H.D. Espinosa and S. Nemat-Nasser, "Low-Velocity Impact Testing,"

Low-Velocity Impact TestingHoracio Dante Espinosa, Northwestern UniversitySia Nemat-Nasser, University of California, San Diego

IMPACT TESTS are used to study dynamicdeformation and failure modes of materials.Low-velocity impact techniques can be classi-fied as plate-on-plate, rod-on-plate, plate-on-rod, or rod-on-rod experiments. Two types ofplate-on-plate impact tests have been devel-oped: wave propagation experiments andthin-layer high-strain-rate experiments. Theplate-on-plate experiments are further classi-fied as nonrecovery or recovery experiments.The focus of this article is on plate-on-plate ex-perimental techniques. At the end of this arti-cle, rod-on-plate and plate-on-rod experimentsare briefly examined.

Observation of plane waves in materials pro-vides a powerful method for understanding andquantifying their dynamic response (Ref 1–9)and failure modes (Ref 10–29). Plate impactexperiments are used to generate such planewaves (Ref 30–32). These experiments providecontrolled extreme stress-state loading condi-tions, involving one-dimensional stress-pulsepropagation. The recovery configurations inplate-on-plate impact experiments are per-formed with the objective of examining themicrostructural changes in the specimen after itis subjected to loading under a uniaxial straincondition. The experiments are designed toachieve a controlled plane-wave loading of thespecimens. In practice, this is limited by the fi-nite size of the plates employed, which gener-ate radial release waves. This has the potentialfor significant contribution to the damage pro-cesses by introducing causes other than the uni-axial straining of the material. Hence, this as-pect of the plate impact experiment has been asubject of considerable research in the past (Ref11, 13, 33–39).

The plate impact experiments are performedin two main modes: normal impact and pres-sure-shear, or oblique, impact. Both modeshave been specialized to several new configura-tions to achieve different aspects of controlover the imposed loading. In these experiments,the time histories of the stress waves are re-corded and used to infer the response of thespecimen with the goal of constitutive model-ing. To enable the formulation of correct con-stitutive behavior for the considered material,knowledge of the micromechanisms of defor-

mation that occur during the passage of thestress waves is necessary. Such knowledge isalso necessary for damage-evolution studies.Hence, it is important that the specimen is re-covered after it is subjected to a well-character-ized loading pulse so that it can be analyzed forany changes in its microstructure. This isachieved in the normal plate impact mode byusing an impedance-matched momentum trapbehind the specimen (Ref 1, 7, 11). Ideally, themomentum-trap plate captures the momentumof the loading pulse and flies away, leaving thespecimen at rest.

Initially, the recovery technique was devel-oped for the normal plate experiments (Ref 1,38, 39), and it has been implemented in thepressure-shear mode to study shear stress-sen-sitive, high-rate deformation mechanisms. Thedifficulty in conducting pressure-shear recov-ery experiments stems from the fact that boththe shear and longitudinal momenta must betrapped and that there is a large difference inthe longitudinal and shear wave velocities forany given material. To overcome this problem,one idea that had been proposed was to use acomposite flyer made of two plates of the samematerial that are separated by a thin layer of alow shear resistance film, such as a lubricant(Ref 40, 41). This design would enable theshear pulse to be unloaded at the interface,while the pressure pulse would be transmittedto the next plate. The pressure pulse would re-turn to the specimen momentum-trap interfaceas an unloading wave after the unloading of theshear wave has taken place. The thickness ofthe momentum-trap plate is chosen such thatthe normal unloading wave from its rear sur-face arrives at this interface much later, andhence, the momentum trap would separate justas in the normal recovery experiment, but aftertrapping both the shear and normal momenta.

The plate impact experiments can be per-formed at different temperatures by providingtemperature-control facilities in the test cham-ber. This may consist of a high-frequency (0.5MHz) induction heating system, for high-tem-perature tests, or a cooling ring with liquid ni-trogen circulating through an inner channel, forlow-temperature experiments (Ref 42–44).

Confined and unconfined rod experimentshave been performed (Ref 45, 46) with the aimof extending the uniaxial strain deformationstates imposed in the plate impact experiments.The bar impact and pressure-shear experimentsprovide a measurement of yield stress at rates of103 to 105/s−1. They also allow the experimen-tal verification and validation of constitutivemodels and numerical solution schemes undertwo-dimensional states of deformation. In-ma-terial stress measurements, with embeddedmanganin gages, are used to obtain axial andlateral stress histories. Stress decay, pulse dura-tion, release structure, and wave dispersion arewell defined in these plate and rod experiments.

Plate Impact Facility

Gas Gun. The low-velocity impact experi-ments are generally performed in single-stagegas guns that are capable of firing projectiles ofcomplex shapes as well as various materialsand weights at limited velocities. Plate impactexperiments discussed in this section were car-ried out on single-stage light-gas guns capableof projectile velocities from a few tens of me-ters per second to 1200 m/s (3940 ft/s).

A light gas gun facility generally has four in-terconnected parts: a pressure chamber or breech,a gun barrel, a target chamber, and a catchertank (Fig. 1). Different types of breeches havebeen used. The most common is a wraparoundbreech, which employs no moving parts underpressure except the projectile itself as a fast-opening valve. The projectile back piston, whichcloses the breech, is designed to withstand thegas pressure. The breech holds gas at pressuresbetween 1.4 and 20.7 MPa (200 and 3000 psi)to accelerate the projectile through the gun bar-rel and into the target chamber. The gun barreldiameter and length may be different, depend-ing on the design. Examples include:

• 76.2 mm (3 in.) diameter and 6.09 m (20 ft)long gun with velocities in the range of 50 to1000 m/s (165 to 3280 ft/s)

• 60 mm (2.4 in.) diameter and 1.2 m (3.9 ft)long gun with moderate velocities up to 200m/s (660 ft/s)

• 56 mm (2.2 in.) diameter and 10 m (33 ft)long high-velocity gun with velocities up to1200 m/s (3940 ft/s)

• 152 mm (6 in.) diameter and 5 m (16.4 ft)long gun with moderate velocities up to 400m/s (1300 ft/s)

• 25 mm (1 in.) diameter and 5 m (16.4 ft) longgun with velocities up to 1200 m/s (3940 fts/s)

The inner surface of the barrel is honed to an al-most mirror polish to reduce friction. To pre-vent projectile rotation, either a keyway is ma-chined along the barrel, or the barrel is lightlybroached. The target chamber is equipped witha special mounting system to hold the target as-sembly at normal or oblique angles. This sys-tem may allow remote rotation of the target, inany direction, to preserve the alignment upontarget heating/cooling or simply prior to firing.The chamber and gun barrel are evacuated us-ing a vacuum pump to a pressure of approxi-mately 50 mtorr. Among other things, this pre-vents the formation of an air cushion betweenthe target and flyer at impact. To avoidoverpressure in the target chamber, after gasexpansion, an exhaust system to ambient airmay have to be implemented if the volume ofthe target chamber and the catcher tank is notadequate. The target and specimen leave thevacuum chamber through a rear port. A catchertank filled with cotton rugs is used to decelerateand recover the projectile and target.

Projectile. The projectile used for these ex-periments consists of a fiberglass tube, usuallyabout 25 cm (10 in.) in length, with an alumi-num back piston on the rear end and a polyvi-nyl chloride (PVC) holder on the front. Theflyer plate or rod is glued to the PVC holder,which has a machined cavity. The fiberglasstube is centerless ground so that it slidessmoothly in the gun barrel. A set of two holesin the fiberglass tube ensures that the pressure

inside the projectile remains essentially thesame as that on the outside. This prevents un-wanted deformation of the projectile when thesystem is under vacuum. The aluminum backpiston is screwed or glued to the fiberglass tubefor high and low velocities, respectively. Itholds a sealing set of two O-rings to withholdthe breech pressure. A plastic key fitting thebarrel keyway is placed in a slot machined onthe wall of the fiberglass tube. The PVC holdercarries the flyer backed by foam material toachieve wave release. All the pieces are gluedtogether with five min epoxy.

Velocity Measurements. The velocity ofthe projectile just prior to impact is measuredby means of a method that is similar to the onedescribed in Ref 47. Ten pins of constantanwire, less than 0.1 mm (0.004 in.) in diameter,are positioned in pairs at the exit of the gun bar-rel. The pins are connected to an electronic boxin which output, recorded in an oscilloscope,consists of steps every time a pair of pins closesthe circuit. The PVC holder is coated with a sil-ver paint to achieve conductivity between pins.The distance between the positive pins is mea-sured with a traveling microscope with a reso-lution of 1 µm or better. When this distance isdivided by the time between steps, as recordedin the oscilloscope, an average velocity is ob-tained. The accuracy of the system is betterthan 1%.

The motion of the target or anvil velocity ismeasured by interferometric techniques (Ref48–51). In the case of low-velocity experi-ments, the variable sensitivity displacement in-terferometer (VSDI) is employed (Ref 52). Al-ternatively, for high- and low-temperatureplanar impact tests, an air-delay-leg normal ve-locity interferometer for any reflecting surface(ADL-VISAR) is used. In both cases, dispos-able mirrors are positioned at a certain distancefrom the rear surface of the specimen to allow

illumination and interrogation of the targetback surface. A side window on the targetchamber provides access to the laser beam ofthe interferometer. Two digital oscilloscopesrecord the interferometer traces and veloc-ity/tilt signals. Maximum sample rate, up to 4million samples per second, 1 GHz bandwidthand 8 MB of memory may be used. The oscillo-scopes are employed at full bandwidth and witha sample rate of 1 million samples per secondor higher.

Tilt Measurement. The tilt during impact ismeasured by means of four contact pins placedon the surface of the target (Ref 1). When thetarget or the anvil plate can be drilled, fourself-insulated metallic pins lapped flush withthe front surface of the target/anvil plate are po-sitioned in the periphery. When these pins aregrounded by the flyer, a staircase signal is re-corded on the oscilloscope at a ratio of 1 to 2 to4 to 8. The tilt can be estimated by fitting aplane through the tilt pins by a least-squareanalysis. When the previous technique cannotbe used, a special shape-conductive coating canbe applied, using a mask, to the target impactsurface and the same principle applied (Ref 7,11). In some cases, such as in high-temperaturetesting, neither of the previous approaches isfeasible, and tilt cannot be measured withoutmajor modifications.

High-and Low-Temperature Facilities. Ahigh-temperature facility consists of an induc-tion heating system and a heat exchanger forcooling the device and the coil around the spec-imen. A schematic of the high-temperature tar-get assembly is shown in Fig. 2. This type ofsystem is capable of delivering 25 kW of con-stant power at high frequency (0.5 MHz). Tem-peratures up to 1200 °C (2200 °F) in metallicand ceramic materials have been achieved incalibration tests. A photograph of the targetchamber and high-temperature setup is shownin Fig. 3. The temperature is externally moni-tored by a K-type thermocouple glued close tothe back face of the sample. An electronic con-trol is employed to regulate the temperature.The system adjusts the heating ramp to mini-mize thermal shock and deformation in thespecimen.

The induction copper coil is mounted in thementioned target holder and connected to theheating system by means of a specially de-signed feedthrough. The coil is made from cop-per tubing. The copper section conducts thehigh-frequency electrical energy, whereas theinner core carries refrigeration water. The in-tense electromagnetic field inside the coil in-duces parasite currents in the magnetic target.A graphite susceptor holder is employed to po-sition the target and heat nonconductive materi-als. Ceramic foam is placed between the sam-ple and the copper coil to confine heat to thesample. A copper tube is connected to a waterline to keep its temperature low and shield elec-tromagnetic radiation. This shield is attached tothe alignment rings, which support the wholetarget assembly.

540 / High Strain Rate Testing

Fig. 1 Gas gun facility for low-velocity impact testing

For low-temperature testing, a cooling ringwith liquid nitrogen circulating through an in-ner channel is used to reduce the temperature ofthe samples down to –150 °C (−238 °F). Thering consists of two pieces of aluminum ma-chined to fit together with special seals for lowtemperature to make the holder leak proof. Ap-propriated stainless steel hoses are used todrive liquid nitrogen from an external reservoirtank. The sample is kept in place inside thecooling ring by means of a disposable alumi-num ring and polymethyl methacrylate(PMMA) pins. The liquid nitrogen is providedby a 175 kPa (25 psi) external tank. Once theheat exchange has taken place, the nitrogen ingaseous state is bled from the vacuum chamber.The temperature is monitored by means of atype J thermocouple glued to the rear surface ofthe specimen (Ref 27).

