower threshold stress-intensity factors for cyclic loading or air as compared with static loading or vacuum The threshold is also a function of crack length and thus related to the crack growth resistance mechanism No dependence on frequency was found between 0.5 and 20 Hz, however, and an effect of R-ratio was found The compact tension specimen has been used frequently to test ceramics (Ref 25, 33, 100, and 101), and longcrack data have been generated for comparison with short-crack data for materials such as SiC-whiskerreinforced alumina, pyrolitic carbon, and magnesia-partially-stabilized zirconia For magnesia-partially-stabilized zirconia, fatigue measurements with long cracks indicate a threshold at ~50% of the fracture toughness and the slowest growth rates for the materials with the most transformation toughening However, for short, naturally developing cracks, growth occurs below the long-crack threshold, and, as with metals, a negative dependency of growth rate on stress intensity is exhibited Short fatigue crack testing of many ceramics is complicated by the infrequent development of natural cracks and the difficulty of detecting such cracks This difficulty can be circumvented by precracking the polished surface of a beam with a Vickers or Knoop indenter The crack size during static or cyclic loading in four-point or cantilever flexure is monitored optically or via electron microscopy (Ref 29, 100, andd 101) Multiple cracks can be placed on a single specimen Ideally, short cracks without the residual stress should be used, as is done in standardized fracture toughness testing (Ref 102) This can be accomplished by polishing the specimen until a sufficient amount of the indentation and crack has been removed A number of more exotic methods, such compressive cyclic fatigue of notched specimens, have also been used to demonstrate cyclically induced fatigue in ceramics (Ref 103, 104) References cited in this section S.M Weiderhorn and L.H Boltz, Stress Corrosion and Static Fatigue of Glass, J Am Ceram Soc., Vol 62 (No 7–8), 1970, p 547–548 14 T.A Michalske, B.C Bunker, and S.W Freiman, Stress Corrosion of Ionic and Mixed Ionic/Covalent Solids, J Am Ceram Soc., Vol 69 (No 10), 1986, p 721–724 25 R.H Dauskardt, W Yu, and R.O Ritchie, Fatigue Crack Propagation in Transformation Toughened Zirconia, J Am Ceram Soc., Vol 70 (No 10), 1987, p C-248–C-252 29 S Horibe and H Hirahara, Cyclic Fatigue of Ceramics Materials: Influence of Crack Path and Fatigue Mechanisms, Acta Metall Mater., Vol 39 (No 6), 1991, p 1309–1317 30 M Okazaki, A.J McEvily, and T Tanaka, On the Mechanism of Fatigue Crack Growth in Silicon Nitride, Metall Trans A, Vol 22A, 1991, p 1425–1434 33 R Dauskardt, Cyclic Fatigue-Crack Growth in Grain Bridging Ceramics, J Eng Mater Technol (Trans ASME), Vol 115, 1993, p 115–251 52 “Standard Test Method for Plane Strain Fracture Toughness of Metallic Materials,” E 399, Annual Book of ASTM Standards, Vol 03.01, ASTM, 1998 77 J.A Salem, L.J Ghosn, and M.G Jenkins, A Strain Gage Technique to Measure Stable Crack Extension in Ceramics, Post Conference Proceedings of the 1997 SEM Spring Conference on Experimental Mechanics, Society for Experimental Mechanics, Bethel, CT, 1997, p 1–8 78 J.A Salem, L.J Ghosn, and M.G Jenkins, Back-Face Strain as a Method for Monitoring Stable Crack Extension in Ceramics, Ceram Eng Sci Proc., Vol 19 (No 3), 1998, p 587–594 79 J.O Outwater and D.J Gerry, “On the Fracture Energy of Glass,” NRL Interim Contract Report, Contract