36 R.A Graham, Impact Techniques for the Study of Physical Properties of Solids under Shock Wave Loading, J Basic Eng (Trans ASME), Vol 89, 1967, p 911–918 40 E.G Zukas, Shock-Wave Strengthening, Met Eng Q., Vol 6, 1966, p 1–20 45 L.M Barker and R.E Hollenbach, Interferometer Technique for Measuring the Dynamic Mechanical Properties of Materials, Rev Sci Instrum., Vol 36, 196, p 1617–1620 46 G.E Dieter, Metallurgical Effects of High-Intensity Shock Waves in Metals, Response of Metals to High Velocity Deformation, P.G Shewmon and V.F Zackay, Ed., Interscience, 1961, p 409–446 47 G.R Fowles, Experimental Technique and Instrumentation, Dynamic Response of Materials to Intense Impulsive Loading, P.C Chou and A.K Hopkins, Ed., Air Force Materials Laboratory, Wright Patterson Air Force Base, 1972, p 405–480 48 P.S DeCarli and M.A Meyers, Design of Uniaxial Shock Recovery Experiments, Shock Waves and High Strain Rate Phenomena in Metals, M.A Meyers and L.E Murr, Ed., Plenum, 1981, p 341–373 49 R.G McQueen and S.P Marsh, High Explosive Systems for Equation-of-State Studies, Shock Waves in Condensed Matter—1987, S.C Schmidt and N.C Holmes, Ed., Elsevier, 1988, p 107–110 50 M.A Meyers, Dynamic Behavior of Materials, Wiley Interscience, 1994 51 G.E Duvall, Shock Waves in the Study of Solids, Appl Mech Rev., Vol 15, 1962, p 849–854 52 E.G Zukas, Shock-Wave Strengthening, Met Eng Q., Vol (No 2), 1966, p 1–20 53 J.N Fritz and J.A Morgan, An Electromagnetic Technique for Measuring Material Velocity, Rev Sci Instrum., Vol 44, 1973, p 215–221 54 L.M Barker and R.E Hollenbach, Laser Interferometer for Measuring High Velocities of Any Reflecting Surface, J Appl Phys., Vol 43, 1972, p 4669–4675 55 R.G McQueen, J.W Hopson, and J.N Fritz, Optical Technique for Determining Rarefaction Wave Velocities at Very High Pressures, Rev Sci Instrum., Vol 53, 1982, p 245–250 56 J.N Fritz, C.E Morris, R.S Hixson, and R.G McQueen, Liquid Sound Speeds at Pressure from the Optical Analyzer Technique, High Pressure Science and Technology 1993, S.C Schmidt, J.W Shaner, G.A Samara, and M Ross, Ed., American Institute of Physics, 1994, p 149–152 57 R.J Clifton, Pressure Shear Impact and the Dynamic Plastic Response of Metals, Shock Waves in Condensed Matter—1983, J.R Asay, R.A Graham, and G.K Straub, Ed., North-Holland, 1984, p 105– 111 58 R.A Graham and J.R Asay, Measurement of Wave Profiles in Shock Loaded Solids, High Temp.— High Press., Vol 10, 1978, p 355–390 59 G.R Fowles, G.E Duvall, J Asay, P Bellamy, F Feistman, D Grady, T Michaels, and R Mitchell, Gas Gun for Impact Studies, Rev Sci Instrum., Vol 41, 1970, p 984–996 60 J.W Taylor, Experimental Methods in Shock Wave Physics, Metallurgical Effects at High Strain Rates, R.W Rohde, B.M Butcher, J.R Holland, and C.H Karnes, Ed., Plenum Press, 1973, p 107–128 61 G.T Gray III, Deformation Twinning in Aluminum-4.8 wt.% Mg, Acta Metall., Vol 36, 1988, p 1745– 1754 62 G.T Gray III, P.S Follansbee, and C.E Frantz, Effect of Residual Strain on the Substructure Development and Mechanical Response of Shock-Loaded Copper, Mater Sci Eng A, Vol 111, 1989, p 9–16 63 D.L Paisley, Laser-Driven Miniature Flyer Plates for Shock Initiation of Secondary Explosives, Shock Compression of Condensed Matter—1989, S.C Schmidt, J.N Johnson, and L.W Davidson, Ed., Elsevier, 1990, p 733–736 64 D.E Mikkola and R.N Wright, Dislocation Generation and Its Relation to the Dynamic Plastic Response of Shock Loaded Metals, Shock Waves in Condensed Matter—1983, J.R Asay, R.A Graham, and G.K Straub, North-Holland, 1984, p 415–418 65 S Larouche, E.T Marsh, and D.E Mikkola, Strengthening Effects of Deformation Twins and Dislocations Introduced by Short Duration Shock Pulses in Cu-8.7Ge, Metall Trans A, Vol 12, 1981 p 1777–1785 66 D.L Paisley, Laser-Driven Miniature Plates for One-Dimensional Impacts at 0.5-ε6 km/s, Shock-Wave and High-Strain-Rate Phenomena in Materials, M.A Meyers, L.E Murr, and K.P Staudhammer, Ed., Marcel Dekker, 1992, p 1131–1141 67 D.L Paisley, R.H Warnes, and R.A Kopp, Laser-Driven Flat Plate Impacts to 100 GPa with SubNanosecond Pulse Duration and Resolution for Material Property Studies, Shock Compression of Condensed Matter—1991 S.C Schmidt, R.D Dick, J.W Forbes, and D.G Tasker, Ed., Elsevier, 1992, p 825–828 68 J.H Shea, A Mazzella, and L Avrami, Equation of State Investigation of Granular Explosives Using a Pulsed Electron Beam, Proc Fifth Symp (Int.) on Detonation, Office of Naval Research, Arlington, Virginia, 1970, p 351–359 69 F Cottet and J.P Romain, Formation and Decay of Laser-Generated Shock Waves, Phys Rev A, Vol 25, 1982, p 576–579 70 F Cottet, J.P Romain, R Fabbro, and B Faral, Measurements of Laser Shock Pressure and Estimate of Energy Lost at 1.05μm Wavelength, J Appl Phys., Vol 55, 1984, p 4125–4127 71 F Cottet and M Boustie, Spallation Studies in Aluminum Targets Using Shock Waves Induced by Laser Irradiation at Various Pulse Durations, J Appl Phys., Vol 66, 1989, p 4067–4073 72 T de Rességuier and M Hallouin, Stress Relaxation and Precursor Decay in Laser Shock-Loaded Iron, J Appl Phys., Vol 84, 1998, p 1932–1938 73 T de Rességuier and M Deleignies, Spallation of Polycarbonate under Laser Driven Shocks, Shock Waves, Vol 7, 1997, p 319–324 74 C.E Ragan, Equation-of-State Experiments using Nuclear Explosions, Proc Int Symp on Behaviour of Condensed Matter at High Dynamic Pressures, Commissariat l'Energie Atomique, Saclay, Paris, 1978, p 477 75 C.E Ragan III, Shock Compression Measurements at to TPa, Phys Rev A, Vol 25, 1982, p 3360– 3375 76 R.F Trunin, Shock Compressibility of Condensed Materials in Strong Shock Waves Generated by Underground Nuclear Explosions, Physics Usp., Vol 37, 1994, p 1123–1145 Shock Wave Testing of Ductile Materials George T (Rusty) Gray III, Los Alamos National Laboratory Design of Shock Recovery and Spallation Fixtures The structure/property relationships in materials subjected to shock wave deformation are very difficult to conduct and complex to interpret due to the dynamic nature of the shock process and the very short time of the test Due to these imposed constraints, the majority of real-time shock process measurements are limited to studying the interactions of the transmitted wave arrival at the free surface or at target-window interfaces To augment these in situ wave profile measurements, shock recovery techniques were developed in the late 1950s to experimentally assess the residual effects of shock wave compression, release, and shock-induced fracture events on materials The object of soft recovery experiments is to examine the terminal structure-property relationships of a material that has been subjected to a known uniaxial shock history then returned to ambient conditions without experiencing radial release tensile wave loading or collateral recovery strains Tensile wave interactions may be mostly mitigated by surrounding the sample with tightly fitting material of the same (or nearly the same) shock impedance, both laterally and axially around the sample This technique, termed momentum trapping, has continued to evolve to prevent large radial release waves from entering the sample and to prevent Hopkinson fracture (spallation) for a variety of sample configurations and shock-loading methods When ideally trapped, the residual strain, εres, in the recovered sample (defined here as the final sample thickness divided by the initial sample thickness) should be on the order of only a few percent Since the inception of shock recovery studies, the use of momentum trapping techniques has been successfully applied to a large number of metallic systems and a more limited number of brittle solids Several review papers chronicle the development and design of shock recovery techniques (Ref 25, 26, 34, 40, 48, 77,and 78) To correctly assess the influence of shock wave deformation on ductile material structure and properties, it is crucial to systematically control the experimental loading parameters and design the shock fixtures to recover the test sample with minimum residual strain With higher peak pressures (from 10 GPa, or 1.5 × 106 psi, upward) however, recovery of shock-loaded samples becomes increasingly difficult For lowpressure shocks, for example, a few times the Hugoniot elastic limit of the material, shock recovery is straightforward independent of whether the shock is generated via HE, launcher impact, or radiation impingement At pressures in excess of 50 to 60 GPa (7.3 × 106 to 8.7 × 106 psi) recovery of bulk metallic samples that have not been seriously compromised by significant shock heating and/or radial release strains is nearly impossible At shock pressures greater than 100 GPa (14.5 × 106 psi) recovery of samples is essentially impossible The techniques described below have been used for both HE- and launcher-driven shock recovery experiments References cited in this section 25 G.T Gray III, Influence of Shock-Wave Deformation on the Structure/Property Behavior of Materials, High-Pressure Shock Compression of Solids, J.R Asay and M Shahinpoor, Ed., Springer-Verlag, 1993, p 187–216 26 D.G Doran and R.K Linde, Shock Effects in Solids, Solid State Phys., Vol 19, 1966, p 230–290 34 G.T Gray III, Shock Experiments in Metals and Ceramics, Shock-Wave and High-Strain-Rate Phenomena in Materials, M.A Meyers, L.E Murr, and K.P Staudhammer, Ed., Marcel-Dekker, 1992, p 899–912 40 E.G Zukas, Shock-Wave Strengthening, Met Eng Q., Vol 6, 1966, p 1–20 48 P.S DeCarli and M.A Meyers, Design of Uniaxial Shock Recovery Experiments, Shock Waves and High Strain Rate Phenomena in Metals, M.A Meyers and L.E