SpecimenPreparation and Alignment

To generate plane waves at impact and uponreflection off interfaces, the faces of the flyerand specimen plates must be flat. The flyer

plate and specimen are lapped flat (using, e.g.,15 µm alumina abrasive first, and then 6 µm di-amond abrasive). The accepted flatness of thesesurfaces is around 1.5 to 2 wavelengths ofgreen light (λ = 550 nm). This is measured bycounting the number of interference fringes(Newton’s rings) formed between the polishedsurface and an optical flat. The procedure iscontinued until only two fringes are visibleover the whole surface. The rear surface of thetarget plate is polished using 1 µm and 1

4 µmdiamond abrasive to obtain a reflective surfacefor interferometric purposes. For a pres-sure-shear recovery experiment, the surfacescorresponding to the solid or liquid lubricantinterface are highly polished. All other surfacesare roughened by lapping with 15 µm diamondpaste. This is to ensure sufficient surfaceroughness to transfer the shear loading by dryfriction. The specimen is cleaned ultrasonicallyin ethyl alcohol. The polished surface is wipedclean with acetone and ethyl alcohol, in that or-der, and stored. The final surface is oftenscanned using a profilometer.

When certain materials are tested at high tem-peratures, oxide thin films may form, which canreduce reflectivity significantly. For instance,Ti-6Al-4V surfaces oxidize very fast. Thin lay-

ers of oxide form at temperatures between 315and 650 °C (600 and 1200 °F). The film isbarely perceptive, but with increasing tempera-ture and time, it becomes thicker and darker,acquiring a straw-yellow color at about 370 °C(700 °F) and dark blue at 480 °C (900 °F).Temperatures high enough to produce oxida-tion may be reached even under a vacuum ofless than 50 mtorr. This oxide layer reduces thereflectivity of the titanium surface, making itdifficult to obtain a good interferometric signal.To overcome this difficulty in Ti-6Al-4V, a plat-inum coating (0.1 µm thick) has been applied tothe back surface of the specimen. A pre-etchingof the surface guarantees a good adhesion of thecoating. Platinum is stable at high temperature;however, due to mismatch in coefficients ofthermal expansion, debonding may occur if thesurface temperature of the specimen is in-creased too fast. Therefore, the induction heat-ing power must be controlled at all times with afeedback loop and coating materials selected tomatch the target thermal properties.

The plate dimensions are selected such that atthe center of the specimen, a unidimensionalstrain state is kept for a few microseconds be-fore release waves from the periphery arrive tothe observation point(s). These dimensions are

Low-Velocity Impact Testing / 541

Ceramic plateFlexiblelead

Coil(in/out)

Coil

B

A

Water tubingfor shield

Ceramic pi

Refractory material

B

Shield andtubing water

Ring#

A

½ in. copper plate16

½ in. watertubing for shield

8


8


8


8

Copper shield

Section A-A

Slot forceramic pins

Fig. 2 Target assembly for high-temperature, low-velocity impact tests. Dimensions in inches. Source: Ref 44

a function of the type of experiment and config-uration and are therefore discussed separately.

The plates are optically aligned at room tem-perature using the technique described in Ref 1.For this technique, the projectile is advanced toa position near the target, and a specially coatedprecision prism is placed between the two sur-faces to be impacted. An autocollimator is usedto first align the prism to the flyer and then thespecimen to the prism. In this way, the surfacesof the flyer and the specimen are aligned withan accuracy of 0.02 milliradians. After align-ment, the projectile is pulled back to the otherend of the launch tube. To preserve targetalignment, especially in the case of high- andlow-temperature experiments, the position of acollimated laser beam, reflected from the rearsurface of the target plate, is monitored on astationary screen roughly 12 m (40 ft) away. Atarget plate tilt of 1 milliradian results in abeam translation of 1.2 cm (0.47 in.) on thisscreen. This remote beam system allows moni-toring of the tilt along the vacuum process andduring the heating or cooling of the sample. Re-mote mechanical controls attached to the targetholder screws are employed to drive the targetback to its original position, thereby ensuringthat the target and the flyer plates maintaintheir original room-temperature alignment. Thequality of the interferometric signals is usuallyan indication of the parallelism at impact.

Surface VelocityMeasurements with LaserInterferometric Techniques

Barker and Hollenbach (Ref 48) developed anormal velocity interferometer (NVI), wherenormally reflected laser light from a targetplate was collected and split into two separatebeams, which are subsequently interfered aftertraveling through different path lengths. Thesensitivity of the interferometer is a function ofthe delay time between the interfering beams.The resulting fringe signal is related directly tochanges in the normal particle velocity. Barkerand Hollenbach (Ref 49) then introduced a sig-nificantly improved NVI system termed a ve-locity interferometer for any reflecting surface(VISAR), developed based on the wide-angleMichelson interferometer (WAM) concept, re-sulting in an interferometer capable of velocitymeasurements from either a spectrally or dif-fusely reflecting specimen surface. Another im-provement incorporated into the VISAR wasthe simultaneous monitoring of two fringe sig-nals 90° out of phase. In most VISAR systems,three signals are recorded—the two quadratureoptical signals obtained from horizontally andvertically polarized components of light thatdiffer in phase because of the retardation plateand the intensity-monitoring signal used in datareduction. However, higher signal-to-noise ra-tios can be obtained by subtracting the twos-polarized beams and the two p-polarized

beams, both pairs 180° out of phase (Ref 53).This feature, known as push-pull, significantlyreduces the noise introduced by incoherentlight entering the interferometer.

Another laser interferometer to emerge in the1970s was the laser Doppler velocimeter(LDV) developed by Sullivan and Ezekiel (Ref54). The LDV can be used to monitor in-planemotion but does not lend itself to the simulta-neous monitoring of normal motion. The needto measure both normal and in-plane displace-ments prompted the development of the trans-verse displacement interferometer (TDI) byKim et al. (Ref 50). The TDI takes advantage ofdiffracted laser beams generated by a gratingdeposited or etched onto the specimen rear sur-face. In this technique, the 0th order reflectedbeam is used to monitor longitudinal motion ina conventional way, for example, by means ofan NVI or normal displacement interferometer(NDI), while any pair of nth order symmetri-cally diffracted beams is interfered to obtain adirect measure of the transverse particle dis-placement history. The sensitivity of the TDI isgiven by 1

2 σ n (mm/fringe) where σ is the grat-ing frequency and n represents the order of theinterfering diffracted beams.

Chhabildas et al. (Ref 55) presented an alter-native interferometric technique particularlysuited for monitoring in-plane particle veloci-ties in shock wave experiments. The techniqueemploys two VISARs that monitor specific dif-fracted laser beams from a target surface.

Both techniques, the two-VISAR and theNDI-TDI, have advantages and disadvantages.The combined NDI-TDI system has a muchbetter resolution at low velocities but requiresthe deposition of grids on the free surface of thetarget plate. On the other hand, the two-VISAR

technique provides velocity profiles directlywithout the need to differentiate displacementprofiles. Although the two-VISAR technique issimpler to use when optical window plates areneeded, it was shown that a combinedNVI-TDI with window interferometer is feasi-ble (Ref 56).

The relatively small range of velocities thatcan be measured by the NDI motivated the de-velopment of the NVI. The sensitivity of theNDI is given by λ/2 (mm/fringe) where λ rep-resents the laser light wavelength. The extremesensitivity of this interferometer severely limitsits application in wave propagation experi-ments due to the inordinately high signal fre-quencies that may be generated. An NVI or aVISAR, on the other hand, has a variable sensi-tivity given by λ /[2τ + (1 + δ)](mm/µs/fringe),where τ represents a time delay between the in-terfering light beams introduced by an air-delayleg or etalon in the interferometer. The factor (1+ δ) is a correction term to account for the re-fractive index of the etalon. An appealing fea-ture of this interferometer is that the fringe re-cord is a direct measure of particle velocity,thereby alleviating the need for differentiationof the reduced signal. Moreover, signal fre-quencies generated by an NVI are proportionalto particle acceleration and are, therefore,lower than equivalent signal frequencies gener-ated by an NDI. However, during an initial timeperiod τ, an NVI is functioning as an NDI sincethe delayed light arriving at the detectorfrom the delay leg or etalon is reflected from astationary target (Ref 57). Ironically, it is theinterpretation of the NVI in the interval whereit operates as an NDI that limits the usefulnessof the NVI in the low-velocity range (0.1–0.25mm/µs). In this velocity range, values of τ in the


Fig. 3 Gas gun vacuum chamber with high-temperature setup. Source: Ref 44

neighborhood of 5 ns or more are required toobtain records with at least three or fourfringes. This in turn leads to a greater aver-aging of the velocity measurements. Further-more, elastic precursors causing velocity jumpsof more than 0.1 mm/µs in a time less than τcannot be detected because the early time NDIsignal frequency may exceed the frequency re-sponse of the light-detection system. This fea-ture is described as lost fringes in Ref 58.

Clearly, the NDI and VISAR principles de-scribed here indicate that there is a velocityrange between 0.1 and 0.25 mm/µs over whichparticle velocities may not be measured withthe desired accuracy. Barker and Hollenbach(Ref 49) investigated the accuracy of theVISAR experimentally. They found that mea-surements with 2% accuracy could be obtainedwhen a delay time of approximately 1 ns corre-sponding to a velocity per fringe constant equalto 0.2 mm/µs is used. Certainly, velocities be-low 0.2 mm/µs can be measured, but the uncer-tainty of the measurement increases becauseonly a fraction of a fringe is recorded. In thiscase, signals in quadrature have to be recordedimmediately before the experiment and assumethe amplitude remains the same during the ex-periment (Ref 59). It should be pointed out thatthe VISAR data reduction is very sensitive tothe position and shape of the Lissajous (Ref59). Despite these minor subtleties, the VISARis currently the more versatile and easy-to-set-up interferometer. Many laboratories aroundthe world have adopted the VISAR as a routinetool for particle velocity measurement in nor-mal impact experiments. Typically, delay timesbetween 1 and 1.5 ns are employed. In thisworking range, the VISAR possesses a veryhigh accuracy and sensitivity.

A common feature of all interferometers dis-cussed in this section is that successful signalacquisition requires good fringe contrast duringthe time of the experiment. Contrast lossesarise from two main causes, interferometer im-perfections and target motion (displacementand tilt). These losses can be, in general, timevarying. For instance, a beam splitter that doesnot split light equally will produce a constantloss of contrast, while unevenly curved sur-faces will produce a variable contrast change asa function of the light path in the interferome-ter. Target rotations that change the light pathcan be very detrimental to most interferome-ters. In this respect, interferometers that usescatter light from the target and fiber optics totransfer the laser light will minimize the loss infringe contrast because the light path in the in-terferometer is fixed. Furthermore, even targetrotations of a few milliradians will not result insignal loss in such systems. By contrast, stan-dard interferometer setups, without fiber optics,require tilts smaller than 1 milliradian to avoida change in the light path that can offset thebeam from the optical components of the inter-ferometer. This feature is particularly relevantin two- and three-dimensional wave propaga-tion problems (e.g., penetration experiments, inwhich significant surface rotations are expected

at diagnostic points). In the early 1990s, Barkerdeveloped a VISAR with these features (Ref58). In 1998, the same company introduced amultipoint fiber optics VISAR to the market.

Espinosa et al. (Ref 52) introduced a variablesensitivity displacement interferometer (VSDI)to provide an alternative to the NDI, as well asto VISAR interferometers as applied to plateimpact experiments, particularly when normaland in-plane velocity measurements need to berecorded simultaneously in the range of 50 to250 m/s (165 to 820 ft/s). The sensitivity of suchan interferometer is variable, and thus, it canoperate over a wide range of particle velocitieswithout exceeding the frequency response of thelight-detection system. The VSDI interferome-ter is discussed in more detail subsequently.

Variable Sensitivity Displacement Inter-ferometer (VSDI) Theory. To examine the re-sults of this method, consider the effect of in-terfering a normally reflected beam with abeam diffracted at an angle θ with respect tothe specimen normal as shown in Fig. 4. Thenormally reflected beam is split at beam splitterBS1. Each half of the normal beam is thenmade to interfere with one of the diffractedbeams via beam splitters BS2 and BS3. The re-sulting signals generated by each interferingbeam pair are monitored by photodetectors.The combined field for either pair of interferingplane waves leads to a classical interference ex-pression, from which the following result is de-duced (Ref 52).