NONR 3219(01)(x), AD 640848, University of Vermont, Burlington, VT, Aug 1966 80 J.O Outwater and D.J Gerry, “On the Fracture Energy, Rehealing Velocity and Fracture Energy of Cast Epoxy Resin,” Paper 13-D, presented at the 22nd Society of Plastic Industry Conference, 1967; also, J Adhes., Vol 1, 1969, p 290–298 81 G.W Weidmann and D.G Holloway, Slow Crack Propagation in Glass, Phys Chem Glasses, Vol 15 (No 5), Oct 1974, p 116–122 82 C.D Beacham, J.A Kies, and B.F Brown, A Constant K Specimen for Stress Corrosion Cracking Testing, Mater Res Standards, Vol 11, 1970, p 30 83 A.G Evans, Method For Evaluating the Time-Dependent Failure Characteristics of Brittle Material and Its Application to Polycrystalline Alumina, J Mater Sci., Vol (No 10), 1972, p 1137–1146 84 A.G Evans and S.M Wiederhorn, Crack Propagation and Failure Prediction in Silicon Nitride at Elevated Temperatures, J Mater Sci., Vol 9, 1974, p 270–278 85 A.G Evans, L.R Russel, and D.W Richerson, Slow Crack Growth in Ceramic Materials at Elevated Temperatures, Metall Trans A, Vol 6A (No 14), 1975, p 707–716 86 K.R McKinney and H.L Smith, Method of Studying Subcritical Cracking of Opaque Materials, J Am Ceram Soc., Vol 56 (No 1), 1973, p 30–32 87 P.N Thornby, Experimental Errors in Estimating Times to Failures, J Am Ceram Soc., Vol 59 (No 11–12), 1976, p 514–517 88 E.R Fuller, Jr., an Evaluation of Double Torsion Testing: Analysis, Fracture Mechanics Applied to Brittle Materials, STP 678, S.W Frieman, Ed., ASTM, 1979, p 3–18 89 B.J Pletka, E.R Fuller, Jr., and B.G Koepke, An Evaluation of Double Torsion Testing: Experimental, Fracture Mechanics Applied to Brittle Materials, STP 678, S.W Frieman, Ed., ASTM, 1979, p 19–37 90 C.G Annis and J.S Cargill, Modified Double Torsion Method for Measuring Crack Velocity in NC-132 Si3N4, Fracture Mechanics of Ceramics, Vol 4, R.C Bradt et al., Ed., Plenum Press, 1978, p 737–744 91 D.P Williams and A.G Evans, A Simple Method for Studying Slow Crack Growth, J Test Eval., Vol (No 4), 1973, p 264–270 92 K.R Linger and D.G Holloway, Fracture Energy of Glass, Philos Mag., Vol 18 (No 156), 1968, p 1269–1280 93 J.A Salem, M.G Jenkins, M.K Ferber, and J.L Shannon, Jr., Effects of Pre-Cracking Method on Fracture Properties of Alumina, Proceedings of Society of Experimental Mechanics Conference on Experimental Mechanics, 10–13 June 1991 (Milwaukee, WI), Society for Experimental Mechanics, Bethel, CT, 1991, p 762–769 94 S.W Freiman, D.R Mulville, and P.W Mast, J Mater Sci., Vol (No 11), 1973, p 1527–1533 95 S Mostovoy, P.B Crosley, and E.J Ripling, Use of Crack-Line-Loaded Specimens for Measuring Plane-Strain Fracture Toughness, J Mat., Vol (No 3), Sept 1967, p 661–681 96 A.G Evans and H Johnson, The Fracture Stress and Its Dependence on Slow Crack Growth, J Mater Sci., Vol 10, 1975, p 214–222 97 T Sadahiro, Transverses Rupture Strength and Fracture Toughness of WC-Co Alloys, J Jpn Inst Met., Vol 45, 1981, p 291–295 98 D.J Martin, K.W Davido, and W.D Scott, Slow Crack Growth Measurement Using an Electric Grid, Am Ceram Soc Bull., Vol 65 (No 7), 1986, p 1052–1156 99 P.K Liaw, H.R Hartmann, and W.A Lodgson, A New Transducer to Monitor Fatigue Crack Propagation, J Test Eval., Vol 11 (No 3), 1983, p 202–207 100 R.H Dauskardt, R.O Ritchie, J.K Takemoto, and A.M Brendzel, Cyclic Fatigue in Pyrolytic Carbon-Coated Graphite Mechanical Heart-Valve Prostheses: Role of Small Cracks in Life Prediction, J Biomed Mater Res., Vole 28, 1994, p 791–804 101 R.H Dauskardt, M.R James, J.R Porter, and