Murr, Ed., Plenum, 1981, p 341–373 77 R.N Orava and R.H Wittman, Techniques for the Control and Application of Explosive Shock Waves, Proc of Fifth Int Conf on High Energy Fabrication, University of Denver, 1975, p 1.1.1 78 M.A Mogilevskii, Shock-Wave Loading of Specimens with Minimum Permanent Set, Combust Explos Shock Waves, Vol 21, 1985, p 639–640 Shock Wave Testing of Ductile Materials George T (Rusty) Gray III, Los Alamos National Laboratory Design Parameters for Flyer-Plate Experiments The variation of the shock parameters (peak pressure and pulse duration) for recovery experiments can be calculated using several simple formulations Equations have been developed by Orava and Wittman (Ref 77) for the design of recovery assemblies to achieve a given peak pressure and pulse duration and to protect the sample from significant radial release and possible subsequent spallation Design of the target-flyer variables to achieve a given set of shock parameters in a shock recovery experiment is typically started by fixing the desired peak shock pressure or true transient strain This is linked to the fact that changes in peak shock pressure are known to produce the most significant variation in post shock material structure-property relations (Ref 24, 25, 26, 28, 29, 30, 40, 42, 44, and 46) When the flyer plate and target assembly are the same material, called symmetric impact, the material velocity behind the shock is exactly one half of the projectile velocity (Ref 77, 79): Vp = + = 2Up (Eq 1) where Vp is the projectile velocity and Up is the particle velocity partitioned between the driver plate, , and the target, Symmetric impact is generally preferred because it is most easily analyzed In the case of dissimilar materials, the particle velocity is divided according to the Hugoniot equations of each by the impedance matching method (Ref 6) In this situation, complex release behavior is typical Hugoniot data for a wide range of materials can be found tabulated in Ref 79 The total equivalent or effective transient strain induced in the sample due to this impact (encompassed as a sum of both the elastic and plastic compression and elastic and plastic release portions of the shock process), εt, is determined from the measured Hugoniot data, which is the dynamic compressibility of the material as a function of pressure where V0 and V are the initial and final volumes of the material during the peak of the shock Assuming that the residual strain remaining in the sample after the shock release is zero (Ref 80), the transient or equivalent total strain imparted to the sample due to the shock-loading impulse and release is given by: (Eq 2) In Fig 4, a time-distance diagram of a symmetric impact by a driver plate with the target backed by a spall plate is presented that ignores strength in the sample The symmetry of impact is reflected in the similar slope of the shock velocity, labeled Us, into the driver and target starting at time zero The length of time the sample remains at pressure is determined by combining the shock wave and release wave transit times through the flyer When the rarefaction wave reaches the flyer-target interface the pressure in the sample is released The release process is stretched in time in the form of a “rarefaction fan” due to the variation in longitudinal and bulk wave speeds as a function of pressure The pulse duration time, tp, at the front of the sample is approximated by (Ref 77): (Eq 3) where dD is the driver plate thickness, is the shock velocity in the driver in shock, and are density of D driver at ambient pressure and under shock, respectively, and C is the bulk sound speed in the compressed (shocked-state) driver Fig Time-distance diagram of a symmetric shock wave impact To assure the recovery specimen experiences uniaxial strain, that is, one-dimensional strain, in nature during both loading and unloading it is necessary to protect the sample from radial release prior to uniaxial release Figure schematically represents the time distance for a symmetric impact and the commensurate particlevelocity time history, which would be visible to an interferometer, such as a VISAR, looking at the rear surface of the sample assembly If the driver plate and target assembly have the same dimension, then immediately after the target assembly is impacted by the driver, radial release waves will be directed toward the interior of the target assembly from the driver edges In order to mitigate these lateral release waves, the sample within the target assembly is surrounded by momentum traps comprised of rings or rails of material similar to the sample The width of the momentum trapping necessary must be sufficient to contain the total shock event in the flyer and target of time, ts (Ref 77) Given simple centered flow conditions where the driver, target, and momentum trapping materials are the same, the minimum trapping width w is given by (Ref 77): (Eq 4) After the shock has traversed the sample, if it is not obstructed, it will reflect off the back surface of the specimen as a release wave This further complicates the loading history of the sample, indeed, if the rear surface release wave is allowed to interact with the forward-moving release wave propagating in from the driver that releases the sample to ambient pressure In this case the two tensile release fans will meet and cause spall fracture when the amplitude is above the dynamic tensile strength of the material To prevent this from occurring in the sample intended for postshock characterization, a spall plate is placed behind the sample to isolate the release wave interactions in the spall plate, thereby protecting the sample spallation (Fig 4) The release time, tR, must be greater than or equal to the shock time To protect the sample from spall interactions, the spall plate thickness must equal or exceed the dimension (Ref 77): (Eq 5) As an example, a 10 GPa (1.5 × 106 psi), μs pulse shock in a mm (0.2 in.) thick high-purity copper sample (symmetric impact, C0 = 3.94 mm/μs, C = 4.425 mm/μs, Us = 4.326 mm/μs, and V/V0 = 0.94) requires an impactor traveling at 0.518 mm/μs (Up = 0.259 mm/μs) using a 2.25 mm (0.09 in.) thick copper impactor or driver plate The minimum momentum trapping and spall plate requirements are then calculated to be 10.45 mm (0.41 in.) and 10.56 mm (0.42 in.), respectively While Eq and pertaining to the momentum trapping and spallation requirements can be corrected for nonsymmetrical impact, this is not usually done Internal impedance mismatching within the assembly will cause additional wave reflections that compromise the simple compression loading history of the sample In instances where symmetric assembly design is impossible, as is typically the case for most brittle solids, other techniques are necessary Figure illustrates an example of a soft shock recovery fixture positioned on a shock support or impact assembly for conducting shock recovery experiments on a gas- and/or propellant-driven launcher Following release of the shock through the sample, the two opposing release waves are designed to interact within the spall plate, thereby isolating the sample from the high tensile stresses resulting from the overlap of the two release fans The central opening in the impact is thereafter utilized to facilitate the escape of the sample assembly into the recovery catch tank area for deceleration This central passageway additionally serves as a mechanism to separate the sample assembly from the continued forward momentum on the projectile Inadequate assembly design to ensure a one-dimensional shock loading and release sequence has been shown to alter the sample shock history and subsequent structure-property response due to the additional plastic work imposed on the sample due to late-time radial release effects (Ref 80, 81) Careful attention to momentum trapping of samples during shock recovery experimentation is therefore required if the structure-property effects quantified in postmortem recovered samples are to be correlated to processes occurring during shock loading Fig Schematic of a soft shock recovery fixture used on a gas/powder launcher assembly References cited in this section R.G McQueen and S.P Marsh, Equation of State for Nineteen Metallic Elements from Shock-Wave Measurements to Two Megabars, J Appl Phys., Vol 31, 1960, p 1253–1269 24 C.S Smith, Metallographic Studies of Metals after Explosive Shock, Trans Metall Soc AIME, Vol 214, 1958, p 574–589 25 G.T Gray III, Influence of Shock-Wave Deformation on the Structure/Property Behavior of Materials, High-Pressure Shock Compression of Solids, J.R Asay and M Shahinpoor, Ed., Springer-Verlag, 1993, p 187–216 26 D.G Doran and R.K Linde, Shock Effects in Solids, Solid State Phys., Vol 19, 1966, p 230–290 28 W.C Leslie, Microstructural Effects of High Strain Rate Deformation, Metallurgical Effects at High Strain Rates, R.W Rhode, B.M Butcher, J.R Holland, and C.H Karners, Ed., Plenum Press, 1973, p 571 29 L.E Murr, Residual Microstructure—Mechanical Property Relationships in Shock-Loaded Metals and Alloys, Shock Waves and High Strain Rate Phenomena in Metals, M.A Meyers and L.E Murr, Ed., Plenum, 1981, p 607–673 30 L.E Murr, Metallurgical Effects of Shock and High-Strain-Rate Loading, Materials at High Strain Rates, T.Z Blazynski, Ed., Elsevier Applied Science, 1987, p 1–46 40 E.G Zukas, Shock-Wave Strengthening, Met Eng Q., Vol 6, 1966, p 1–20 42 G.T Gray III, Shock-Induced Defects in Bulk Materials, Materials Research Society Symp Proc., Vol 499, 1998, p 87–98 44 S Mahajan, Metallurgical Effects of Planar