For purely normal motion (desensitized nor-mal displacement interferometer, DNDI):

normal displacement

fringe=

−=

− −

λθ

λ

λσ1 1 1 2cos ( )n

where σ = 1/d represents the frequency of a dif-fraction grating with pitch d. The fringe con-stant varies from infinity at θ = 0° to λ(mm/fringe) at θ = 90°. Therefore, a VSDI isobtained that is particularly well suited for nor-mal plate impact experiments with particle ve-locities in excess of 100 m/s (330 ft/s). Clearly,the selection of the appropriate angle θ shouldbe based on deductive knowledge of the fre-quency range that will be spanned.

For purely in-plane motion (desensitizedtransverse displacement interferometer, DTDI):

transverse displacement

fringe= =λ

θ σsin

1

n

The DTDI sensitivity ranges from a completeloss of sensitivity at θ = 0° to a theoretical sen-sitivity limit of λ (mm/fringe) at θ = 90°. Theinterferometer is “desensitized” in the sensethat, for the same diffraction orders, it exhibitsone-half the sensitivity of the transverse dis-placement interferometer (TDI) (Ref 50).

For combined normal and in-plane motions(VSDI system):

This last sensitivity is the same as the one ex-hibited by the TDI (Ref 50). It should also benoted that the normal displacement sensitivityis twice the sensitivity obtained by a singleVSDI system in the case of pure normal motionprincipally because the signal obtained by theaddition of two VSDI systems exhibits a dou-ble recording of the normal displacement.

Plate ImpactSoft-Recovery Experiments

Normal and pressure-shear plate impactsoft-recovery experiments (Ref 16–18) offer at-tractive possibilities for identifying the princi-pal mechanisms of inelasticity under dynamictension and compression, with and without anaccompanying shearing. The samples are re-covered, allowing their study by means of mi-croscopic characterization. This feature, to-gether with the real-time stress histories, maybe used to assess the validity of constitutivemodels (Ref 8, 14, 20–22, 29, 60). This kind ofexperiment on brittle materials provides infor-mation on the onset of elastic precursor decay,spall strength, and material softening due tomicrocracking.

A plate impact experiment involves the im-pact of a moving flat plate, called a flyer, withanother stationary plate, called the target,which may be the specimen. In the normal plateimpact experiment, the specimen is subjectedto a compression pulse, and the material at thecenter of the specimen is under a strictly uniax-ial strain condition. In the pressure-shear exper-iment, the specimen undergoes a combinedcompression and shearing. Thus, the materialundergoes a transverse shearing while it is in acompressed condition. The wave propagation isone dimensional, since both the pressure andshear pulses travel along the same axis.

The recovery configuration in the normal im-pact mode employs a backing plate for the tar-get to capture the longitudinal momentum. Inthe pressure-shear recovery mode (Ref 16–19,52) two flyer plates that are separated by a thinlubricant layer (which is a thin film of minimalshearing resistance and very high bulk modu-lus) are used along with the backing plate tocapture the longitudinal and shear momenta. Aliquid lubricant was used by Machcha andNemat-Nasser (Ref 16), while a solid lubricant(photoresist AZ 1350J-from Hoechst Celanese)was used by Espinosa and coworkers (Ref 17–19,52). In practice, the amount of the trapped shearmomentum depends on the shear properties ofthe lubricant thin film. All plates have to bereasonably impedance matched to obtain goodresults. Good discussions of the requirementsfor normal recovery can be found in Ref 7, 11,and 38. Figure 5 shows the configuration ofthe plates and the time-distance, t-X, diagramfor the normal impact recovery experiment(Ref 1, 7, 11). Figures 6 and 7 show the exper-imental layouts and t-X diagrams for thehigh-strain-rate (Ref 17–19) and wave propaga-


normal displacement

fringe

transverse displ

=−

λθ2 1( cos )

acement

fringe= λ

θ2 sin

tion (Ref 16, 18, 19) pressure-shear recoveryexperiments, respectively.

To reduce the boundary release wave effects,guard rings and confining fixtures have beenused around the circumference of the sample(Ref 33, 36, 37). This requires close tolerances

in machining, making the specimen preparationand assembly difficult. A better approach wasproposed by Kumar and Clifton (Ref 38), whomade use of a star geometry for the flyer to re-direct the release waves and decrease theirdamaging effect at the center. This approach

was implemented in experimental studies by anumber of researchers (Ref 11, 13, 14, 35, 37,61, 62). Three-dimensional simulations on dif-ferent configurations have also been con-ducted by many authors (Ref 13, 36, 63, 64)for the normal impact configuration, leading to


M0

Beamexpander

Argon ion laser

Photodetector 1

( VSDI system)Θ+

Photodetector 2M4 BS3

M2

b′− d′−

e′–

d eM3

BS2Photodetector 3

( VSDI system)Θ–

M1

c′M5

cBS1

b

aVacuum chamber Focusing lens (F)

LeCroy

Target

Projectileand flyerBreech

High-pressuregas tank

Vacuum pump

Velocitypins

+nth order Θ+

–nth order Θ–

Grating

0th order

Path lengths:

Θ− System:

Θ+ System: abce = ade

Tilt box

Triggersignal

Oscilloscope(velocity signal)

Photodector 4

l 0 = l + = l –

ac′e′ = ab′d′–e′–

Fig. 4 Optical layout of a variable sensitivity displacement interferometer (VSDI) system. The Θ± system is obtained by combining a normally reflected beam and a diffractedbeam at an angle Θ±. In this figure, mirrors M0–M5 and beam splitters BS1–BS3 are used to obtain the VSDI systems. The lens with focal length F is used to focus the beam

at the grating plane in the anvil back surface. Source: Ref 52

Fig. 5 Soft-recovery, normal impact testing. (a) Test configuration. (b) Lagrangian time-distance (t-X) diagram for soft recovery experiment. Source: Ref 7

several recommendations to improve this con-figuration. Experimental evidence shows that itis difficult to recover brittle specimens intact,even at moderate stresses of about 2.0 GPa(290 ksi). Results from numerical simulationssuggest that thin flyer plates must be used,which lead to short loading duration. This isdifficult to implement in the pressure-shear re-covery experiments since very thin plates pro-duce negligible shear pulse duration. Investiga-tion of the release effects in the pressure-shearand normal plate impact recovery experi-ments on brittle materials shows that the ge-ometry of the plates may be used to mitigate re-lease effects (Ref 16–19). Independently of thegeometry of the pressure-shear configuration,some fraction of the energy always remains inthe sample as shear momentum and may af-fect the radial release waves before they aretrapped. The question of the residual shearpulse, which arises because of the shearstrength of the lubricant layer, must always beaddressed.

Normal Plate Impact

Experimental facilities, projectile character-istics, measurement techniques, and specimen

preparation and alignment are discussed in thepreceding sections of this article. To illustratethe basic procedure and the corresponding re-sults, consider first the normal configurationshown in Fig. 5(a), with the t-X diagram of Fig.5b, in the context of the investigation of inelas-ticity in a ceramic composite (Ref 7). The fiber-glass tube projectile carries steel and star-shaped Ti-6Al-4V flyer plates that are sepa-rated by a low-impedance foam to prevent re-loading of the specimen by reflected waves.The Ti-6Al-4V flyer has sufficiently high yieldstrength and acoustic impedance lower than thetested ceramic composite sample. The targetassembly consists of an inner cylinder for sup-porting the specimen and an outer anvil forstopping the projectile. The anvil has a dispos-able brass nose, which absorbs part of the im-pact energy. The 22 by 22 mm2 (0.87 by 0.87in.2) specimen is a thin plate of AlN/AlN/Alcomposite, backed up by the same size plate,which, ideally, has matching impedance. Thisplate flies off the back of the specimen after themain compressive pulse reflects from the rearsurface and returns to the interface.

Experimental Procedure. A 63 mm (2.5 in.)gas gun was used (Ref 7). The specimen char-acteristics and relevant test data are reported inTables 1 and 2. For the purpose of aligning and

triggering the oscilloscopes, a multilayer thinfilm mask was sputtered onto the impact face ofthe specimen. Since the AlN/AlN/Al compositeis conductive, a 1 µm thick insulating layer ofAl2O3 was first sputtered. Then, by using amask, a 0.1 µm thick layer of aluminum wassputtered in the form of four diagonal strip pinsat the corners and two ground strips crossing atthe center. Tilt and impactor velocity weremeasured using the techniques discussed in thesection “Plate Impact Facility” in this article.The normal motion at four points on the rearsurface of the momentum-trap plate was moni-tored by means of a normal displacement inter-ferometer (NDI) to identify nonplanar motionsthat can be correlated with the microcrackingprocess and the unloading waves from thestar-shaped flyer.

Wave Propagation Analysis. At impact,plane compression waves are produced in boththe thin star-shaped flyer and the specimen.The reflection from the foam-flyer interface un-loads the compressive wave, resulting in acompressive pulse of duration equal to theround-trip travel time through the thickness ofthe star flyer. When the compressive pulsereaches the rear surface of the specimen, thegap between the specimen and the momentum-trap plate produces a reflected wave, which un-


Fiberglass tube Target

Multiplateflyer

Specimen

α

V Θ– VSDI

(a)

Multiple flyer t

AnvilPlate

1Plate

2

Wafer

Shear wave

Normalwave

4

3

21

Interferometerwindows

Shearmotion

Normalmotion

First signal

x

Solid or liquidlubricant

Specimen

d1 d2 d3

(b)

Fig. 6 Pressure-shear high-strain-rate testing. (a) Test configuration. (b)Lagrangian t-X diagram for pressure-shear high-strain-rate recovery experi-

ment. Source: Ref 18, 19

Multiplateflyer

Specimen Momentumtrap

(a)

Compression

Shear

Compression releaseat lubricant interface

Interferometerwindows

Plate 1

Plate 2

Lubricantfilm

Shearmotion

Normalmotion

Transmission ofshear motion

Specimen Momentumtrap

s

Us

UL

d2 d3d1

Residualshearwave

Normalwave

(b)

x

tMultiplateflyer

Fig. 7 Pressure-shear wave propagation testing. (a) Test configuration. (b)Lagrangian t-X diagram for pressure-shear wave propagation recovery ex-

periment. Source: Ref 18, 19

loads the compressive pulse. Tensile stressesare generated after crossing the compressed re-gion. By the time this pulse reaches theflyer-specimen interface, separation betweenthe flyer and specimen has taken place, and thepulse reflection causes compressive stresses.The initial compressive pulse, minus the pulsereflected at the gap, propagates into the mo-mentum trap and reflects back. When this ten-sile pulse reaches the interface between thespecimen and the momentum trap, the momen-tum trap separates because this interface cannotwithstand tension. At this time, the specimen isleft unstressed and without momentum. Be-cause of the impedance mismatch between thespecimen and the momentum trap, an addi-tional compressive wave is reflected at the in-terface and makes a round trip through thespecimen. This relatively small compressive re-loading occurs later than the principal loadingof interest and is expected to have minor influ-ence on the observed damage.

This one-dimensional analysis is valid in thecentral region of the specimen (Ref 38), wherethe effects of diffracted waves from the cornersand the edges of the flyer are minimized. Theonly cylindrical wave, which passes throughthe central octagonal region, is a shear wavediffracted from the boundary upon the arrivalof a cylindrical unloading wave at 45°. To fullyassess the role of the cylindrical waves dif-fracted from the edges of the star and the spher-ically diffracted waves from the corners of theflyer and the specimen, three-dimensional elas-tic computations have been performed (Ref13). The principal unloading waves that travelin the central octagonal region are diffractedspherical waves emanating from the corners of

the flyer. These waves produce tensile stresseswithin the sample. The maximum amplitudesof such stresses occur for transverse tensilestresses at the rear surface of the specimen.These amplitudes are of the order of 15% of thelongitudinal compressive stress in the incidentplane wave. It should be pointed out that thisamplitude represents an upper bound for suchstresses. First, in real experiments there is alack of simultaneity for the time of contact ofthe eight corners due to the tilt between theflyer and the specimen. Second, the divergenceof the unloading waves from the corners willinduce microcracking near these corners andthereby reduce the level of tensile stresses thatpropagate into the central octagonal region to avalue below a fracture stress threshold. Thesefeatures have been observed systematically inAl2O3 and AlN/AlN/Al composite tested sam-ples.