R.O Ritchie, Cyclic Fatigue-Crack Growth in a SiC-Whisker-Reinforced Alumina Ceramic Composite: Long- and Small-Crack Behavior, J Am Ceram Soc., Vol 75 (No 4), 1992, p 759–771 102 “Standard Test Methods for Fracture Toughness of Advanced Ceramics,” C 1421, Annual Book of ASTM Standards, ASTM, Vol 15.01, 2000, p 631–662 103 L Ewart and S Suresh, Dynamic Fatigue Crack Growth in Polycrystalline Alumina under Cyclic Compressive Loads, J Mater Sci., Vol 5, 1986, p 774–778 104 L Ewart and S Suresh, Crack Propagation in Ceramics under Cyclic Loads, J Mater Sci., Vol 22, 1987, p 1173–1192 Fatigue Testing of Brittle Solids J.A Salem, Glenn Research Center at Lewis Field; M.G Jenkins, University of Washington Comparison of Indirect and Direct Methods Several researchers (Ref 105, 106, and 107) have noted that indirect techniques, such as dynamic fatigue, can result in large errors in the estimated fatigue parameters of polycrystalline ceramics exhibiting environmentally induced crack growth when the failure times are relatively short Further, such methods cannot be used to accurately predict the life of components unless some precautions are taken For example, for a mullite with a region I fatigue parameter of n = 41 as measured with the double-torsion method, the use of stress rates greater than MPa/s resulted in an estimated value of n = 19 (Ref 105) For a silicon nitride with a parameter of n = 66, the values estimated from dynamic fatigue was n = 100 Similar differences were shown to exist between flexural data and double torsion data for magnesium alumina silicate (n = 51 versus 84) (Ref 89, 107) This is a result of the fact that indirect methods average all three regions of the fatigue curves into a single region, and for short duration tests, all the regions are significant However, in a component with a long life, region I is dominant One exception to this is static fatigue tests, in which the failure times tend to be long and the crack growth dominated by region I The dynamic fatigue test might be made more applicable to the generation of design data for long-term applications by using stress rates that are sufficiently slow References cited in this section 89 B.J Pletka, E.R Fuller, Jr., and B.G Koepke, An Evaluation of Double Torsion Testing: Experimental, Fracture Mechanics Applied to Brittle Materials, STP 678, S.W Frieman, Ed., ASTM, 1979, p 19–37 105 F Sudreau, C Olagnon, and G Fantozzi, Lifetime Prediction of Ceramics: Importance of Test Method, Ceram Int., Vol 10, 1994, p 125–135 106 E.M Rockar and B.J Pletka, Fracture Mechanics of Alumina in a Simulated Biological Environment, Fracture Mechanics of Ceramics, Vol 4, R.C Bradt et al., Ed., Plenum Press, 1978, p 725–735 107 Pletka and Wiederhorn, Subcritical Crack Growth in Glass-Ceramics, Fracture Mechanics of Ceramics, Vol 4, R.C Bradt et al., Ed., Plenum Press, 1978, p 745–759 ... frequency and strain range Strain rate ( ), s-1, at strain (ε) of: ε = 1 0-2 , m/m ε = 1 0-5 , m/m ε = 1 0-4 , m/m ε = 1 0-3 , m/m 10 1 0-4 1 0-3 1 0-2 1 0-1 100 1 0-3 1 0-2 1 0-1 -2 -1 1,000 10 10 10 10,000 1 0-1 ... Experiments have been undertaken and models have been proposed for both the full- and partial-slip regimes and are based on empirical observations Full-slip and partial-slip conditions can be achieved... measurements under high-frequency resonance excitation (a) Center-cracked specimen (b) Single-edge-cracked specimen (c) Double-edge-cracked specimen (d) Single-edge-cracked specimen (e) Center-cracked specimen