Shock Waves in Metals and Alloys, Phys Status Solidi (a), Vol 2, 1970, p 187–201 46 G.E Dieter, Metallurgical Effects of High-Intensity Shock Waves in Metals, Response of Metals to High Velocity Deformation, P.G Shewmon and V.F Zackay, Ed., Interscience, 1961, p 409–446 77 R.N Orava and R.H Wittman, Techniques for the Control and Application of Explosive Shock Waves, Proc of Fifth Int Conf on High Energy Fabrication, University of Denver, 1975, p 1.1.1 79 S.P Marsh, LASL Shock Hugoniot Data, University of California Press, 1980 80 G.T Gray III, P.S Follansbee, and C.E Frantz, Effect of Residual Strain on the Substructure Development and Mechanical Response of Shock-Loaded Copper, Mater Sci Eng A, Vol 111, 1989, p 9–16 81 A.L Stevens and O.E Jones, Radial Stress Release Phenomena in Plate Impact Experiments: Compression-Release, J Appl Mech (Trans ASME), Vol 39, 1972, p 359–366 Shock Wave Testing of Ductile Materials George T (Rusty) Gray III, Los Alamos National Laboratory Shock Recovery and Spallation Studies of Ductile Materials As described previously, shock wave research includes analysis of samples subjected to an impact excursion to examine the postmortem signature of the shock prestraining on the substructure and mechanical behavior of a material in addition to damage evolution of a ductile material when subjected to a spallation uniaxial strain loading history A few examples of the types of experimental data and post mortem characterization results typically quantified for both shock recovery and spallation research are introduced below Defect Generation during Shock Loading as Quantified Using Shock Recovery Experiments In an ideal isotropic homogeneous material, the passage of an elastic shock through a bulk material should leave behind no lattice defects or imperfections In practice, the severe loading path conditions imposed during a shock induce a high density of defects in most materials (i.e., dislocations, point defects, and/or deformation twins) In addition, during the shock process some materials may undergo a pressure-induced phase transition that affects the material response If the high-pressure phase persists upon release of pressure to ambient conditions (although metastable) the postmortem substructure and mechanical response will also reflect the high-pressure excursion Interpretation of the results of shock wave effects on materials must therefore address all of the details of the shock-induced deformation substructure in light of the operative metallurgical strengthening mechanisms in the material under investigation and the experimental conditions under which the material was deformed and recovered Microstructural examinations of shock-recovered samples have characterized the differing types of lattice defects (dislocations, point defects, stacking faults, deformation twins, and, in some instances, high-pressure phase products) generated during shock loading The specific type of defect or defects activated and their density and morphology within the shock-recovered material have, in turn, been correlated to the details of the starting material chemistry, microstructure, and initial mechanical behavior or hardness, and the postmortem mechanical behavior of the shock-prestrained material Several in-depth reviews have summarized the microstructural and mechanical response of shock-recovered metals and alloys (Ref 24, 25, 26, 28, 29, 30, 40, 42, 44, and 46) In general, the deformation substructures resulting from modest shock loading (up to 40 GPa, or × 106 psi) in metals are observed to be very uniformly distributed on a grain-to-grain scale The specific type of substructure developed in the shock in a given metal (e.g., dislocation cells, twins, or faults) has been shown to critically depend on a number of factors These include the crystal structure of the metal or alloy, the relevant strengthening and deformation mechanisms in the material (such as alloying, grain size, second phases, and interstitial content), temperature, stacking fault energy, and the shock-loading parameters and experimental conditions The overall substructure, while macroscopically uniform, can vary within single grains The substructure can consist of homogeneously distributed dislocation tangles or cells, coarse planar slip, stacking faults, or twins (i.e., be locally heterogeneous) The type of substructure formed depends on the deformation mechanisms operative in the specific material under the specific shock conditions These shock-induced microstructural changes in metallic systems in turn correlate with variations in the postmortem mechanical properties For example, the formation of deformation twins is facilitated in many materials due to the very high strain rate during shock loading (Ref 61) Shock loading in most metals and alloys has been shown to manifest greater hardening than quasi-static deformation for the same total strain, particularly if the metal undergoes a polymorphic phase transition, such as is observed in pure iron (Ref 42) Figure compares the stress-strain response of annealed copper and annealed tantalum samples that have been quasi-statically loaded with the quasi-static reloading responses of the samples that have been shock prestrained The shock-loaded stress-strain curves are plotted offset at the approximate total transient shock strains, calculated as ; 1n (V/V0) for the shock (where V and V0 are the compressed volumes during the shock and the initial volumes, respectively) The offset curve for copper shows that the reload behavior of the shock-prestrained sample (compared at an equivalent strain level) exhibits a reload flow stress considerably higher than the unshocked copper Other face-centered cubic metals and alloys (e.g., copper, nickel, and aluminum) have been seen to exhibit similar behavior (Ref 24, 25, 26, 28, 29, 30, 40, 42, 44, and 46) On the contrary, the reload stress-strain response of tantalum shock prestrained to and 20 GPa (1 and × 106 psi) is observed to display essentially no enhanced shock hardening in comparison to quasi-static loading to an equivalent plastic strain Fig Stress-strain response of tantalum and copper illustrating the varied effect of shock prestraining on postshock mechanical behavior Spallation “Hopkinson Fracture” Studies of Ductile Materials Spallation is the failure in a material due to the action of tensile stresses developed in the interior of a sample or component through the overlap of two release waves Since the early work of Hopkinson (Ref 14), numerous researchers have studied this phenomena (Ref 15, 16, 20, 22, and 82) Early work by Rinehart (Ref 16), through systematic studies on a range of engineering metals and alloys, demonstrated that a critical shock stress is needed to produce scabbing in a material The characteristic nature of this material quantity, as well as its importance to understanding interactions between shock and the structure, continues to make spallation research of primary scientific and engineering interest A systematic representation of the idealized process of release wave overlap driving a material into a dynamic tension, uniaxial strain, loading state is shown in Fig The elastic wave in this figure is assumed to be negligible compared to the plastic I wave; no additional waves, such as a phase transition plastic II wave, are present Measurements of the spall strength are based on analysis of the one-dimensional motion of compressible, contiguous, condensed matter following the reflection of the shock pulse from the surface of the sample or component Figure shows the shock trajectory that a sample undergoes during the path in a spallation experiment The shock that is imparted into the target through the jump in particle velocity upon impact with the driver plate (or impactor) is thereafter unloaded through the release wave originating (in one dimension) from the rear surface of the driver plate that diminishes the free surface velocity If the impactor is sufficiently thin, the rarefaction will overtake the shock because the release wave is traveling into the precompressed solid and, therefore, its wave speed is higher than the shock velocity In this case, the rarefaction will attenuate the shock This unloading wave is actually a fan of characteristics, which erodes the shock down toward ambient pressure This reduces the particle velocity from the peak Hugoniot State achieved by the imposed shock For thicker impactors, as in Fig 4, the release fan arrives at the rear surface of the target well after the arrival of the main shock At the free rear surface of the target, the shock wave is reflected as an unloading wave that travels back toward the interior of the target Overlap of the release fans causes the material in the overlap region to be loaded in tension The maximum tensile stress is reached in the central area of the overlap of the two release fans, termed the spall plane If the maximum tensile stress achieved exceeds the local fracture, strength damage is initiated in the target Fracture of the material at the spall plane causes the tensile stress to decrease rapidly to zero As a result, a compression wave forms in the matter adjacent to the spall plane region These waves propagate in each direction away from the spall plane At the rear surface of the target, as in Fig where the particle velocity is monitored, this compression wave is manifested as a jump in velocity When the target spalls, a stress wave is trapped between the spall plane and the rear of the target Later reverberations of this stress wave lead to a damped oscillation in the