Experimental Results. A summary of theexperiments is given in Tables 1 and 2. The ve-locity-time histories of two typical results aregiven in Fig. 8(a) and (b). The reported stressesare at the interface between the specimen andthe momentum trap. The maximum shear stressis given. The stress-time histories at the frontsurface of the momentum trap can be read fromthe secondary vertical axis. Dashed lines in theplot are the elastic solution results, which areused as a reference to discuss several observedinelastic effects. The main compressive pulse,with duration between 240 and 195 ns, is fol-lowed by a second compressive pulse corre-sponding to the tensile pulse generated by anintentional gap of 30 and 85 ns in Fig. 8(a) and(b), respectively. The third pulse results fromthe reflection of the main pulse at the interface

between the specimen and the momentum trap.Its close resemblance to the main pulse is an in-dication of the dominance of plane waves in thecentral region of the sample. In the experimentat lower impact velocity (Fig. 8a), the compres-sive pulse has the full amplitude of the elasticprediction. This implies that, initially, the ma-terial did not undergo inelastic processes at thislevel of stresses. The small reduction in ampli-tude at the end of the pulse can be interpretedfrom the analysis of release waves from thestar-shaped flyer corners (Ref 13). The tail atthe end of the first compressive pulse appearsto be the result of the inelastic strain rate pro-duced by the nucleation and propagation ofmicrocracks (Fig. 8a). If so, the duration of thetail can be associated with the time required forthe stress, at the wave front, to relax to thethreshold value required for initiating crackpropagation. Strong evidence of microcrackingis found in the attenuation and spreading of thesecond compressive pulse. In Fig. 8(b), someindication of inelasticity in compression ap-pears toward the end of the pulse. This featureis consistent with the increase in dislocationdensity, within the AlN filler particles, the AlNreaction product, and the Al phase, observed intransmission electron microscopy (TEM) sam-ples made from the recovered specimens (de-tails can be found in Ref 7).

Pressure-Shear Plate Impact

Inclining the flyer, specimen, and targetplates with respect to the axis of the projectileproduces compression-shear loading. By vary-ing the inclination angle, a variety of loading


Table 1 Properties of materials used in normal impact recovery experiments

Longitudinal wave Transverse wave Acoustic impedance, Shear impedance,Material Density, g/cm3 speed, mm/µs speed, mm/µs GPa · µs/mm GPa · µs/mm

Hampden steel 7.86 5.983 3.264 47.03 25.66Ti-6Al-4V 4.43 6.255 3.151 27.71 13.96AlN/AlN/Al 3.165 9.50 5.5 30.07 17.41

Source: Ref 7

Table 2 Summary of results from normalimpact recovery experiments

Projectile Normal stress Shear stressShot No. velocity, mm/µs GPa ksi MPa ksi

91-01 0.0804 1.417 206 475 6991-02 0.1070 1.889 273 633 92

Source: Ref 7

Nor

mal

vel

ocity

, mm

/µs

0.08

0.06

0.04

0.02

0

Experimental records

Elastic solution

0 200 400 600 800 1000 1200 1400Time, ns

2000

1500

1000

500

0

Nor

mal

str

ess,

MP

a

Nor

mal

vel

ocity

, mm

/µs

0.10

0.08

0.06

0.04

0

Experimental records

Elastic solution

0 200 400 600 800 1000 1200 1400Time, ns

2500

2000

1500

500

0

Nor

mal

str

ess,

MP

a

0.02

1000

(a) (b)

Fig. 8 Velocity-time profiles for normal impact recovery experiments. (a) Profile for shot No. 91-01 in Table 2. Second compressive pulse is attenuated due to material dynamicfailure in tension. (b) Profile for shot No. 91-02 in Table 2. A strong spall signal and attenuation of the first compressive pulse are observed. Source: Ref 7

states may be achieved. For small angles of in-clination, small shear stresses are produced,which can be used to probe the damage inducedby the accompanying pressure. This pres-sure-shear plate impact experiment was modi-fied by Ramesh and Clifton (Ref 6) to study theelastohydrodynamic lubricant response at veryhigh strain rates. The idea of recovery pres-sure-shear plate impact experiment was pre-sented by Nemat-Nasser et al. (Ref 40),Espinosa (Ref 41), and Yadav et al. (Ref 65)and was first successfully implemented to studythe response and failure modes of alumina ce-ramics by Machcha and Nemat-Nasser (Ref 16)and later by Espinosa et al. (Ref 17–19, 52) intheir studies of dynamic friction and failure ofbrittle materials.

Wave Propagation Analysis. The Lagrangiantime-distance (t-X) diagrams for pressure-shearhigh-strain-rate and wave propagation configu-rations, designed for specimen recovery, areshown in Fig. 6(b) and 7(b). In the case of pres-sure-shear high-strain-rate experiments, thespecimen is a thin wafer, 100 to 500 µm thick,sandwiched between two anvil plates. At im-pact, plane compression waves and shear wavesare produced in both the impactor and the tar-get. Since the shear wave velocity is approxi-mately half the longitudinal wave velocity, athin film with very low shear resistance needsto be added to the flyer plate such that the ar-rival of the unloading shear wave, to the impactsurface, precedes the arrival of the unloadinglongitudinal wave generated at the back surfaceof the second flyer plate. The longitudinal andshear wave fronts arriving to the anvil-free sur-face are shown in Fig. 6(b). These wave frontsdetermine the longitudinal and shear windowsmeasured interferometrically. These velocityhistories contain information on the samplestress history as discussed in the next para-graph. A similar wave analysis applies to thewave propagation pressure-shear configuration(Fig. 7b).

According to one-dimensional elastic wavetheory (Ref 5), the normal stress is given byσ = ρc1 u0/2, in which ρc1 is the flyer and anvillongitudinal impedance, and u0 is the nor-mal component of the impact velocity V (i.e.,u0 = V cos θ). The strain rate is given by thevelocity difference between the two faces ofthe sample divided by its thickness (i.e.,& ( ) / ( ) /λ = − = −v v h v v hf a fs0 ), where vf and vaare the flyer and anvil transverse velocities, re-spectively, at their interfaces with the speci-men, and v0=V sin θ and vfs are, respectively,the transverse components of the impact veloc-ity and the velocity of the free surface of the an-vil plate. The integration of the strain rate overtime gives the shear strain γ(t). One-dimen-sional elastic wave theory can be used again toexpress the shear stress in terms of the mea-sured free surface transverse velocity (i.e., τ =ρc2vfs/2), where ρc2 is the anvil shear imped-ance. These equations can be used to constructτ − γ curves at strain rates as high as 1 × 105 s−1

and pressures in the range of 2 to 5 GPa (290 to725 ksi). It must be emphasized that this analy-

sis is based on the assumption that inelasticitytakes place only in the specimen. An investiga-tion of this requirement at high strain rate andtemperatures can be found in Ref 42.

Numerical simulations have been performedby Machcha and Nemat-Nasser (Ref 23) for thepressure-shear recovery experiments. The re-sults confirm the advantages of the star-shapedgeometry. Machcha and Nemat-Nasser posi-tioned the star-shaped flyer as a second flyerplate, which does not fully mitigate lateral re-lease waves, in the central portion of the sam-ple. Espinosa and coworkers (Ref 18, 19) posi-tioned the star-shaped flyer plate as the firstplate of the multiplate flyer assembly. The se-lection of materials for the manufacturing offlyer plates depends on the application forwhich experiments are conducted. In the char-acterization of hard materials, demanding re-quirements are placed on the manufacturing offlyer and momentum-trap plates. These platesmust be hard enough in compression and shearto remain elastic at the high stress levels re-quired for the inelastic deformation of the spec-imen. The momentum trap must be strongenough in tension to prevent failure at 45°when the shear wave propagates through theunloaded region adjacent to the rear surface ofthe momentum trap. These requirements aremet by using Speed Star (Carpenter Technol-ogy Corp.—Specialty Alloys, Reading, PA)steel plates with a 0.2% offset yield stressgreater than 2200 MPa (320 ksi) in shear and atensile strength in excess of 1500 MPa (220ksi). Another important feature in the selectionof the flyer material is that its longitudinal andshear impedances must be smaller or equal tothose of the specimen. In this way, a singlecompression-shear pulse is introduced in thesample. Moreover, the longitudinal and shearimpedances of the momentum-trap plate mustmatch the impedances of the sample to avoidwave reflections at the specimen momentum-trap interface. Density, wave speeds, and im-pedances for the materials used in this investi-gation are reported in Table 3.

Experimental Procedure. The 76 mm (3.0in.) gas gun described in the section “Plate Im-pact Facility” was used. The multiplate flyerand target plates were made of Speed Star steel.The specimens were made with two types ofceramics. In the high-strain-rate pressure-shearexperiment, an Al2O3/SiC nanocomposite wa-fer was used. TiB2 plates were employed in thewave propagation pressure-shear experiments.In the latter case, two specimen configurationswere investigated. The first one consisted of asquare specimen with the same dimensions asthe star-shaped flyer. The second configurationconsisted of a hollow square steel plate inwhich a TiB2 ceramic rod 12.7 mm (0.5 in.) indiameter was shrunk fitted.

The target rear surface was polished, andthen a thin layer of positive photoresist was de-posited using a spinning machine. A holo-graphic phase grating was constructed by inter-ference of two laser beams. The angle betweenthe beams was selected such that a sinusoidal

profile with 1000 lines/mm was obtained. Thisgrating was used to measure the normal andtransverse displacements by means of a vari-able sensitivity displacement interferometer(VSDI) (Ref 52). The signals generated by eachinterfering beam pair were monitored by siliconphotodetectors.

Experimental Results. A summary of theseexperiments is presented in Table 4. The nor-mal velocity-time profile obtained from thehigh-strain-rate pressure-shear recovery config-uration is shown in Fig. 9(a). The normal parti-cle velocity shows a velocity reduction after aninitial jump indicating the presence of a smallgap between the Al2O3/SiC nanocomposite andthe multiplate flyer. Upon reverberation ofwaves within the specimen, the normal velocityrises to a value of about 140 m/s (460 ft/s) atapproximately 0.4 µs and remains almostconstant until release waves from the bound-ary reach the observation point. The peaknormal stress in this shot, computed accord-ing to σ = ρc1ufs/2, reaches 3.45 GPa (500 ksi).The transverse particle velocity history for thisexperiment is shown in Fig. 9(b). The velocityrises progressively and then drops for a fewnanoseconds. Since in this experiment, shearmotion is transferred by friction, a reduction innormal traction at the specimen-steel plate in-terface results in a drop of the transmitted shearmotion. When the gap closes, the transverse ve-locity increases until it reaches a maximumvalue of 22 m/s (72 ft/s) at about 500 ns. It thendecays continuously while the normal velocityremains constant (Fig. 9a). The maximum shearstress, given by τ = ρc2vfs/2, is 280 MPa (41ksi). This value is well below the expectedshear stress of 575 MPa (83 ksi), assumingelastic material response. The progressive re-duction in anvil-free surface transverse velocityimplies a variable strain rate and absence of ahomogeneous stress state in the sample. In thisexperiment, round plates were used and thesample was precracked through a sequence ofmicroindentations in a diameter of 38 mm (1.5in.) Lateral trapping of release waves was at-tempted by forming a circular crack with theunloaded sample in the central region. Despitethese efforts, the degree of damage was severeenough that the ceramic sample was reduced tofine powder upon unloading. This feature ofmaterial pulverization upon unloading was in-vestigated by Zavattieri et al. (Ref 22) by simu-lating compression-shear loading on represen-


Table 3 Properties of materials used inpressure-shear impact recoveryexperiments

Wave speed, Impedance,Density, mm/µs GPa · mm/µs

Material kg/m3 c1 c2 ρc1 ρc2

Speed-StarSteel

8138 5.852 3.128 47.62 25.46

TiB2 4452 10.93 7.3 48.66 32.5Al2O3/SiC 3890 10.56 6.24 41.08 24.27

Source: Ref 19

tative volume elements at the grain level. Theseinvestigators show that a ceramic micro-structure containing a dilute set of microcracksmay pulverize in unloading due to the storedelastic energy within the grains.

