IntroductionThe field of tribology - defined in Webster’s Dictionary as “a science that deals with the design, fric-tion, wear and lubrication of interacting surfaces in relative motion” - has a long and important his-tory in science and technology[1]. The ancient Egyptians, for example, used water to lubricate thepath of sleds employed to transport extremely heavy objects. The first scientific studies of frictionwere carried out in the 16th century by Leonardo da Vinci who observed that the weight, but notthe shape of an object influences its frictional force. Da Vinci was also the first to introduce the con-cept of a friction coefficient as the ratio of frictional force to normal load. This and similar observa-tions led 200 years later to the development of Amonton’s Law, that states that the frictional forcebetween two objects is proportional to the normal load and independent of the apparent contactarea. In the 18th century, Coulomb verified these observations and clarified the difference betweenstatic and dynamic friction[1].

Our current understanding of the tribological properties of engineering materials recognizes thatmacroscale surfaces are never in flat contact, but rather are in contact through asperities, typically ofvarying sizes and shapes (Figure 1). At very low loads, the friction and wear properties of macroscalesystems are dominated by surface forces. These include van der Waals interactions, hydration forces,and electrostatic or double-layer forces, depending on the materials and conditions of contact[2]. Athigher loads, frictional forces reflect the properties of the asperities. The interactions between asper-ities during sliding may result in energy loss through elastic deformation, plowing, and formation ofwear debris. In steels for example, asperities under certain sliding conditions may undergo aMartensitic transformation to hard and brittle structures. These brittle structures may break off dur-ing sliding to form interfacial debris that produce wear tracks[3].

Volume 5, Number 3Mysteries of Friction and Wear Unfolding: CMS Advances the Field of Tribology

By Donald W. Brenner, Department of Materials Science and Engineering, North Carolina State University, Raleigh, NC 27695-7907

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Spotlight on Technology: Bridging The Experimental – Computational Gap:The Taylor Test as an Effective Tool to Validate Constitutive Models

George T. (Rusty) Gray III, Paul J. Maudlin, and Shuh Rong ChenLos Alamos National Laboratory, Los Alamos, New Mexico 87545

Part Two of a Two Part Special:

Computational Materials Science

Spotlight on Technology … 1

From the Editor’s Desk … 2

Calendar … 9

Modeling Ceramic Armor … 10

AMPTIAC Directory … 15

MaterialEASE 15 center insert

Tools of the Trade:

CMS Software and Hardware

The AMPTIAC Newslet ter, 2001

IntroductionFundamental and engineering studies of highstrain rate material behavior have two concerns:• Quantifying the variation of mechanical

properties, such as strength and ductility,which can vary with strain rate and tempera-ture.

• Developing physics-based models capable ofpredicting material response for use in large-scale code simulations to address engineeringproblems.Historically, little scientific or engineering

attention was paid to the effects of high strainrates on material behavior until the advent ofhigh-strain manufacturing techniques (e.g.high-speed wire drawing and cold rolling).

Additionally, the emergence of military tech-nologies concerned with ballistics, armor, anddetonation physics necessitated further knowl-edge. Interest in the high-rate mechanicalbehavior of materials has grown continuallyduring each of the last four decades. This raisedlevel of interest has been driven by the demandsfor an increased understanding of materialresponse in impact events, most notably in sup-port of conventional munitions developmentprograms. High-rate tests also provide the criti-cally-needed mechanical property data requiredas input to derive predictive constitutive modeldescriptions of materials. These descriptionsstrive to capture the fundamental synergistic

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From the Editor’s Desk“Too much of a good thing is wonderful,” Mae West once said. We at AMPTIAC recently found ourselves in a similar situation. Whenwe first broached the idea of a newsletter issue dedicated to computational materials science, we nearly took a pass. We knew it was anemerging field with a growing following, but were uncertain as to how prevalent CMS had become within the materials community.

When we sought out leaders in the field, and solicited articles from potential authors, we received about double the usual number ofpapers! On one hand, this told us that we had struck gold; that our finger was on the pulse of the materials community. On the otherhand, we had a problem – we had more first-rate articles than we could possibly hope to cram into an issue of the Newsletter!

Well, the solution to the problem was obvious. In an unprecedented move, we decided to publish two sequential issues of the news-letter dedicated to the topic of CMS. What remained was to figure out how to divide the articles between the two issues. The body of all submitted works, both from outside contributors and the AMPTIAC technical staff, proved to be an equitable balance of articlesdealing with general CMS concepts and those which addressed specific applications of CMS technology. If you read our last issue (theAMPTIAC Newsletter, Volume 5, Number 2), then you already know that it provided an introduction to the fundamentals of CMS.Consequently, it is our goal that this issue leaves our readers with an appreciation for the more practical aspects of the science.