particle velocity record This “ringing,” or period of oscillations, can be used to determine the thickness of the spalled layer or scab produced Monitoring of the rear surface velocity of the sample or of the sample-window interface using a manganin pressure gage or VISAR quantifies the sample particle velocity history A representation of the correlation between the spallation process within a sample and its manifestation on the sample rear surface or samplewindow surface is shown on the right side of Fig Measurements of the wave profile of a sample driven to spall provides information on the time-dependent wave propagation and intersection processes leading to damage evolution in a material if the tensile stresses are sufficiently high Shock studies designed to study spallation in a material therefore use the wave profile and, specifically, the details of the magnitude of the “pullback” signal to quantify the energy necessary to nucleate and propagate damage Figure presents a VISAR wave profile of high-purity zirconium subjected to spall loading (Ref 83) The arrow A identifies the Hugoniot elastic limit for this material and the pull-back signal documents that this shock amplitude is sufficient to cause damage evolution in this material; in this case, however, no scab was formed but rather only incipient spall Fig Rear surface velocity shock wave profile (developed using VISAR interferometry) showing spallation in zirconium Source: Ref 83 Profiles such as Fig provide quantitative data to compare with one-dimensional wave propagation finitedifference and finite-volume code calculations that model dynamic fracture Additional insight into the physics and materials science controlling the process of spallation can be provided through examining the postshocked and damaged samples, just as Hopkinson did in his first steel studies Figure shows a metallographic cross section through an incipiently spalled high-purity tantalum sample following impact loading In this example, nearly spherical ductile voids are observed to have nucleated and grown, as a function of position from the central fracture plane, and begun to coalesce under the imposed tensile stress history Given sufficient tensile stress amplitude and appropriate geometry, damage can lead to scab formation and, therefore, complete separation of the sample into multiple pieces Identification of the final fracture modes manifesting complete separation can be obtained by soft recovering the scab formed and then examining its fracture surface Figure presents an example of a fracture surface of a spalled Ta-10W sample illustrating cleavage fracture behavior Parameters for Cyclic Loading For cyclic loading, there are two parameters considered to be applicable for tests involving cyclic loading Again, the testing conditions, definitions, and necessary calculations for each parameter are outlined below ΔJc Parameter The ΔJc parameter is simply a time integral of C* or J* over the hold time, th, involved in trapezoidal waveform loading (Ref 1) The parameter was first introduced by Jaske and Begley (Ref 32) and Taira et al (Ref 33) in order to correlate with the time-dependent creep crack growth during a trapezoidal waveform loading at elevated temperatures Its definition is: ΔJc = C* (dt) (Eq 35) where th is the hold time at the maximum load of a trapezoidal load form When a material is subjected to trapezoidal waveform loading, its response can be divided into two parts: the loading portion and the hold time portion Creep deformation may occur at the crack tip during both portions When integrated over the hold time, the ΔJc parameter gives the total energy input in the crack-tip area due to creep deformation that occurs during the hold time (Ref 1) During the loading portion, the amount of creep deformation generally depends on the rate of loading If the loading is conducted quickly, the creep deformation is small compared to the elastic and plastic deformation Thus, it is usually a negligible effect, and, therefore, no time-dependent fracture-mechanics parameter has been defined for such instances However, in the case of slow loading, creep deformation can dominate the elastic and plastic deformation In this instance, Ohtani et al (Ref 34) and other researchers (Ref 35, 36, and 37) have proposed a method to use for estimation of ΔJc This method functions on the assumption that creep deformation occurs under extensive creep conditions Because trapezoidal waveform loading involves both elastic and plastic deformations, the total energy output for the entire cycle should be described by the sum of the cycle-dependent and time-dependent parts (Ref 1) Therefore, the ΔJc parameter can be integrated into the total J-integral (ΔJT) defined as: ΔJT = ΔJf + ΔJc (Eq 36) where ΔJf is the cycle-dependent integral associated with time-independent plasticity (Ref 1) (Ct)avg Parameter The (Ct)avg parameter is, as the notation denotes, the average value of the Ct parameter during the hold time periods of a trapezoidal waveform (Ref 1) The parameter was first defined by Saxena as the following (Ref 38, 39, and 40): (Eq 37) The definition of the (Ct)avg parameter given in Eq 37 is applicable only for creep deformation encountered during the hold time, th In general, along with the creep deformation during this time, there is elastic deformation as a result of stress relaxation With longer hold times, the creep zone expands from small-scale to extensive creep, so eventually the elastic deformation will become insignificant As can be seen through Eq 37, as Ct approaches C*, (Ct)avg · th becomes equal to ΔJc (Ref 1) It is important to note, however, that under smallscale creep conditions, the (Ct)avg · th and ΔJc parameters will not be equal This is especially true when the values are calculated as opposed to being experimentally obtained (Ref 1) According to which method is used to estimate the deflection rate of the cracked body, there are two ways to determine the value of (Ct)avg For a CT specimen test, where the load and load-line deflection as functions of time can be determined experimentally, the value of (Ct)avg is experimentally measured However, for the case of a cracked component, where the deflection rate can only be predicted analytically, (Ct)avg is found by calculation When measured experimentally, (Ct)avg can be obtained from the following: (Eq 38) where ΔP is the applied load range and ΔVc is the load-line deflection due to creep during the hold period The value of (Ct)avg, when determined analytically, is found through the employment of equations that depend on material conditions If a material has low resistance to cyclic plasticity, where the cyclic plastic zone is larger than the creep zone during the first hold time, (Ct)avg may be determined from the following equation (Ref 39) as elastic-cyclic plastic-secondary creep conditions: (Eq 39) where ΔK is the range of the stress intensity factor, tpl is the factor added to account for retardation in the creep zone expansion rate due to cyclic plasticity, and α and β are constants In order to estimate tpl, the following may be used: (Eq 40) where m′ is the cyclic strain-hardening exponent, is the cyclic yield strength determined as the stress amplitude (Δσ/2) corresponding to a plastic strain amplitude (Δεp/2) of 0.2%, and ξ is a constant On the other hand, for materials having high resistance to cyclic deformations, where creep rates are high and the creep zone size quickly exceeds the cyclic plastic zone size, the value of (Ct)avg may be calculated from a different equation (Ref 41): (Eq 41) where N is the number of fatigue cycles For more detail concerning these last few equations, consult Ref 39 and 41 References cited in this section W Ren, “Time-Dependent Fracture Mechanics Characterization of Haynes HR160 Superalloy,” Ph.D dissertation, School of Material Science and Engineering, University of Tennessee, 1995 R.H Norris, P.S Grover, B.C Hamilton, and A Saxena, Elevated Temperature Crack Growth, Fatigue and Fracture, Vol 19, ASM Handbook, ASM International, 1996 12 A Saxena, Fracture Mechanics Approaches for Characterizing Creep-Fatigue Crack Growth, Int J JSME A, Vol 36 (No 1), 1993, p 15, 16 13 J.D Landes and J.A Begley, A Fracture Mechanics Approach to Creep Crack Growth, Mechanics of Crack Growth, STP 590, ASTM, 1976, p 128–148 14 K.M Nikbin, G.A Webster, and C.E Turner, Relevance of Nonlinear Fracture Mechanics to Creep Cracking, Cracks and Fracture, STP 601, ASTM, 1976, p 47–62 15 S Taira, R Ohtani, and T Kitamura, Application of J-integral to High-Temperature Crack Propagation, J Eng Mater Technol (Trans ASME), Vol 101, 1979, p 154 16 V Kumar, M.D German, and C.F Shih, “An Engineering Approach to Elastic-Plastic Analysis,” Technical Report EPRI NP-1931, Electric Power Research Institute, 1981 17 J Hutchinson, Singular Behavior at the End of a Tensile Crack in a Hardening Material, J Mech Phys Solids, Vol 16, 1968, p 13 18 J Rice and G.F Rosengren, Plane Strain Deformation near a Crack Tip in a Power-Law Hardening Material, J Mech Phys Solids, Vol 16, 1968, p 1–12 19 N.L Goldman and J.W Hutchinson, Fully Plastic Crack Problems: The Center-Cracked Strip Under Plane Strain, Int J Solids Struct., Vol 11, 1975, p 575–591 20 C.P Leung, D.L McDowell, and A Saxena, Consideration of Primary Creep at Stationary Crack Tips: Implications for the Ct Parameter, Int J Fract., Vol 36, 1988 21 A Saxena, Creep Crack Growth in Creep-Ductile Materials, Eng Fract Mech., Vol 40 (No ), 1991, p 721 22 P.K Liaw, A Saxena, and J Schaefer, Estimating Remaining Life of