In the case of the wave propagation pres-sure-shear recovery configuration, round andsquare-shaped TiB2 plate specimens were used.The longitudinal and shear waves recorded inthe case of the square-shaped TiB2 specimenare shown in Fig. 10(a) and (b), respectively.The velocity profile in the first microsecond isshown in solid lines, while the remaining partof the signal is shown in dashed lines. Figure10(a) shows the normal velocity rises to a valuepredicted by one-dimensional elastic wave the-ory. After approximately 200 ns, the longitudi-nal particle velocity progressively decays and

then rises again at approximately 500 ns. Thislongitudinal velocity history is very close to theone-dimensional elastic wave propagation pre-diction if the effect of spherical waves emanat-ing from the star-shaped flyer corners is takeninto account (Ref 13). Another source of stressdecay is the presence of a thin polymer layer inthe multiplate flyer. As previously discussed,longitudinal stress decay occurs until a homo-geneous deformation state is reached in thepolymer film. The transverse particle velocityshown in Fig. 10(b) also presents clear features.Upon wave arrival to the back surface of themomentum-trap plate, an in-plane velocity ofabout 10 m/s (33 ft/s) is measured interfero-metrically. After shear wave arrival, accordingto the t-X diagram discussed previously, thetransverse velocity rises to a maximum of 38

m/s (125 ft/s). This value is below the shearwave velocity predicted by one-dimensionalwave propagation theory. Hence, the materialclearly exhibits an inelastic behavior in shear.At approximately 800 ns, the transverse veloc-ity decays progressively.

Understanding these complex velocity histo-ries requires complete three-dimensional simu-lations of the compression-shear experiment in-cluding damage and tilt effects. In this experi-ment, the steel plates are fully recovered. Incontrast to the shrink-fitted specimen, the ce-ramic specimen is fragmented with varyingfragment sizes (Fig. 11). The larger fragment isseveral millimeters in size, but its location inthe square plate could not be identified unam-biguously. In this case, the star-shaped flyeralso is fragmented in the central region. In ad-dition, long cracks are observed running paral-lel to the edges. Severe indentation is observedin the second flyer plate, although its hard-ness was measured to be 55 HRC. In this con-figuration, the momentum-trap plate remainsintact with no cracks observable to the nakedeye. Additional details can be found in Ref 18and 19.

Pressure-Shear Friction Experiments

This technique was originally introduced byPrakash and Clifton (Ref 66). Its main objec-tive was to investigate time-resolved friction atslipping speeds (5 to 30 m/s, or 16 to 98 ft/s)and pressures (1 to 3 GPa, or 145 to 435 ksi)typical of high-speed machining processes. Asdiscussed in Ref 66, the technique can be easilyinterpreted within the one-dimensional wavepropagation theory. By using characteristicequations it can be shown that the shear and


Table 4 Summary of parameters for pressure-shear recovery experiments

Specimen thickness Impactor thickness Target thickness Projectile velocityShot No. Specimen mm in. mm in. mm in. m/s ft/s Tilt, mrad Configuration

7-1025 Al2O3/SiC 0.54 0.021 2.42–3.65 0.095–0.144 7.99 0.31 148 486 1.3 High strain-rate recovery7-1115 TiB2 4.15 0.163 1.04–2.55 0.041–0.100 4.53 0.18 130 427 20.3 Wave propagation recovery8-0131 TiB2 8.9 0.35 0.92–3.0 0.036–0.12 4.05 0.16 133 436 1.32 Wave propagation recovery

Source: Ref 19

Nor

mal

vel

ocity

, m/s

160

140

120

100

80

60

40

20

00 0.5 1 1.5 2

Time, µs(a)

Tran

sver

se v

eloc

ity, m

/s

24

22

20

1816

14

12

10

8

6420

0 0.5 1 1.5Time, µs

(b)

Fig. 9 Velocity histories from a pressure-shear high-strain-rate experiment (shot No. 7-1025 in Table 4). (a) Normalvelocity history. The time scale starts with the arrival of the longitudinal wave to the anvil-free surface.

(b) Transverse velocity history. The time scale starts with the arrival of the shear wave to the anvil-free surface. Source:Ref 18, 19

Nor

mal

vel

ocity

, m/s

300

250

200

150

100

50

00 0.25 0.5 0.75 1

Time, µs

Tran

sver

se v

eloc

ity, m

/s

40

30

20

10

00 0.25 0.5 0.75 1

Time, µs

Shear wave arrival

(a) (b)

Fig. 10 Velocity histories from a pressure-shear wave propagation experiment (shot No. 8-0131 in Table 4). (a) Normal velocity history. The time scale starts with the arrival ofthe longitudinal wave to the momentum-trap-free surface. (b) Transverse velocity history. The time scale starts with the arrival of the shear wave to the momen-

tum-trap-free surface. Source: Ref 19

normal stresses at the sliding interface aregiven by:

τ(t) = 0.5(ρc2)tvfs(t)

σ(t) = 0.5(ρc1)tufs(t)

in which (ρ)t is the target material density, (c1)tand (c2)t are the longitudinal and shear wavevelocities of the target material, and vfs and ufsare the shear and longitudinal free-surface ve-locities interferometrically measured. Further-more, the slipping velocity is given by:

V Vc c

cvslip

t f

2 ffs= −

+

sin

( ) ( )

( )θ

ρ ρρ

2 2

2

The friction coefficient is obtained by the ratioτ(t)/σ(t). More details about the derivation ofthese formulas can be found in Ref 67.

The pressure-shear friction experimentaltechnique discussed in this section is an exten-sion of the technique introduced by Prakashand Clifton (Ref 66) in the sense that the exper-iment is designed for specimen recovery. Here,the specimen is the interface formed after im-pact by the flyer and target plates rather thanthe thin specimen shown in Fig. 6. Certainly, acoating may be deposited on the flyer and/orthe target plates to examine its frictional prop-erties under pressure and sliding velocities typ-ical of manufacturing processes or ballistic pen-etration events. The preparation of the plates,assembly of the target, and alignment followthe procedures outlined in the section “Speci-men Preparation and Alignment” in this article.

In an experiment reported in Ref 52, 4340steel tribopair was used. Typical VSDI signalsobtained in these experiments are shown in Fig.12(a) and (b). In Fig. 12(a), the normal free-surface velocity history is plotted together withthe Θ− VSDI amplitude corrected signal. Uponarrival of the longitudinal wave to the tar-get-free surface, the normal velocity exhibits anincrease in velocity to a level of approximately80 m/s (260 ft/s) followed by a reduction andincrease in velocity due to wave reverberationsin the thin polymer layer used in the multiplateflyer. A few bumps are observed in the first 900ns of the normal velocity history. These varia-tions in normal velocity are likely the result ofthe low signal-to-noise ratio in the early part ofthe record (Fig. 12a). They are also due in partto errors in data reduction arising from the in-sensitivity of the displacement interferometerat the peaks and valleys of the trace (Ref 7).Experience suggests that signals with higherfrequencies are less sensitive to errors causedby signal noise. The noise level can be ob-served in the part of the record preceding thelongitudinal wave arrival. In later experiments,the angle θ used in the Θ− VSDI has been in-creased with good results. An approximatelyconstant velocity of 115 m/s (377 ft/s) is moni-tored in the next 1.8 µs, which is in agreementwith the elastic prediction. It should be noted thatthis normal velocity would lead to a frequency

of 450 MHz in an NDI, while in the VSDI sys-tem, a much smaller frequency is recorded.

In Fig. 12(b) the transverse velocity historyand the TDI amplitude corrected signal areshown. A transverse velocity well below theimpact shear velocity is measured, indicatinginterface sliding. Small fluctuations in thetransverse velocity are due in part to errors indata reduction arising from the insensitivity ofthe TDI at the peaks and valleys of the trace(Ref 7). An in-plane wave release is observedat approximately 2 µs. This wave release is inagreement with the wave release predicted byone-dimensional elastic wave theory. It shouldbe noted that the reduction in in-plane motion isprogressive. A residual transverse velocity of 5m/s (16 ft/s) is recorded, likely due to the shearresistance of the thin polymer film used in themultiplate flyer. Modeling of the experiment,including the frictional behavior of the steel in-terface and the nonlinear behavior of the poly-mer thin film, is required to fully interpret thetransverse velocity history. Further evidence onthe shear wave duration can be observed in Fig.13 in which an optical micrograph shows slid-ing marks, approximately 50 µm in length.From the transverse velocity history, an aver-age sliding velocity of 26 m/s (85 ft/s) is com-puted. This velocity during 2 µs leads to a slid-ing length of 52 µm, which correlates very wellwith the sliding marks observed on the micro-graphs.

Prakash and Clifton (Ref 66) and Prakash(Ref 67) reported dynamic friction coefficientsfor various tribopairs, namely, WC/4340 steeland WC/Ti-6Al-4V. This work was later ex-tended by Rajagopalan et al. (Ref 68) concern-ing the estimate of temperature histories in thetwo plates. Pressure-shear friction experimentson preheated target plates were conducted byFrutschy and Clifton (Ref 69). In their work,the friction phenomenon is investigated at hightemperatures. Additional insight into the dy-namic friction experimental technique can befound in these references.


(a) (b)

(c) (d)

Fig. 11 Optical micrograph of recovered plates froma pressure-shear wave propagation experi-

ment (shot No. 8-0131 in Table 4). (a) Second flyer plate.(b) Back momentum-trap plate. (c) Star-shaped flyerplate. (d) Fragmented specimen. Source: Ref 19

Nor

mal

vel

ocity

, m/s

150

100

50

00 1000 2000 3000

Time, ns

2

1

0

–1

–21.4000E-5

1.5000E-51.6000E-5

1.7000E-51.8000E-5

1.9000E-5

Tran

sver

se v

eloc

ity, m

/s

20

15

10

00 1000 2000 3000

Time, ns

2

1

0

–1

–21.5000E-5

1.5500E-51.6000E-5

1.6500E-51.7000E-5

1.7500E-5

Wave reverberationat thin film

5

500 1500 2500

1.8000E-5

Shear wave release

(a) (b)

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

Nor

mal

str

ess,

GP

a

250

200

150

100

50

0

She

ar s

tres

s, M

Pa

Fig. 12 Particle velocity-time profiles for a dynamic friction recovery experiment. (a) Normal profile; impact velocity, 125 m/s (410 ft/s). The inset shows the Θ− VSDI trace afteramplitude correction. (b) Transverse profile; impact shear velocity, 38.62 m/s (126.7 ft/s). The inset shows the TDI trace after amplitude correction. Source: Ref 52


High-TemperaturePlate Impact Testing

Understanding materials response at high tem-peratures and high strain rates is essential tothe development of constitutive models de-scribing dynamic failure of advanced materi-als. Such models are of crucial importance tomany applications, for example, crack arrestin engineering structures, failure of turbine en-gine blades, foreign object impact on satellites,automotive crashworthiness, and military ap-plications such as projectile deformation andarmor penetration. Current understanding ofbasic properties such as plastic flow and dy-namic fracture strength in the high-temperatureand high-strain-rate regime is very limited.This is due to the scarcity of experimental stud-ies with the needed spatial and temporal resolu-tion to identify damage and failure mecha-nisms.

It has been shown that high strain rates in-crease the yield stress in metals (Ref 70–73),whereas it is generally accepted that a rise intemperature tends to reduce the resistance toflow by lowering activation barriers associatedwith the atomic mechanisms of deformation(Ref 74–77). When a metallic material is sub-jected to dynamic and high-temperature load-ing, a competition process between work hard-ening (resulting from the production, motion,and interaction of dislocations and other de-fects) and thermal softening occurs. Extensiveresearch on the stress-strain temperature-de-pendent behavior in many body-centered cubicand face-centered cubic metals has been carriedout (Ref 78–81). These results show that tem-perature has a much greater effect on materialstrength than strain rate if the deformation isperformed under both high-strain-rate and high-temperature conditions.

Even though inelastic mechanisms at highstrain rates are not completely understood, re-searchers agree on the definition of the Hugoniotelastic limit (HEL) as the axial stress, under

one-dimensional strain, leading to the onset ofmaterial inelasticity. Hence, the evolution ofthe HEL or its equivalent, the dynamic yieldstress, with temperature can be identified bymeans of normal impact high-temperature ex-periments. Frutschy and Clifton (Ref 42) car-ried out pioneer work on the temperature andrate dependence of the dynamic yield stress inoxygen-free high-conductivity copper. Insteadof the normal impact experiment described,they performed pressure-shear high-tempera-ture experiments.