What better way to start off this issue than with a solid, application-oriented feature? Dr. Donald Brenner, of North Carolina StateUniversity, pens this issue’s Feature Article, Mysteries of Friction and Wear Unfolding: CMS Advances the Field of Tribology. Most peopletend to think of CMS applications in terms of modeling material compositions and process simulation, but this timely feature high-lights the utility of CMS methods in the sciences of wear, friction, and lubrication (Tribology). Dr. Brenner provides the reader with agreater appreciation for both CMS and the science of tribology.

One of the oldest laws of computer science is the “Garbage in – Garbage out” principle, or GIGO, as most people know it. Modelingresults are no better or worse than the input or model used to produce it. All CMS models are ultimately nothing more than mathe-matical expressions embedded into computer algorithms. Our feature article in our last issue stressed the need to provide meaningfuldata for these models. This issue’s Spotlight on Technology addresses the importance of verifying and validating the accuracy and reality of these models. Dr. George Gray and his colleagues at the Los Alamos National Laboratory discuss some of the tools and techniques used to evaluate the efficacy and realism of constitutive models.

If you’re looking for something more hands-on, then how about testing armor? Dr. Timothy Holmquist of the Army HighPerformance Computing Research Center (AHPCRC) has kindly provided us with an article on his recent work predicting ceramicarmor behavior. Nothing beats direct experimentation, so the single best way to validate a model is to go test it for real and comparethe results against the model. This is exactly what Dr. Holmquist and his research team did with a series of ceramic armor configura-tions. You can see side-by-side comparisons of predicted and actual results from a series of projectile impact tests performed on ceram-ic armor test articles – very impressive results!

To apply the principles of CMS in the real world, you need hardware and software, which are the subjects of this issue’s edition ofMaterialEASE. If you want a snapshot of the state-of-the-art in CMS hardware and software (and we do mean a snapshot – it’s a moving target!), then this edition is for you.

Lastly, all of us at AMPTIAC would like to thank our readers for all the positive feedback we have received from our first CMS issue,including a record number of new subscription requests. We trust you will enjoy this issue just as much.

Chris Grethlein

Editor-in-Chief

The AMPTIAC Newsletter, Volume 5, Number 32

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Figure 1: Illustration of Multi-Asperity Contact Characteristic of

Engineering Materials.

Sliding surfaces often exhibit “stick-slip” behaviorrather than continuous forces. In this case, relativemotion does not occur until some critical shear stress isachieved, after which the interfaces slip to relieve theresultant stress. This occurs when the static frictionalforce is greater than the kinetic frictional force duringsliding. Stick-slip behavior depends on a number ofproperties, including the surface topology, lubrication,and the elastic, plastic and inertial properties of the slid-ing materials.

The development of magnetic storage devices, micro-electromechanical systems (MEMS), and the growinginterest in mechanical devices with nanoscale compo-nents have led to recent intense interest in micro- andnanotribology. At this scale, contact areas can reflect sin-gle-asperity conditions, and are often effectively mod-eled by flat surfaces. Several experimental methods haverecently led to new insights into this tribological regime.

In Atomic-Force Microscopy (AFM), for example,normal and tangential forces are measured as anextremely sharp tip is scanned across a surface[4]. AFMhas been used to measure friction between tips and sur-faces, and to measure frictional forces as nanoscaleobjects are manipulated along a substrate[5,6]. Anothermethod that has proven especially useful for character-izing surface interactions is the Surface ForceApparatus[7]. This instrument uses a crossed-cylinderconfiguration to measure surface forces as a function ofdistance with atomic resolution. Also worthy of note isthe use by Krim and coworkers of a Quartz CrystalMicrobalance to measure frictional forces between sur-faces and thin adsorbed layers[8].

Computational Approaches to Nano- andMicrotribologyDespite the long history of tribology, it has only beenrecently that researchers have begun to unravel the fun-damental science of friction and wear. Computer simu-lations have generated much of this new understanding,especially when the simulations are coordinated withexperimental methods like those mentioned above. Themost widely used of these simulation methods is molec-ular dynamics, a technique in which the motion of a col-lection of virtual atoms is followed by numerically inte-grating coupled classical equations of motion. Forces on

the atoms are typically modeled one of two ways.In the first, the influence of the electrons is replaced by

some analytic expression that gives interatomic forcesand energies as a function of relative atomic positions[9].This approach is well suited for large systems, and formodeling collective motion that is not especiallydependent on the details of the interatomic interactions.The second approach is to specifically include electrons,and derive interatomic forces from some approximatesolution to Schroedinger’s equation[10]. This approachis generally necessary when the results of the simulationsdepend on the details of the interatomic interactions.However, this approach can be computationally inten-sive, in some cases severely limiting the number of atomsand the total time that can be simulated.