Elevated Temperature Steam Pipes, Part I: Material Properties, Eng Fract Mech., Vol 32, 1989, p 675 23 “Standard Test Method for Measurement of Creep Crack Growth Rates in Metals,” ASTM E 1457, American Society for Testing and Materials, 1998 24 H Riedel, Creep Deformation at Crack Tips in Elastic-Viscoelastic Solids, J Mech Phys Solids, Vol 29, 1981, p 35 25 K Ohji, K Ogura, and S Kubo, Stress-Strain Field and Modified J-Integral in the Vicinity of a Crack Tip Under Transient Creep Conditions, Int J JSME, Vol 790 (No 13), p 18, 1979 26 J.D Bassani and F.A McClintock, Creep Relaxation of Stress Around a Crack Tip, Int J Solids Struct., Vol 7, 1981, p 479 27 R Ehlers and H Riedel, A Finite Element Analysis of Creep Deformation in a Specimen Containing a Macroscopic Crack, Advances in Fracture Research: Proc of the Fifth Int Conf of Fracture, ICF-5 ,Vol 2, Pergamon Press, 1981, p 691–698 28 J.L Bassani, K.E Hawk, and A Saxena, Evaluation of the Ct Parameter for Characterizing Creep Crack Growth Rate in the Transient Regime, Time-Dependent Fracture, Vol 1, Nonlinear Fracture Mechanics, STP 995, ASTM, 1986, p 7–26 29 H Riedel and V Hetampel, Creep Crack Growth in Ductile, Creep Resistant Steels, Int J Fract., Vol 34, 1987, p 179 30 D.L McDowell and C.P Leung, Implication of Primary Creep and Damage for Creep Crack Extension Criteria, Structural Design for Elevated Temperature Environments—Creep, Ratchet, Fatigue and Fracture, Pressure Vessel and Piping Division, Vol 163, July 23–27 1989 (Honolulu), American Society of Mechanical Engineers 31 A Saxena, Creep Crack Growth Under Nonsteady-State Conditions, ASTM STP 905, Seventeenth ASTM National Symposium on Fracture Mechanics, American Society for Testing and Materials, 1986, p 185–201 32 B.E Jaske and J.A Begley, An Approach to Assessing Creep/Fatigue Crack Growth, Ductility and Toughness Considerations in Elevated Temperature Service, MPC-8, ASTM, 1978, p 391 33 S Taira, R Ohtani, and T Komatsu, Application of J-Integral to High Temperature Crack Propagation, Part II: Fatigue Crack Propagation, J Eng Mater Technol (Trans ASME), Vol 101, 1979, p 162 34 R Ohtani, T Kitamura, A Nitta, and K Kuwabara, High-Temperature Low Cycle Fatigue Crack Propagation and Life Laws of Smooth Specimens Derived from the Crack Propagation Laws, STP 942, H Solomon, G Halford, L Kaisand, and B Leis, Ed., ASTM, 1988, p 1163 35 K Kuwabara, A Nitta, T Kitamura, and T Ogala, Effect of Small-Scale Creep on Crack Initiation and Propagation under Cyclic Loading, STP 924, R Wei and R Gangloff, Ed., ASTM, 1988, p 41 36 R Ohtani, T Kitamura, and K Yamada, A Nonlinear Fracture Mechanics Approach to Crack Propagation in the Creep-Fatigue Interaction Range, Fracture Mechanics of Tough and Ductile Materials and Its Application to Energy Related Structures, H Liu, I Kunio, and V Weiss, Ed., Materials Nijhoff Publishers, 1981, p 263 37 K Ohji, Fracture Mechanics Approach to Creep-Fatigue Crack Growth in Role of Fracture Mechanics in Modern Technology, Fukuoka, Japan, 1986 38 K.B Yoon, A Saxena, and P.K Liaw, Int J Fract., Vol 59, 1993, p 95 39 K B Yoon, A Saxena, and D L McDowell, Influence of Crack-Tip Cyclic Plasticity on Creep-Fatigue Crack Growth, Fracture Mechanics: Twenty Second Symposium, STP 1131, ASTM, 1992, p 367 40 A Saxena and B Gieseke, Transients in Elevated Temperature Crack Growth, International Seminar on High Temperature Fracture Mechanics and Mechanics, EGF-6, Elsevier Publications, 1990, p iii–19 41 N Adefris, A Saxena, and D.L McDowell, Creep-Fatigue Crack Growth Behavior in 1Cr-1Mo-0.25V Steels I: Estimation of Crack Tip Parameters, J Fatigue Mater Struct., 1993 Creep Crack Growth Testing B.E Gore, Northwestern University, W Ren, Air Force Materials Laboratory, P.K Liaw, The University of Tennessee Creep-Fatigue Crack Growth Testing The following description of the experimental test method for creep crack growth tests using a compact specimen geometry, under cyclic or static loading, is in agreement with the ASTM E 1457 “Standard Test Method for Measurement of Creep Crack Growth Rates in Metals” (Ref 23) The aforementioned technique entails applying a constant load to a heated, precracked specimen until significant crack extension or failure occurs During the test, the crack length, load, and load-line deflections must be monitored and recorded, and upon test completion, the final crack length must be measured Analysis of the test data involves an examination of the crack growth rate with respect to time, da/dt, in terms of the magnitude of an appropriate elevated-temperature crack growth parameter (Ref 5, 23) The various crack growth parameters are presented earlier in this article Specimen Configuration and Dimensions The recommended specimen for creep crack growth testing is the CT specimen Figure illustrates the specimen geometry, including details of the design specifications Although other configurations have also been used, such as the center-cracked tensile (CCT) panel and the single-edge notch (SEN) specimen, the CT specimen is considered to be more suitable for creep and creep-fatigue crack growth testing (Ref 5) and remains most convenient In terms of suitability, the transition time for extensive creep conditions to develop is longer in CT than in CCT specimens for the same K and a/W for samples of identical width (Ref 42) Due to the extended transition time, during creep-fatigue testing, the necessary condition that tc/t1 « 1, with tc representing cyclic time, and t1 being the aforementioned transition time, is more easily met In terms of convenience, an advantage of the CT specimen is that a clip gage can be easily attached for the measurement of load-line deflection, which is one of the components required in the calculation of crack-tip parameters In addition, one of the most important advantages is that the magnitude of the applied load needed to obtain a particular value of K is significantly lower for CT than for CCT specimens Hence, machines with smaller load capacities and small fixtures can be used for testing (Ref 5) Fig Drawing of standard CT specimen Source: Ref 22 Testing Machines Three different types of machines can be used to run crack growth tests: dead-weight, servomechanical, and servohydraulic machines Regardless of the choice of machine, it is necessary to be able to maintain a constant load over an extended period of time (variations are not to exceed ±1.0% of the nominal load value at any time) Note that to fulfill this requirement, if lever-type, dead-weight creep machines are used, care must be taken to ensure that the lever arm remains in a horizontal position More detailed specifications of the testing machine may be found in ASTM E 4, “Practices for Load Verification of Testing Machines” (Ref 43) Additionally, it is recommended that precautions be taken to ensure that the load is applied as nearly axial as possible Control Parameter For those tests run under creep-fatigue conditions where a trapezoidal waveform is employed, a choice between testing conducted under a load-controlled or displacement-controlled conditions must be made Figure 4(a) shows a schematic representation of the displacement versus time and crack size versus time for a load-controlled case Displacement-controlled testing schematics of the load versus time and crack size versus time are shown in Fig 4(b) for comparison (Ref 5) Fig Schematic comparison of (a) load-controlled and (b) displacement-controlled testing under trapezoidal loading Source: Ref Due to matters of convenience, tests are most frequently conducted under load-controlled conditions However, there are a few advantages of displacement-controlled testing that should be considered For instance, due to a continuous rise in the net section stress ahead of the crack in load-controlled tests during crack growth, K continually increases as the size of the remaining ligament decreases Consequently, this means that the scale of creep in the specimen increases as the test progresses, which causes ratcheting in the specimen as the inelastic deflection accumulates with the completion of each cycle (Ref 5) Comparatively, as can be seen in Fig 4(b), the applied load decreases with crack extension in displacement-controlled tests, so ratcheting is avoided (Ref 44) Also, data can be collected for greater crack extensions in displacement-controlled tests than in loadcontrolled tests Overall, load-controlled tests are more suitable for low crack growth rates, and displacementcontrolled tests are suited for higher crack growth rates (greater than × 10-6 mm/cycle) and tests with extensive hold times (Ref 5) Grips and Fixtures For the CT specimen, a pin and clevis assembly should be used at both the top and bottom of the specimen This assembly will allow in-plane rotation as the specimen is loaded Materials for the grips and pull rods should be creep resistant and able to withstand the temperature environment to which they will be exposed during the test Examples of current elevated-temperature materials being used include AISI grade 304 and 316 stainless steels, grade A 286 steel, Inconel 718, and Inconel X750 The loading pins should be machined from temperature-resistant steels, such as A 286, and should be heat treated to ensure that they acquire a high resistance to creep deformation and rupture Heating Devices Samples are generally heated by means of either an electric resistance furnace or a laboratory convection oven Before the application of load and for the duration of the test, the difference between the temperature indicated by the device and the nominal