Simultaneous nucleation, growth, and coales-cence of microvoids or microcracks govern thespall process in advanced materials. Thermalenergy plays an important role in the deforma-tion mechanisms leading to strain inhomo-geneities that drive the failure process. Limitedexperimental work exists to define the role ofthermal activation on spall behavior of materi-als. Recently, studies from Kanel et al. (Ref 82)and Golubev and Sobolev (Ref 83) on alumi-num and magnesium have been published. Ithas been found that spall strength drops withtemperature, but no further investigations havebeen carried out to establish the role of themicrostructure in the spallation process.

This section describes the experimental tech-nique developed for shock impact testing athigh temperature and reports the variation ofHEL and spallation with temperature inTi-6Al-4V. Microstructural analyses that pro-vide insight into the deformation mechanismsof high-temperature-shocked materials are re-ported in Ref 44 and 84.

Wave Propagation Analysis for HEL andSpallation Identification. The Dynamic In-elasticity Laboratory described in the section“Plate Impact Facility” in this article possessesthe instrumentation to perform planar impact

experiments at different temperatures. Thesetup is similar to the one developed byFrutschy and Clifton (Ref 42, 43) for pres-sure-shear impact experiments.

The selected experimental configuration is asymmetric planar impact or spall configuration(Fig. 14a). The elastic wave fronts and their in-teraction can be understood by examining theLagrangian (t-X) diagram shown in Fig. 14(b).At impact, plane compression waves are pro-duced in both the flyer and the specimen (state1). Reflection from the foam-flyer interface un-loads almost completely the compressive wave,resulting in a compressive pulse duration equalto the round-trip travel time through the flyerthickness. When the compressive pulse reachesthe rear surface of the specimen, a reflectedwave is generated. This wave unloads the com-pressive pulse (state 2). Tensile stresses aregenerated when the two unloading waves, onefrom the flyer and the other from the specimenback surface, meet in the central part of thespecimen (state 3). By the time this pulsereaches the flyer-specimen interface, separationtakes place and the pulse reflection causes fur-ther compressive stresses (state 4).

For the experiments reported in this subsec-tion, the thickness of the targets was close to 8mm (0.3 in.) for all specimens with a corre-sponding half thickness for the flyers. Hence,the spall plane was located near the middle ofthe target plate. The impact velocity range wasselected such that the lowest velocity wasenough to induce dynamic yield in Ti-6Al-4V(about 900 MPa, or 130 ksi, according to Ref85), whereas the highest velocity would inducespallation.

Experimental Procedure. The experimentalprocedure follows the technique discussed in thesection “Specimen Preparation and Alignment.”

Fig.13 Optical micrograph of impact surface from re-covered flyer plate. Sliding marks approxi-

mately 50 µm in length are observed. Source: Ref 52

Ti-6Al-4V flyer plate

PVCholder

Impactdirection

Ti-6Al-4Vtarget plate

Backing foam(a)

Normalmotion

Spall region

State 4

State 3

State 2

State 1

Flyer Target

x

t

(b)

Fig. 14 High-temperature spall experiments. (a) Impact configuration. (b) Lagrangian t-X diagram of spall configu-ration. Source: Ref 44

Something unique to the high-temperaturetarget setup is the assembly of the target plateto the target holder. The Ti-6Al-4V sample isplaced hand tight inside a graphite susceptorand glued using high-temperature epoxy. Thetwo pieces together are slipped into a ce-ramic-foam sleeve that fits inside the coilshown in Fig. 2 and 3. The sleeve is firmly at-tached by high-temperature epoxy and four ce-ramic pins to the surrounding copper coil.

The induction heating process generates atemperature gradient in the sample. In fact, theinduced currents tend to stay on the surface ofthe specimen, generating more heat at the sur-face than in the bulk of the material (Ref 86).Titanium alloys have low thermal conductivity;therefore, the heating gradient can be impor-tant. A reduction in the coil diameter generatesa denser electromagnetic field that can pene-trate the shield generated by the induced cur-rents, achieving a more homogeneous heating(Ref 86). A more practical approach is to em-ploy a material with high electrical conductiv-ity and heat thermal capacity to hold the targetand minimize transient time. The graphitesusceptor shown in Fig. 2 is introduced in thedeveloped setup with this aim. Temperature ismeasured by a thermocouple attached to therear face of the specimen, as close as possibleto the center point.

The high velocities required in this studygenerated a strong shock wave within the targetchamber upon the exit of the projectile from thelaunch tube. To protect the high-temperatureassembly, an extension was added to the gunbarrel. Following aerodynamic considerations,the extension was designed to keep the high-temperature target assembly outside of thegas-flow cone emanating from the end of thegun barrel. An exploded view of the describedexperimental assembly is presented in Fig. 15.The assembly and alignment of the plates andthe measurement of projectile velocity followthe techniques described in the section “Speci-men Preparation and Alignment.”

A disposable mirror is suspended at a certaindistance from the rear face of the specimen toallow the laser beam to monitor the motion ofthe rear surface of the specimen. The targetchamber has a side window to provide accessfor the laser beam that is used in the air-delay-leg normal velocity interferometer for any re-flecting surface (ADL-VISAR) (Ref 44) de-picted in Fig. 16. To avoid overheating of themirror employed to collect light for the interfer-ometer, a ceramic foam is used to close the ce-ramic sleeve that contains the target (Fig. 2). Asmall hole is drilled on the center of the cup,and the laser light is sent in and collected backthrough it.

Tested Material. Details on the hot-rolledcommercial grade plates Ti-6Al-4V, its chemi-cal composition, and metallographic examina-tion of the as-received plates can be found inRef 44. It is interesting to point out the high in-terstitial oxygen content (0.18%) and grainelongation in the rolling direction. The targetand flyer plates were all machined from the

as-received plates in such a way that the impactaxis was perpendicular to the rolling direction.The hardness was measured to be 35.6 HRC. At

room temperature, the longitudinal wave speed,ultrasonically measured, is cL = 6232 m/s(20,446 ft/s), and the material density is 4430


Back Piston

Fiber-glasstube

PVC HolderTarget

Ceramicpin

InductionCoil

Cup

Ceramicsleeve

Graphitesusceptor

FlyerFoam

Key

Gun barrelextension

Fig. 15 Exploded view of gas gun extension. Source: Ref 44

Beam expander

Argon ion laserMirror

PBS

Intensity monitoringbeam

Retroreflector

M1

M3′

A′(t)

B′(t)

B(t)

PBS-1

PBS-2

λ/2

λ/4

Beam splitterLens 1

M2

Lens 2

M3

S

P A(t)P

S

Differentialamplifier

Differentialamplifier

Retroreflector/PZTSignals

Oscilloscope

Vacuum chamber

Lens

MirrorProjectile and flyer

Breech

Highpressuregas tank

Vacuum pump

Trigger signal

Velocity measurement(oscilloscope)

Fig. 16 Schematic of ADL-VISAR interferometer. Source: Ref 87

kg/m3; therefore, the acoustic impedance is27.608 GPa/mm/µs.

Experimental Results. A summary of per-formed high-temperature impact experiments ispresented in Tables 5 and 6. A first experiment,98-0924, was performed to have a reference ofthe material behavior at room temperature. Itstime-velocity history is shown in Fig. 17. Ascan be observed in this figure, the elastic pre-cursor in this experiment was lost due to the

low velocity per fringe (18.75 m/s, or 62 ft/s)employed in the interferometer. Twelve fringeswere added to the fringe count to match theboundary conditions (Ref 49). The velocityjump corresponding to the HEL is 200.5 m/s(657.8 ft/s) in good agreement with the 201 m/s(659 ft/s) reported in Ref 88.

The transition between elastic-plastic behav-ior is clearly captured; there is a sharp elasticunloading followed by a dispersive unloading

tail. The dispersion in the unloading tail is dueto the severe plastic deformation the materialunderwent in the loading phase. The reloadingpulse that is generated by the reflection at theflyer-specimen interface is greatly reducedwith respect to the expected elastic behavior.Even though some hardening is expected due tothe passage of the first loading pulse, the hard-ening must appear as a change in the slope ofthe second loading pulse instead of the ob-served attenuation. The attenuation indicatesthat part of the energy is dissipated in the formof shock-induced damage at the applied stresslevel. Note that no spall signal is observed inthe free-surface velocity record. Hence, thestress-pulse attenuation is indicative of damageinitiation without the formation of a spall re-gion within the sample. This was confirmed byscanning electron microscopy (SEM) studiesperformed on the recovered samples. Micro-voids at the α−β interface were observedthrough the thickness of the target plate. Detailscan be found in Ref 44.

An interesting feature of experiment 98-0924is the oscillation of the velocity profile close tothe end of the first unloading. Mescheryakov etal. (Ref 89) reported that oscillations in theirVISAR signal appeared to indicate a shock-induced phase transformation in Ti-6Al-4V.Their post-test SEM studies performed oversamples recovered right after the experiment ina water chamber presented evidence of an ω re-sidual phase in the microstructure. The setupfor this experiment did not allow for coolingthe samples right after impact, but the similar-ity with Mescheryakov et al. (Ref 89) in theinterferometric records indicates the presenceof a shock-induced phase transformation inTi-6Al-4V. The stress level for the transforma-tion is 2.17 GPa (315 ksi), close to ω-start pres-sure reported by Vohra et al. (Ref 90) but lowerthan the phase transition reported byMescheryako, 2.95 GPa (428 ksi). The directtransformation is not observed because it isovercome by the elastic wave.

A second experiment, 98-1210, performed at298 °C (568 °F) shows the effect of tempera-ture on damage kinetics at similar stress andstrain rate levels. The elastic precursor is alsolost in this experiment; several fringes wereadded to match boundary conditions. A higherplastic deformation expected at high tempera-ture makes the slope of the plastic wave morepronounced, as can be observed in Fig. 17. Thesmoothness of the velocity profile shows a pro-gressive deformation of the free surface, whichis a clear indication of high plastic deformationwithin the target plate. The velocity jump cor-responding to the HEL is lower, 166 m/s (545ft/s), showing a decrease in the dynamic yieldstress with temperature. The so-called precur-sor decay is also more pronounced due to theincreased rate of plastic deformation. In this ex-periment, the temperature rise was estimated tobe 17 °C (31 °F), giving a final temperature of315 °C (600 °F) well below the β-transus tem-perature range for Ti-6Al-4V (570–650 °C, or1060 to 1200 °F). No evidence of shock-in-


Table 5 Summary of parameters for high-temperature impact experiments

Impactor thickness Target thickness Impact velocity Normal stressShot No. mm in. mm in. m/s ft/s GPa ksi

T98-0924 3.60 0.142 7.6 0.30 251 823 3.46 506T98-1210 3.51 0.138 7.79 0.307 272 892 3.56 516T99-0602 3.32 0.131 6.69 0.263 417 1368 5.44 789T99-1008 3.61 0.142 6.795 0.268 594 1949 7.45 1080

Source: Ref 44, 84

Table 6 Summary of results for high-temperature impact experiments

Preheat Dynamic yieldtemperature Strain rate, Transient Hugoniot elastic limit stress Spall strength

Shot No. °C °F s–1 × 105 strain GPa ksi MPa ksi GPa ksi

T98-0924 22 72 1.47 0.0135 2.77 402 1402 203.3 5.10(a) 740(a)T98-1210 298 568 1.61 0.0153 2.11 306 917 133.0 … …T99-0602 315 599 2.27 0.0239 2.105 305 914 132.6 4.47 648T99-1008 513 955 3.26 0.0356 1.98 287 858 124.4 4.30 624

(a) Reported in the literature

Free

sur

face

vel

ocity

, m/s

600

500

400

300

200

100

00 1 2 3 4 5

Time, µs

98-1210T: 298 °C

98-0924T: 22 °C

99-0602T: 315 °C

99-1008T: 513 °C

8

7

6

5

4

3

2

1

0

220

200

180

160

140

120

Vel

ocity

, m/s

0 0.01 0.02 0.03 0.04 0.05Time, µs

Str

ess,

GP

a

Fig. 17 Velocity histories of normal high-temperature impact experiments. Source: Ref 44, 84

duced phase transition appears in this experi-ment (see first unloading in Fig. 17).

Experiment 99-0602 was carried out at 315°C (600 °F). This temperature is close to thetemperature in experiment 98-1210, but the im-pact velocity is higher. For this experiment theinterferometer was modified to a higher veloc-ity per fringe, 95.1 m/s (312 ft/s). Even thougha shorter delay leg was used, part of the elasticprecursor overcame the recording system, andone fringe needed to be added to match theboundary conditions. According to the velocityprofile shown in Fig. 17, the velocity jump cor-responding to the HEL coincides with the onein experiment 98-1210 (same temperature).The plastic wave slope is higher, indicating astronger hardening due to the higher inelasticstrain rate. The unloading is dispersive andshows again the reverse-phase transformation.Between the first and second loading pulse, aclear spall signal appears. Spallation occurs at alower stress than the one reported by other in-vestigators (e.g., Ref 91). Some researchers at-tribute this to an incomplete fracture at the spallplane. There are several approaches to calculatespall strength. For consistency with results re-ported in the literature, for other metallic mate-rials, the approach stated by Kanel et al. (Ref82) is employed. Such an approach establishesthe spall strength for a symmetric impact, ac-cording to 0.5 ρC0∆V, where ∆V is the velocitydrop from the peak velocity to the spall signal.According to this equation, experiment99-0602 presents spall strength of 4.47 GPa(648 ksi). This value represents a reduction of~10% from the value of 5.1 GPa (740 ksi) atroom temperature, reported in Ref 88 and 91.The reduction in spall strength with tempera-ture was previously reported by Kanel et al.(Ref 82) in magnesium and aluminum. Oscilla-tions in the free-surface velocity profile duringunloading again indicate the phase transitionω→α. This phase transition happens at a com-pressive stress level of approximately 2.25 GPa(434 ksi), slightly higher than the phase transi-tion at room temperature. The temperature risewas estimated to be 40 °C (72 °F), giving a fi-nal temperature of 351 °C (664 °F). As in theprevious case, the final temperature is well be-low the β-transus; hence, allotropic transforma-tions were not likely to occur.

To further explore the spall behavior, experi-ment 99-1008 was carried out at a temperatureclose to the limit of applicability of Ti-6Al-4V,that is, ~500 °C (930 °F). The impact velocitywas set to about 590 m/s (1935 ft/s) to ensure aclear spallation process. The velocity per fringein the interferometer was 97.2 m/s (318.9 ft/s),resulting in a partial loss of the elastic precur-sor as in experiment 98-1210. The free-surfacevelocity profile for this last experiment isshown in Fig. 17. A consistent reduction of theHEL with temperature can be observed. Theplastic wave slope is steeper than in the otherdiscussed experiments, indicating an evenstronger hardening. A Hugoniot state is clearlyachieved followed by a dispersive unloadingpulse as in previous experiments. The overall

wave profile is smooth, indicating a progres-sive deformation when the wave travelsthrough the target. Between the expected firstand second loading pulses, a fast-risingpull-back signal and clear spallation signal ap-pear, which indicates the formation of awell-defined spall fracture plane. The higherrate of velocity increase during spallation is ev-idence that the fracture process is more violentthan the one in experiment 99-0602. In fact, therecovered target was split into two pieces (Ref44). Using the approach developed by Kanel etal. (Ref 82), the spall strength was estimated at4.30 GPa (624 ksi). This indicates a reductionof 5% in the spall strength with an increment of~200 °C (360 °F). The decrease in spallstrength is in agreement with the results re-ported in Ref 82 for magnesium and aluminum.The inverse shock phase transformation α − ωwas not present in this experiment. The spallsignal rings at a higher stress than the level cor-responding to the inverse shock transformationpreviously observed. Therefore, it is not possi-ble to conclude whether the increase of thepeak shock stress can trigger the inverse shocktransformation despite the increase in tempera-ture. The temperature rise for this experimentwas estimated to be 81 °C (146 °F), resulting ina final temperature of 593 °C (1100 °F). The fi-nal value is close to the β-transus temperature.Thermomechanical properties change with al-lotropic transformations in Ti-6Al-4V (Ref 92).

A comprehensive microscopy study on thefailure and damage modes of Ti-6Al-4V as afunction of temperature can be found in Ref 44and 84.

Impact Techniques with In-MaterialStress and Velocity Measurements

Several research efforts have been made forin-material measurements of longitudinal andshear waves in dynamically loaded solids. Suc-cessful experiments where velocity historieshave been obtained at interior surfaces by in-serting metallic gages in a magnetic field andmeasuring the current generated by their mo-tion have been reported (Ref 93–95); thesegages are called electromagnetic particle veloc-ity (EMV) gages. This technique can be appliedonly to nonmetallic materials.

Another technique developed for in-materialmeasurements employs manganin gages placedbetween the specimen and a back plate to mea-sure the time history of the longitudinal stress,or by placing a manganin gage at an interfacemade in the direction of wave propagation tomeasure lateral stresses (Ref 96, 97). In thisconfiguration, the dynamic shear resistance ofthe material can be obtained by simultaneouslymeasuring the axial and lateral stresses.

An alternative technique for the in-materialmeasurement of the dynamic shear resistanceof materials is the use of oblique impact withthe specimen backed by a window plate (Ref56). In this technique, longitudinal and shear

wave motions are recorded by a combined nor-mal displacement interferometer (NDI) or anormal velocity interferometer (NVI) (Ref 48)and a transverse displacement interferometer(TDI) (Ref 50). Alternatively, the VSDI inter-ferometer previously discussed can be used.The velocity measurements are accom-plished by manufacturing a high-pitch diffrac-tion grating at the specimen-window interface(Ref 56).

In-Material Stress Measurements withEmbedded Piezoresistant Gages. Many ma-terials exhibit a change in electrical resistivityas a function of both pressure and temperature.Manganin, an alloy with 24 wt% Cu, 12 wt%Mn, and 4 wt% Ni, was first used as a pressuretransducer in a hydrostatic apparatus byBridgman in 1911 (Ref 98). Manganin is agood pressure transducer because it is muchmore sensitive to pressure than it is to tempera-ture changes. Impact experiments performed byBernstein and Keough (Ref 99) and DeCarli etal. (Ref 100) showed a linear relationship be-tween axial stress σ1, in the direction of wavepropagation, and resistance change; namely,σ1=∆R/kR0 in which R0 is the initial resistanceand k is the piezoresistance coefficient. Formanganin, DeCarli et al. (Ref 100) found k =2.5 × 10−2 GPa−1. The value of this coefficientis a function of the gage alloy composition;therefore, a calibration is required. Manganingages are well suited for stress measurementsabove 4 GPa (580 ksi) and up to 100 GPa (15 ×106 psi). At lower stresses, carbon and ytter-bium have a higher-pressure sensitivity (Ref101), resulting in larger resistance changes and,hence, more accurate measurements. Carbongages can be accurately used up to pressures of2 GPa (290 ksi), while ytterbium can be usedup to pressures of 4 GPa (580 ksi).

In plate impact experiments, the gage elementis usually embedded between plates to measureeither longitudinal or transverse axial stresses.A schematic of the experimental configurationis shown in Fig. 18. If the gage is placed be-tween conductive materials, it needs to be elec-trically insulated by packaging the gage usingpolyester film, mica, or polytetrafluoroethylene.Another reason for using a gage package is toprovide additional protection in the case of brit-tle materials undergoing fracture.

Through the use of metallic leads, the gage isconnected to a power supply that energizes thegage prior to the test. The power supply com-prises a capacitor that is charged to a selectedvoltage and discharged upon command into abridge network by the action of a timer and apower transistor. The current pulse that is de-livered to the bridge is quasi-rectangular withduration between 100 and 800 µs. The bridgenetwork is basically a Wheatstone bridge that isexternally completed by the gage. The gage,which is nominally 50 Ω, is connected to thebridge with a 50 Ω coaxial cable. The reasonfor using a pulse excitation of the bridge, ratherthan a continuous excitation, is that such an ap-proach permits high outputs without the needfor signal amplification and avoids excessive


Joule heating effects that can result in gage fail-ure. The bridge output is connected to an oscil-loscope for the recording of voltage changes re-sulting from changes in resistance. The relationbetween voltage and resistance change is ob-tained by means of a calibration with a variableresistor.

A concern with this technique is the perturba-tion of the one dimensionality of the wavepropagation due to the presence of a thin layer,perpendicular to the wave front, filled with amaterial having a different impedance and me-chanical response. Calculations by Wong andGupta (Ref 102) show that the inelastic re-sponse of the material being studied affects thegage calibration. In 1994, Rosenberg and Brar(Ref 103) reported that in the elastic range ofthe gage material, its resistance change is afunction of the specimen elastic moduli. In ageneral sense, this is a disadvantage in the lat-eral stress-gage concept. Nonetheless, theiranalysis shows that in the plastic range of thelateral gage response, a single calibration curvefor all specimen materials exists. These find-ings provide a methodology for the appropriateinterpretation of lateral gage signals and in-crease the reliability of the lateral stress-mea-suring technique.

Example: Identification of Failure Wavesin Glass. In-material axial and transverse stressmeasurements have been successfully used inthe interpretation of so-called failure waves inglass (Ref 24, 25, 45). By using the configura-tion shown in Fig. 18 with the longitudinalgage backed by a PMMA plate, the dynamictensile strength of the material was determined(Ref 45). In these experiments, manganin gageswere used. Soda-lime and aluminosilicate glassplates were tested. The density and longitudinalwave velocity for the soda-lime glass were 2.5g/cm3 and 5.84 mm/µs, respectively. The alu-minosilicate glass properties were density =2.64 g/cm3, Young’s modulus = 86 GPa (12 ×106 psi), and Poisson’s ratio = 0.24.

By appropriate selection of the flyer-platethickness, the plane at which tension occurs forthe first time within the sample was locatedclose to the impact surface or close to the speci-men-PMMA interface. In experiment 7-0889, a5.7 mm (0.22 in.) thick soda-lime glass targetwas impacted with a 3.9 mm (0.15 in.) alumi-num flyer at a velocity of 906 m/s (2972 ft/s).The manganin gage profile is shown in Fig. 19.The spall plane in this experiment happened tobe behind the failure wave. The profile showsthe arrival of the compressive wave with a du-ration of approximately 1.5 µs, followed by arelease to a stress of about 3 GPa (435 ksi) anda subsequent increase to a constant stress levelof 3.4 GPa (493 ksi). The stress increase afterrelease is the result of reflection of the tensilewave from material that is being damaged un-der dynamic tension and represents the dy-namic tensile strength of the material (spallstrength). From this trace, it was concluded thatsoda-lime glass shocked to a stress of 7.5 GPa(1088 ksi) has a spall strength of about 0.4 GPa(58 ksi) behind the so-called failure wave. Theexperiment was repeated with a 2.4 mm (0.09in.) thick aluminum flyer (7-1533); the resultwas complete release from the back of the alu-minum impactor (Fig. 19). A pull-back signalwas observed after approximately 0.45 µs witha rise in stress of about 2.6 GPa (377 ksi). Itshould be noted that the spall plane in this ex-periment was in front of the failure wave.These two experiments clearly show that thespall strength of glass depends on the locationof the spall plane with respect to the propagat-ing failure wave. For soda-lime glass, a dy-namic tensile strength of 2.6 and 0.4 GPa (377and 58 ksi) was measured with manganin gagesin front of and behind the failure wave, respec-tively. Dandekar and Beaulieu (Ref 104) ob-tained similar results using a VISAR.

Additional features of the failure-wave phe-nomenon were obtained from transverse gageexperiments performed on soda-lime and alu-minosilicate glasses (Ref 24). In these experi-ments, one or two narrow 2 mm (0.08 in.) widemanganin gages (type C-8801113-B) were em-bedded in the glass target plates in the directiontransverse to the shock direction as shown inFig. 18. A thick back plate of the same glass

was used in the target assembly. Aluminum orglass impactor plates were used to induce fail-ure waves. The transverse stress, σ2, was ob-tained from the transverse gage record. Figure19 shows measured transverse gage profile attwo locations (shot 7-1719) in the aluminosili-cate glass. The two-wave structure that resultsfrom the failure wave following the longitudi-nal elastic wave can clearly be seen. The firstgage, at the impact surface, shows an increasein lateral stress to the value predicted byone-dimensional wave theory, 2.2 GPa (319ksi) in Fig. 19, immediately followed by a con-tinuous increase to a stress level of 4.2 GPa(609 ksi). The second gage, at 3 mm (0.12 in.)from the impact surface, initially measures aconstant lateral stress of 2.2 GPa (319 ksi) fol-lowed by an increase in stress level on arrivaland passage of the failure wave. It should benoted that the initial slope was measured by lat-eral gage G2. This can only be the case if thefailure wave does not have an incubation timeso the increase in lateral stress with the sweep-ing of the failure wave through the gage in-creases the initial slope in gage G1. By con-trast, gage G2 sees the arrival of the failurewave about 700 ns after the arrival of the elas-tic wave (see step at 2.2 GPa). Furthermore,these traces also confirm that the failure waveinitiates at the impact surface and propagatesto the interior of the sample. This interpreta-tion is in agreement with the impossibility ofmonitoring impact surface velocity with aVISAR system (Ref 104) when failure wavesare present.