test temperature is not to exceed ±2 °C (±3 °F) for temperatures at or below 1000 °C (1800 °F) It is to remain within ±3 °C (±5 °F) for temperatures above 1000 °C (1800 °F) In the initial heating of the specimen, it is important to avoid temperature overshoots that could potentially affect test results In order to measure the specimen temperature, a thermocouple must be attached to the specimen The thermocouple should be placed in the uncracked ligament region of the sample to mm (0.08–0.2 in.) above or below the crack plane If the width of the specimen exceeds 50 mm (2 in.), it is advisable to attach multiple thermocouples at evenly spaced intervals in the uncracked ligament region around the crack plane, as stated previously Thermocouples must be kept in intimate contact with the specimen In order to avoid short circuiting, ceramic insulators should cover the individual wires of the temperature circuit Fatigue Precracking In order to eliminate the effects of the machined notch and to provide a sharp crack tip for crack initiation, it is necessary to precrack creep and/or creep-fatigue test specimens An extensively detailed method for the process can be found in ASTM E 399, “Test Method for Plane-Strain Fracture Toughness of Metallic Materials” (Ref 45) Specimen precracking must be conducted in the same condition as it is going to be tested The temperature is to be at or above room temperature and must not exceed the designed test temperature For the process of precracking, equipment must be used that is capable of applying a symmetric load with respect to the machined notch and must be able to control the maximum stress intensity factor, Kmax, to within ±5% The fatigue load used during the process must remain below the following maximum value (Ref 23): (Eq 42) where BN is the corrected specimen thickness, W is the specimen width, a0 is the initial crack length measured from the load line, and σys is the yield strength While the fatigue precrack is in the final 0.64 mm (0.025 in.) of extension, the maximum load shall not exceed Pf or a load such that the ratio of the stress intensity factor range to Young's modulus (ΔK/E) is equal to or less than 0.0025 mm 1/2 (0.0005 in 1/2), whichever is less (Ref 23) In this manner, it is ensured that the final precrack loading will not exceed that of the initial creep or creepfatigue crack growth test The crack length for the fatigue precrack can be measured using the same methods described in the next section, “Test Procedure,” for monitoring crack length during crack growth testing Measurements of the fatigue precrack must be accurate to within 0.1 mm (0.004 in.) Measurements must be taken on both surfaces, and their values must not differ by more than 1.25 mm (0.05 in.) If surface cracks are allowed to exceed this limit, further extension will be required until the aforementioned criteria are met (Ref 5) The total initial crack length (the starter notch plus fatigue precrack) must be at least 0.45 times the width, but no longer than 0.55 times the width References cited in this section R.H Norris, P.S Grover, B.C Hamilton, and A Saxena, Elevated Temperature Crack Growth, Fatigue and Fracture, Vol 19, ASM Handbook, ASM International, 1996 22 P.K Liaw, A Saxena, and J Schaefer, Estimating Remaining Life of Elevated Temperature Steam Pipes, Part I: Material Properties, Eng Fract Mech., Vol 32, 1989, p 675 23 “Standard Test Method for Measurement of Creep Crack Growth Rates in Metals,” ASTM E 1457, American Society for Testing and Materials, 1998 42 A Saxena, Limits of Linear Elastic Fracture Mechanics in the Characterization of High-Temperature Fatigue Crack Growth, Basic Questions in Fatigue, Vol 2, STP 924, R Wei and R Gangloff, Ed., ASTM, 1989, p 27–40 43 “Practices of Load Verification of Testing Machines,” E 94, Annual Book of Standards, Vol 3.01, ASTM, 1994 44 A Saxena, R.S Williams, and T.T Shih, Fracture Mechanics—13, STP 743, ASTM, 1981, p 86 45 “Test Method for Plane-Strain Fracture Toughness of Metallic Materials,” E 399, Annual Book of ASTM Standards, Vol 3.01, ASTM, 1994, p 680–714 Creep Crack Growth Testing B.E Gore, Northwestern University, W Ren, Air Force Materials Laboratory, P.K Liaw, The University of Tennessee Test Procedure Number of Tests Data collected during creep crack growth rate testing will inherently exhibit scatter Values of da/dt at a given value of C*(t) can vary by as much as a factor of two (Ref 23, 46) This inherent scatter can be further augmented by variables, such as microstructural differences, load precision, environmental control, and data processing techniques (Ref 23) It is thus advised that replicate tests be conducted; when this is impractical, multiple specimens must be tested in order to obtain regions of overlapping da/dt versus C*(t) data Assurance of the inferences drawn from the data is augmented by increasing the number of tests conducted Test Setup Prior to testing, it is necessary to take measures to prepare for the measurements of the crack length, load-line displacement, temperature, and number of completed cycles As discussed in subsequent sections, the electric potential drop method, in which fluctuations in potential in a constructed voltage loop are monitored, is often used to calculate the crack length during testing In order to prepare for this method, the specimen must be fitted with current input and voltage leads to the current source and potentiometer, respectively The fitting can be conducted either prior to or just after specimen installation according to preference In order to avoid contact with other components in the test setup that could potentially skew results, the leads can be covered with protective ceramic insulators In order to begin installation of the specimen, both clevis pins must be inserted, after which a small load of approximately 10% of the intended test load should be applied in order to bolster the axial stability of the load train At this point, the extensometer must be placed along the load line of the specimen in order to monitor load-line displacements Care must be taken to make sure that the device is in secure contact with the knife edges Subsequently, the thermocouples must be attached to the specimen by being placed in contact with the crack plane in the uncracked ligament region Lastly, the furnace must be brought into position, and heating of the specimen should begin The initialization of the current for the electric potential system must be in concordance with the point of turning on the furnace This is because resistance heating of the specimen will occur as a result of the applied current In order to avoid overshoots in temperature exceeding the limits set forth previously, it is recommended that the heating of the specimen be slow and steady It may even be desirable to stabilize the temperature at an increment of to 30 °C (10–50 °F) below the final testing temperature and then make adjustments as necessary Once the appropriate test temperature is achieved and stabilized, it should be held for a given amount of time necessary to ensure that the temperature will be able to be maintained within the aforementioned limits This time is to be, at minimum, hour per 25 mm (1 in.) of specimen thickness After these requirements have been met, a set of measurements must be recorded while in the initial no-load state for reference It follows that the next step is the application of the load The load must be applied carefully in order that shock loads or inertial loads can be avoided, and the length of time for the application of the load should remain as short as possible The load or K-level chosen depends on the required crack growth rates during the test For effective testing, the crack growth rates must be selected to mimic those encountered during the service life of a material Without delay, upon the completion of loading the sample, another set of measurements of electric potentials and displacements must be taken to be used as the initial loading condition (time = 0) Data Acquisition during Testing The electric potential voltage, load, load-line displacement, test temperature, and number of cycles must be monitored and recorded continuously throughout the test if autographic strip chart recorders or voltmeters are used If digital data acquisition systems are employed, a full set of readings must be taken no less frequently than once every fifteen minutes The resolution of these data acquisition systems must be at least one order of magnitude better than the measuring instrument (Ref 5) Crack Length Measurement When monitoring creep crack propagation, the chosen technique should be able to resolve crack extensions of at least 0.1 mm (0.004 in.) Surface crack length measurements by optical means, such as a travelling microscope, are not considered reliable as a primary method due to the fact that crack extension across the thickness of the specimen is not always uniform However, optical observation may be used as an auxiliary measurement method For the aforementioned reason, the selected crack length measurement technique must be capable of measuring the average crack length across the specimen thickness The most commonly used method for the determination of crack length in creep-fatigue crack growth testing is the electric potential drop method This method involves applying a fixed electric current and monitoring any changes in the output voltage across the output locations Because any increase in crack length (corresponding to a decrease in the uncracked ligament) would result in an increase in the electric resistance, the final result is an increase in the output voltage (Ref 5) The electric potential drop method is considered to be the most compatible with elevated-temperature creep crack growth testing The input current and voltage lead locations for a typical CT specimen are shown in Fig The leads may be attached either by welding them to the material or by connecting them to the material with screws The choice of the method essentially depends on the material and test conditions For a soft material tested at relatively low temperatures, threaded connections are fine, but for harder materials, it is recommended that the leads be welded, especially for tests conducted at elevated temperatures (Ref 5) The leads must be long enough to allow current input devices and output voltage measuring instruments to be far enough away from the furnace so as to avoid excessive heating In addition, leads should be about the same length to minimize lead resistance, which contributes to the thermal voltage, Vth, as described below Concerning material choice for the leads, mm (0.08 in.) diameter stainless steel wires have been shown to work very well due to excellent oxidation resistance at elevated temperatures Nonetheless, any material that is resistant to oxidation and is capable of carrying a current that is stable at the test temperature should be suitable In the past, nickel and copper wires have been effectively used as a lead material for tests conducted at lower temperatures (Ref 5) Fig Input current and voltage lead locations for which Eq 43 applies Source: Ref 22 In order to calculate the crack size for the setup shown in Fig from the measured output voltage and initial voltage values, V and V0, the following closed-form equation should be used (Ref 47, 48): (Eq 43) where is the instantaneous crack length, W is the specimen width, Y0 is the half distance between the output voltage leads, V is the instantaneous output voltage, and a0 is the reference crack size with respect to the reference voltage, V0 Usually a0 is the initial crack size after precracking, and V0 is the initial voltage Often the voltages, V and V0, used for determining the crack size in the equation differ from their respective indicated readings when using a direct current technique This is due to Vth, which can be caused by many factors, including differences in the junction properties of the connectors, differences in the resistance of the output leads, varying output lead lengths, and temperature fluctuations in output leads themselves (Ref 5) Measured values of Vth should be recorded before the load application and periodically throughout testing To make these measurements, the current source must be turned off; then the output voltage should be recorded Before calculations are made, the Vth value must be subtracted from the respective V and V0 so that the actual crack extension length can be established When testing materials that have high electrical conductivity, fluctuations in Vth are often seen This type of fluctuation can be of the same magnitude as the fluctuation in voltage that accompanies crack growth and could, therefore, veil this information Because of this potential variation, it is recommended that the direct current electric potential drop method not be the only nonvisual method for crack length measurements chosen Other more sophisticated techniques, such as the reversing current potential method, are recommended for use The reversing direct current electrical potential drop (RDCEPD) method is simply a variation of the electrical potential drop method described by Johnson (Ref 47) This method is more sensitive to crack growth near the specimen surface In the RDCEPD method, a direct current is used, but the polarity is reversed at a fairly low frequency (Ref 49) This step compensates for zero drift errors Refer to Caitlin, et al (Ref 50) for a more detailed description of this crack length monitoring method It is imperative to keep in mind, while performing creep crack propagation tests, the importance of maintaining a nearly straight crack front The initial and final crack lengths must fluctuate no more than 5% across the specimen thickness Often the maintenance of a straight crack front depends on the material and the sample thickness It has been noted before that thicker specimens sometimes experience crack tunneling, or nonstraight crack extension Crack tunneling (thumbnail-shaped crack fronts) is common in specimen configurations that are not side grooved (parallel-sided) (Ref 5, 7) Side-grooving the specimens can minimize the occurrence of crack tunneling Side grooves of 20% reduction have been found to work well in several materials, although reductions of up to 25% are considered to be acceptable The included angle of the grooves is usually less than 90° with a root radius less than or equal to 0.4 ± 0.2 mm (0.016 ± 0.008 in.) It is important to perform the precracking of the specimen before the side grooving, as it is difficult to detect the precrack when located in the grooves Load-Line Displacement Measurements Load-line displacements can be described as those that occur at the loading pins due to the crack associated with the accumulation of creep strains In order to be able to ultimately determine the crack-tip parameters, it is necessary to continually record the displacement measurements These displacement measurements must be taken as close to the load line as possible The measuring device must be attached on the knife edges of a CT specimen Alternatively, for CCT specimens, the displacement should be measured on the load line at points ±35 mm (±1.40 in.) from the crack centerline (Ref 5) In order to directly measure the displacement, an elevated-temperature clip gage may be attached to the specimen (strain gages for up to approximately 150 °C, or 300 °F, or capacitance gages for higher temperatures), and then the entire assembly should be placed in the furnace Instead, if the devices mentioned previously are not available, the displacements can be transferred outside the furnace using a rod and tube assembly In this case, the transducer—a direct current displacement transducer (DCDT), linear variable displacement transducer (LVDT), or capacitance gage—is placed outside the furnace It is important that the rod and tube be made of materials that are thermally stable and be fabricated of the same material to avoid any adverse effects caused by differences in thermal expansion coefficients (Ref 23) The deflection measurement devices should have a resolution of at least 0.01 mm (0.0004 in.) (Ref 5) Post-Test Measurements When the test has been completed, whether due to specimen failure or to the acquisition of sufficient crack growth data, the load should be removed, and the furnace be turned off Once the specimen has cooled down adequately, it should be removed from the machine The initial crack length (due to precracking) and the final crack length (resulting from creep crack growth) should be measured at nine points equidistant from each other along the face of the crack The collected data can be processed using a computer program that uses either the secant method or the seven-point polynomial method to calculate the deflection rates, dV/dt, crack growth rates, da/dt, and the crack-tip parameters For a more detailed description of these methods refer to ASTM E 1457 (Ref 23) References cited in this section R.H Norris, P.S Grover, B.C Hamilton, and A Saxena, Elevated Temperature Crack Growth, Fatigue and Fracture, Vol 19, ASM Handbook, ASM International, 1996 A Saxena, “Recent Advances in Elevated Temperature Crack Growth and Models for Life Prediction,” Advances in Fracture Research: Proc Seventh Int Conf on Fracture, March 1989 (Houston, TX), K Salama, K Ravi-Chander, D.M.R Taplin, and P Rama Rao, Ed., Pergamon Press, 1989, p 1675–1688 22 P.K Liaw, A Saxena, and J Schaefer, Estimating Remaining Life of Elevated Temperature Steam Pipes, Part I: Material Properties, Eng Fract Mech., Vol 32, 1989, p 675 23 “Standard Test Method for Measurement of Creep Crack Growth Rates in Metals,” ASTM E 1457, American Society for Testing and Materials, 1998 46 A Saxena and J Han, “Evaluation of Crack Tip Parameters for Characterizing Crack Growth Behavior in Creeping Materials,” ASTM Task Group E24-04-08/E24.08.07, American Society for Testing and Materials, 1986 47 H.H Johnson, Mater Res Stand., Vol (No 9), 1965, p 442–445 48 K.H Schwalbe and D.J Hellman, Test Evaluation, Vol (No 3), 1981, p 218–221 49 P.F Browning, “Time Dependent Crack Tip Phenomena in Gas Turbine Disk Alloys,” doctoral thesis, Rensselaer Polytechnic Institute, Troy, NY, 1998 50 W.R Caitlin, D.C Lord, T.A Prater, and L.F Coffin, The Reversing D-C Electrical Potential Method, Automated Test Methods for Fracture and Fatigue Crack Growth, STP 877, W.H Cullen, R.W Landgraf, L.R Kaisand, and J.H Underwood, Ed., ASTM, 1985, p 67–85 Creep Crack Growth Testing B.E Gore, Northwestern University, W Ren, Air Force Materials Laboratory, P.K Liaw, The University of Tennessee Life-Prediction Methodology In recent years, the subject of remaining-life prediction has drawn considerable attention The interest in the issue of remaining-life prediction stems from the necessity to avoid costly forced outages, from the need to extend the component life beyond the original design life for economic reasons, and from safety considerations (Ref 7, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, and 62) A closer look at the method of predicting the life of materials can be found in Ref 61 Here, high-temperature structural