The impact parameters used in these experi-ments are summarized in Table 7. Measuredprofiles of manganin gages were converted tostress-time profiles following the calibrationsof longitudinal and transverse manganin gagesunder shock loading given in Ref 105 and 103,respectively.

Low-VelocityPenetration Experiments

In many ballistic impact tests, often only theincident and residual velocities are recorded.


Long

itudi

nal s

tres

s, G

Pa

8

6

4

2

00 2 4 6

Time, µs

Shot 7-0889 Shot 7-1533

Spall signal

Completerelease

(a)

Tran

sver

se s

tres

s, G

Pa

4

2

00 2 4 6

Time, µs(b)

6

Shot 7-1719Front gage-G1

Shot 7-1717Front gage-G1

Gage failure

Shot 7-1719Back gage-G2

Failurewave arrival

Fig. 19 In-material gage profiles from spall experiments. (a) Longitudinal profiles. Gage profile on the left shows astrong reduction in spall strength (measurement behind the so-called failure wave front). (b) Transverse

profiles showing transverse stress histories at two locations within the glass specimen. Source: Ref 87

Flyer plate

Target plate

Backing plate

Fig. 18 Manganin gage experiment configuration.Gages G1 and G2 record transverse stress at

two locations. Gage G3 records the longitudinal stress atthe specimen back plate interface. Source: Ref 87

To understand how targets defeat projectiles,the complete velocity history of the projectilemust be recorded. Moreover, multiple instru-mentation systems are highly desirable becausethey provide enough measurements for theidentification of failure through modeling andanalysis. In this section, a new experimentalconfiguration that can record tail-velocity his-tories of penetrators and target back surfaceout-of-plane motion in penetration experimentsis presented. The technique provides multiplereal-time diagnostics that can be used in modeldevelopment. Laser interferometry is used tomeasure the surface motion of both projectiletail and target plate with nanosecond resolu-tion. The investigation of penetration in wovenglass fiber reinforced polyester (GRP) compos-ite plates also is discussed.

Experimental Setup. Penetration experi-ments were conducted with a 75 mm (3 in.)light gas gun with keyway. The experimentswere designed to avoid complete destruction ofthe target plate so that microscopy studiescould be performed in the samples. Impactortail velocity and back surface target plate veloc-ity histories were successfully measured by us-ing the setups shown in Fig. 20(a) and (b), di-rect and reverse penetration experiments,respectively.

In the case of direct penetration experiments(Fig. 20a), the projectile holder was designedsuch that a normal velocity interferometercould be obtained on a laser beam reflectedfrom the back surface of the projectile. In addi-tion to this measurement, a multipoint interfer-ometer was used to continuously record themotion of the target back surface. It should benoted that the NVI system used in this configu-ration has variable sensitivity so its resolutioncan be adjusted to capture initiation and evolu-tion of failure. The NVI records contain infor-mation on interply delamination, fiber breakageand kinking, and matrix inelasticity as theseevents start and progress in time.

A cylindrical target plate 100 mm (4 in.) indiameter and 25 mm (1 in.) thick was posi-tioned in a target holder with alignment capa-bilities. The target was oriented so that impactat normal incidence was obtained. A steelpenetrator with a 30° conical tip was mountedin a fiberglass tube by means of a PVC holder.This holder contained two mirrors and aplano-convex lens along the laser beam path.The focal distance of the plano-convex lenswas selected to focus the beam at the penetratorback surface. Penetrator tail velocities weremeasured by means of the normal velocity in-terferometer (NVI), with signals in quadrature(Fig. 20a). The interferometer beams werealigned while the penetrator was at the end ofthe gun barrel (i.e., on conditions similar to theconditions occurring at the time of impact). Thealignment consisted of adjusting mirrors M1,M2, and M3 such that the laser beam, reflectedfrom the penetrator tail, coincided with the in-cident laser beam. Through motion of the fiber-glass tube along the gun barrel, it was observedthat the present arrangement preserves beam


Table 7 Summary of parameters and results for manganin gage experiments

Thickness ofaluminum impactor Target thickness Impact velocity Normal stress

Shot No. Material mm in. mm in. m/s ft/s GPa ksi

7-0889 Soda-lime glass 3.9 0.15 5.7 0.22 906 2972 7.5 10887-1533 Soda-lime glass 2.4 0.09 5.7 0.22 917 3009 7.6 11027-1717 Aluminosilicate glass 12.7 0.50 19.4 0.76 770 2526 6.1 8857-1719 Aluminosilicate glass 14.5 0.57 19.4 0.76 878 2881 6.97 1011

9.3" 1"

PVC-ring

Impactor

Multibeamsplitter

Beamexpander

(a)

Aluminum holder

Fiberglass tube

Composite sample

Penetrator

Steel anvil

Bronze ring

To NVI/NDIaxial velocity

(b)

Fig. 20 Low-velocity penetration experiments. (a) Setup for direct penetration experiment (rod-on-plate). (b) Setupfor reverse penetration experiment (plate-on-rod). Source: Ref 107

alignment independently of the position of thepenetrator in the proximity of the target. There-fore, a considerable recording time could be ex-pected before the offset of the interferometer. Afew precautions were taken to avoid errors inthe measurement. First, the PVC holder was de-signed such that the penetrator could movefreely along a cylindrical cavity (i.e., no inter-action between the steel penetrator and PVCholder was allowed and, therefore, true deceler-ation was recorded). The penetrator was held inplace during firing by means of epoxy depos-ited at the penetrator periphery on the front faceof the PVC holder. Second, in order to avoidprojectile rotation that could offset the interfer-ometer alignment, a polytetrafluoroethylenekey was placed in the middle of the fiberglasstube. Target back surface velocities were mea-sured with a multipoint normal displacementinterferometer (NDI). Since woven compositesare difficult to polish, the reflectivity of theback surface was enhanced by gluing a 0.025mm (0.001 in.) mylar sheet, and then a thinlayer of aluminum was vapor deposited.

In the case of reverse-penetration experi-ments (Fig. 20b), composite flyer plates werecut with a diameter of 57 mm (2.25 in.) and athickness of 25 mm (1 in.). The compositeplates were lapped flat using 15 µm silicon car-bide powder slurry. These plates were mountedon a fiberglass tube by means of a backing alu-minum plate. The penetrator, a steel rod with a30° conical tip, was mounted on a target holderand aligned for impact at normal incidence. Inthese experiments, the penetrator back-surfacevelocity was simultaneously measured by

means of NDI and NVI systems. A steel anvilwas used to stop the fiberglass tube and allowthe recovery of the sample.

Experimental Results: Velocity Measure-ments. A summary of experiments is given inTable 8. The NVI signals in quadrature wereanalyzed following the procedure described inRef 106. The NDI signals were converted toparticle velocities according to the proceduredescribed in Ref 52. The impactor velocity dur-ing the penetration event, in experiments5-1122 and 6-1117, is given in Fig. 21. A ve-locity reduction of approximately 32 m/s (105ft/s) in shot 5-1122 and about 20 m/s (66 ft/s) inshot 6-1117 are observed after 100 µs of the re-corded impact. A progressive decrease in ve-locity is observed in the first 30 µs followed byan almost constant velocity and a sudden veloc-ity increase of 7 m/s (23 ft/s) at approximately60 µs. Further reduction in velocity is mea-sured in the next 40 µs. In the case of shot6-1117, the tail velocity shows a profile withfeatures similar to the one recorded in shot5-1122. These velocity histories present astructure that should be indicative of the con-tact forces that develop between penetrator andtarget, as well as the effect of damage in thepenetration resistance of GRP target plates. Itshould be noted that a projectile traveling at200 m/s (656 ft/s) moves a distance of 20 mm(0.8 in.) in 100 µs.

Back-surface velocity histories at the speci-men center measured by means of a normal dis-placement interferometer (NDI) are shown inFig. 22 for shot 5-1122, 6-0531, and 6-1117. Avelocity increase to a value of 22 m/s (72 ft/s),

followed by a decrease and increase to a maxi-mum velocity of about 50 m/s (164 ft/s), after20 µs, is measured in shot 5-1122. The tracefrom shot 6-0531 and 6-1117 shows featuressimilar to the features present in the velocityhistory recorded in experiment 5-1122. How-ever, significant differences in amplitude areobserved. A maximum particle velocity of 18m/s (59 ft/s) is observed at about 37.5 µs. Thesevelocity histories present variations such assmall humps with some apparent periodicity.Numerical simulation of the experiments, in-corporating the observed failure modes, is re-quired to interpret the various features ob-served in the velocity traces.

To confirm the velocities measured in the di-rect penetration experiment, two reverse pene-tration experiments were conducted at impactvelocities of 200 and 500 m/s (656 and 1640ft/s), experiments 6-0308 and 6-0314, respec-tively. Another objective of these experimentswas to examine rate effects in the penetrationresistance of woven-fiber composites. The inter-ferometrically measured penetrator tail veloci-ties are plotted in Fig. 23. The steel penetratorvelocity shows a progressive increase and a de-crease to almost zero velocity upon arrival ofan unloading wave generated at the penetrator-free surface. The arrival time of approximately14 µs coincides with the round-trip time of thewave through the penetrator nose back to thepenetrator tail. This feature is observed in bothexperiments. A continuous increase in velocityis recorded with velocities of 20 m/s and 32 m/s(66 and 105 ft/s) after 42 µs, respectively. Amaximum velocity of 50 m/s (164 ft/s) is re-corded in experiment 6-0314 after 65 µs. Acomparison of the velocity histories in thesetwo experiments clearly reveals that compositefailure presents moderate rate sensitivity.Moreover, velocities recorded in experiment6-0308 appear to confirm the velocity reduc-tion interferometrically recorded in experiment5-1122 (direct-penetration experiment).

Microscopy studies were performed in recov-ered samples to assess the amount of delami-nation and fiber fracture and kinking. The de-tails of this study can be found in Ref 107.


Table 8 Summary of parameters for rod-on-plate and plate-on-rod impact experiments

Impact velocity Specimen diameterExperiment No. m/s ft/s mm in. Type of experiment

5-1122 200(a) 656(a) 102 4 Direct penetration6-0308 200(a) 656(a) 57 2.25 Reverse penetration6-0314 500(a) 1640(a) 57 2.25 Reverse penetration6-0531 181.6 596 102 4 Direct penetration6-1117 180.6 593 102 4 Direct penetration

Note: For all experiments, specimen thickness was 24 mm (1 in.); impactor dimensions were 14 mm (0.56 in.) diam; 30o conical, 64 mm (2.5 in.)length. (a) Velocity estimated from gas gun calibration curve based on breech pressure. Source: Ref 107

Pen

etra

tor

velo

city

, m/s

200

195

190

185

180

175

170

165

160

0 50 100Time, µs

Shot 5-1122(V = 200 m/s)

Shot 6-1117(V = 180 m/s)

Fig. 21 Penetrator tail velocity histories recordedwith normal velocity interferometer (NVI) us-

ing the direct penetration configuration. V, velocity.Source: Ref 107

Targ

et v

eloc

ity, m

/s

50

40

30

20

10

0 20 30Time, µs

Shot 5-1122(V = 200 m/s)

Shot 6-1117(V = 180 m/s)

Shot 6-0531(V = 180 m/s)0

10

Fig. 22 Back surface normal velocity histories at thecenter of glass fiber-reinforced epoxy com-

posite target. V, velocity. Source: Ref 107

Axi

al v

eloc

ity, m

/s

5550

45

40

35

30

25

20

15

0 50

Time, µs

Shot 6-0314 (500 m/s)

Shot 6-0308 (200 m/s)10

50

10 20 30 40 60

Fig. 23 Penetrator tail velocity histories recorded withnormal displacement interferometer (NDI) in

reverse penetration configuration. Source: Ref 107

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