components in power plants are analyzed Steam pipes, for example, are generally subject to elevated-temperature operating conditions Because of the high-temperature exposure and the simultaneous internal-pressure loading, the pipes are prone to creep damage Thus, material properties including creep data of in-service or ex-service steels are critical input parameters for accurate life assessment of steam-pipe systems Figure 1, again, shows a schematic of the general remaining-life-prediction methodology for high-temperature components (Ref 52) The life-prediction methodology can be separated into three steps In step 1, two kinds of pertinent material testing are performed (i.e., creep crack growth and creep deformation and rupture experiments) By combining the results of these two tests and tensile tests, the rates of creep crack propagation, da/dt, can be characterized by the creep crack growth rate correlating parameter (Ct) (Ref 9, 31, 51, 52, and 63) In step 2, the value of Ct for a structural component containing a defect is calculated and used to estimate the creep crack growth rate In step 3, the creep crack propagation rate equation—da/dt versus Ct—and the calculated value of Ct for the structural component are combined to develop residual life curves, such as a plot of initial crack size versus remaining life The final life of the structural component can be determined based on certain failure criteria (e.g., fracture toughness) References cited in this section A Saxena, “Recent Advances in Elevated Temperature Crack Growth and Models for Life Prediction,” Advances in Fracture Research: Proc Seventh Int Conf on Fracture, March 1989 (Houston, TX), K Salama, K Ravi-Chander, D.M.R Taplin, and P Rama Rao, Ed., Pergamon Press, 1989, p 1675–1688 P.K Liaw, A Saxena, and J Schaefer, Predicting the Life of High-Temperature Structural Components in Power Plants, JOM, Feb 1992 31 A Saxena, Creep Crack Growth Under Nonsteady-State Conditions, ASTM STP 905, Seventeenth ASTM National Symposium on Fracture Mechanics, American Society for Testing and Materials, 1986, p 185–201 50 W.R Caitlin, D.C Lord, T.A Prater, and L.F Coffin, The Reversing D-C Electrical Potential Method, Automated Test Methods for Fracture and Fatigue Crack Growth, STP 877, W.H Cullen, R.W Landgraf, L.R Kaisand, and J.H Underwood, Ed., ASTM, 1985, p 67–85 51 P.K Liaw, A Saxena, and J Schaefer, Eng Fract Mech., Vol 32, 1989, p 675, 709 52 P.K Liaw and A Saxena, “Remaining-Life Estimation of Boiler Pressure Parts—Crack Growth Studies,” Electric Power Research Institute, EPRI CS-4688, Project 2253-7, final report, July 1986 53 P.K Liaw, M.G Burke, A Saxena, and J.D Landes, Met Trans A, Vol 22, 1991, p 455 54 P.K Liaw, G.V Rao, and M.G Burke, Mater Sci Eng A, Vol 131, 1991, p 187 55 P.K Liaw, M.G Burke, A Saxena, and J.D Landes, Fracture Toughness Behavior in Ex-Service CrMo Steels, 22nd ASTM National Symposium on Fracture Mechanics, STP 1131, ASTM, 1992, p 762– 789 56 P.K Liaw and A Saxena, “Crack Propagation Behavior under Creep Conditions,” Int J Fract., Vol 54, 1992, p 329–343 57 W.A Logsdon, P.K Liaw, A Saxena, and V.E Hulina, Eng Fract Mech., Vol 25, 1986, p 259 58 A Saxena, P.K Liaw, W.A Logsdon, and V.E Hulina, Eng Fract Mech., Vol 25, 1986, p 289 59 V.P Swaminathan, N.S Cheruvu, A Saxerna, and P.K Liaw, “An Initiation and Propagation Approach for the Life Assessment of an HP-IP Rotor,” paper presented at the EPRI Conference on Life Extension and Assessment of Fossil Plants, 2–4 June 1986 (Washington, D.C.) 60 N.S Cheruvu, Met Trans A, Vol 20, 1989, p 87 61 R Viswanathan, Damage Mechanisms and Life Assessment of High-Temperature Components, ASM International, 1989 62 C.E Jaske, Chem Eng Prog., April 1987, p 37 63 P.K Liaw, A Saxena, and J Schaefer, Creep Crack Growth Behavior of Steam Pipe Steels: Effects of Inclusion Content and Primary Creep, Eng Fract Mech., Vol 57, 1997, p 105–130 Creep Crack Growth Testing B.E Gore, Northwestern University, W Ren, Air Force Materials Laboratory, P.K Liaw, The University of Tennessee Acknowledgments B.E Gore is thankful for the support of the University of Tennessee, Knoxville, especially her fellow group members, Dr Yuehui He, Bing Yang, Liang Jiang, J.T Broome, Glen Porter, and Leslie Miller P.K Liaw is grateful for the financial support provided by the National Science Foundation (DMI-9724476 and EEC9527527 with Dr D Durham and Ms M Poats as contract monitors, respectively) Creep Crack Growth Testing B.E Gore, Northwestern University, W Ren, Air Force Materials Laboratory, P.K Liaw, The University of Tennessee References W Ren, “Time-Dependent Fracture Mechanics Characterization of Haynes HR160 Superalloy,” Ph.D dissertation, School of Material Science and Engineering, University of Tennessee, 1995 H Riedel and J.R Rice, Tensile Cracks in Creep Solids, Fracture Mechanics: Twelfth Conf., STP 700, ASTM, 1980, p 112–130 M Okazaki, I Hattori, F Shiraiwa, and T Koizumi, Effect of Strain Wave Shape on Low-Cycle Fatigue Crack Propagation of SUS 304 Stainless Steel at Elevated Temperatures, Metal Trans A, Vol 14, 1983, p 1649–1659 A Saxena and P.K Liaw, “Remaining Life Estimations of Boiler Pressure Parts—Crack Growth Studies,” Final Report CS 4688 per EPRI Contract RP 2253-7, Electric Power Research Institute, 1986 R.H Norris, P.S Grover, B.C Hamilton, and A Saxena, Elevated Temperature Crack Growth, Fatigue and Fracture, Vol 19, ASM Handbook, ASM International, 1996 A Saxena, “Life Assessment Methods and Codes,” EPRI TR-103592, Electric Power Research Institute, 1996 A Saxena, “Recent Advances in Elevated Temperature Crack Growth and Models for Life Prediction,” Advances in Fracture Research: Proc Seventh Int Conf on Fracture, March 1989 (Houston, TX), K Salama, K Ravi-Chander, D.M.R Taplin, and P Rama Rao, Ed., Pergamon Press, 1989, p 1675–1688 W.A Logsdon, P.K Liaw, A Saxena, and V.E Hulina, Residual Life Prediction and Retirement for Cause Criteria for Ships Service Turbine Generator (SSTG) Upper Casings, Part I: Mechanical Fracture Mechanics Material Properties Development, Eng Fract Mech., Vol 25, 1986, p 259–288 P.K Liaw, A Saxena, and J Schaefer, Predicting the Life of High-Temperature Structural Components in Power Plants, JOM, Feb 1992 10 J.T Staley, Jr., “Mechanisms of Creep Crack Growth in a Cu-1 wt % Sb Alloy,” MS thesis, Georgia Institute of Technology, 1988 11 J.L Bassani and V Vitek, Proc Ninth National Congress of Applied Mechanics—Symposium on NonLinear Fracture Mechanics, L.B Freund and C.F Shih, Ed., American Society of Mechanical Engineers, 1982, p 127–133 12 A Saxena, Fracture Mechanics Approaches for Characterizing Creep-Fatigue Crack Growth, Int J JSME A, Vol 36 (No 1), 1993, p 15, 16 13 J.D Landes and J.A Begley, A Fracture Mechanics Approach to Creep Crack Growth, Mechanics of Crack Growth, STP 590, ASTM, 1976, p 128–148 14 K.M Nikbin, G.A Webster, and C.E Turner, Relevance of Nonlinear Fracture Mechanics to Creep Cracking, Cracks and Fracture, STP 601, ASTM, 1976, p 47–62 15 S Taira, R Ohtani, and T Kitamura, Application of J-integral to High-Temperature Crack Propagation, J Eng Mater Technol (Trans ASME), Vol 101, 1979, p 154 16 V Kumar, M.D German, and C.F Shih, “An Engineering Approach to Elastic-Plastic Analysis,” Technical Report EPRI NP-1931, Electric Power Research Institute, 1981 17 J Hutchinson, Singular Behavior at the End of a Tensile Crack in a Hardening Material, J Mech Phys Solids, Vol 16, 1968, p 13 18 J Rice and G.F Rosengren, Plane Strain Deformation near a Crack Tip in a Power-Law Hardening Material, J Mech Phys Solids, Vol 16, 1968, p 1–12 19 N.L Goldman and J.W Hutchinson, Fully Plastic Crack Problems: The Center-Cracked Strip Under Plane Strain, Int J Solids Struct., Vol 11, 1975, p 575–591 20 C.P Leung, D.L McDowell, and A Saxena, Consideration of Primary Creep at Stationary Crack Tips: Implications for the Ct Parameter, Int J Fract., Vol 36, 1988 21 A Saxena, Creep Crack Growth in Creep-Ductile Materials, Eng Fract Mech., Vol 40 (No ), 1991, p 721 22 P.K Liaw, A Saxena, and J Schaefer, Estimating Remaining Life of Elevated Temperature Steam Pipes, Part I: Material Properties, Eng Fract Mech., Vol 32, 1989, p 675 23 “Standard Test Method for Measurement of Creep Crack Growth Rates in Metals,” ASTM E 1457, American Society for Testing and Materials, 1998 24 H Riedel, Creep Deformation at Crack Tips in Elastic-Viscoelastic Solids, J Mech Phys Solids, Vol 29, 1981, p 35 25 K Ohji, K Ogura, and S Kubo, Stress-Strain Field and Modified J-Integral in the Vicinity of a Crack Tip Under Transient Creep Conditions, Int J JSME, Vol 790 (No 13), p 18, 1979 26 J.D Bassani and F.A McClintock, Creep Relaxation of Stress Around a Crack Tip, Int J Solids Struct., Vol 7, 1981, p 479 27 R Ehlers and H Riedel, A Finite Element Analysis of Creep Deformation in a Specimen Containing a Macroscopic Crack, Advances in Fracture Research: Proc of the Fifth Int 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Short No Preheat Strain rate, temperature s-1 × 105 °C °F T9 8-0 92 4 22 72 1.47 T9 8-1 210 298 568 1.61 T9 9- 0 602 315 599 2.27 T9 9- 1 008 513 95 5 3.26 (a) Reported in the literature Transient Hugoniot... Society, 199 0, p 3 89? ?? 392 37 S.-N Chang, D.-T Chung, Y.F Li, and S Nemat-Nasser, Target Configurations for Plate-Impact Recovery Experiments, J Appl Mech., Vol 92 -APM-18, 199 2, p 1–7 38 P Kumar and. .. thickness mm in T9 8-0 92 4 3.60 0.142 T9 8-1 210 3.51 0.138 T9 9- 0 602 3.32 0.131 T9 9- 1 008 3.61 0.142 Source: Ref 44, 84 Shot No Target thickness mm in 7.6 0.30 7. 79 0.307 6. 69 0.263 6. 795 0.268 Impact