Relative interface motion under both dry and lubri-cated conditions have been simulated, leading to impor-tant new insights into friction at the atomic scale. Evenat this scale, surfaces are not flat, but rather have topolo-gies in the surface potential that reflect atomic positions.As two surfaces slide, these “bumps” pass over oneanother, leading to energy dissipation via surface heat-ing, and depending on the material, electronic excita-tion. This conversion of the sliding work to heat isresponsible for the frictional force.

Ideally commensurate interfaces (e.g. identical sys-tems sliding past one another) lead to relatively largepotential ‘peaks’ and ‘valleys’ in the topography of theinterface. The result, recognized in simple models, dat-ing back to the 1920’s and 1930’s[11,12], is the rela-tively large frictional forces from energy dissipation asthe system moves between the relatively high potentialenergy peaks and valleys.

For incommensurate lattices, the potential energytopography during sliding is much smoother, leading toless energy dissipation and lower friction. This resultwas recently verified experimentally using a quartz crys-tal microbalance, where it was found that adsorbedgasses that form incommensurate overlayers have lowerfriction compared to similar systems that form com-mensurate overlayers[13].

A number of researchers have studied the mechanismof work-to-heat during sliding of both lubricated anddry interfaces using molecular dynamics simulations, aswell as analytic models describing heat dissipation tophonon baths. As expected, incommensurate interfacesunder dry sliding conditions are predicted to have lowerfriction[14]. In fact, Hirano and Shinjo suggested thepossibility of zero friction (or “superlubricity”) betweenincommensurate solids based on simulations that pre-dict zero static frictional force, and in some cases, pre-dict a vanishing dynamic friction[15]. Robbins haspointed out, however, that these simulations assumedharmonic interatomic interactions in the substrates[14].This assumption precludes vibrational energy transferbetween normal modes and may lead to unrealisticallylow energy dissipation during sliding.

Harrison and co-workers have examined detailed

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mechanisms of energy transfer and resulting frictionbetween diamond surfaces terminated by hydrogen andby CH3, C2H5 and C3H7 hydrocarbon species[16,17].“Collision” of the terminating species during slidingresulted in energy transfer and frictional forces withoscillating magnitudes that reflected the surface topolo-gy, and whose average values all increased with increas-ing load. However, it was found that the flexibility in thelonger chains compared to H and CH3 terminationallowed the chains to more easily avoid direct collisionsduring sliding, resulting in an effectively “smoother” sur-face and relatively lower friction at high loads.

A number of researchers have used atomic simulationsto model sliding surfaces terminated with self-assembledmonolayers (SAMs) and Langmuir-Blodgett (LB)films[18,19,20,21]. SAMs and LB films are generallycomposed of hydrocarbon chains with ten or moremonomer units. Rather than lying parallel to the surface,the hydrogen chains in SAMs and LB films lie nearly nor-mal to the surface, with the angle away from the surfacenormal (the tilt angle) determined by the chain packing,interchain interactions, and chain-surface forces.Analogously, one could imagine this with the example ofdensely packed grass on a field, with every blade beingthe same length and arranged almost vertically.

An example of a SAM is thiol chains on gold, wherethe sulfur atoms terminating the chains are chemisorbedto the gold. In contrast, LB films are initially producedin a trough, and then transferred to the interface wherethey are relatively weakly bound to the surfaces.

In simulations of sliding SAMs, Glosli andMcClelland observed two modes of energy dissipation,depending on temperature and interaction strength[18].The first (termed “plucking”) consists of an alternatingstorage of mechanical energy as strain in the films, fol-lowed by strain release and dissipation of kinetic energyinto the chains. The second was a continuous viscousflow. The dominant mechanism was dependent on thestiffness and temperature of the chain system. Similarsimulations have shown alternating frictional forces thatreflect the periodicity of the underlying lattice or perio-dicity in the tilt angles of the films[19,20].

Simulations by Harrison and co-workers examinedcorrelations between chain length, chain disorder due togauche defects and friction for hydrocarbon chains [e.g.CH3(CH2)n-1, where n = 8,13, or 22] chemisorbed todiamond surfaces[16,17]. The longer chains wereobserved to have a lower degree of disorder and lowerfriction, indicating a strong relation between disorderand energy dissipation. This trend in friction with chainlength is in agreement with experimental studies.

An area of current debate in nanotribology is the rela-tive role of energy dissipation to phonons versus elec-tronic excitations during sliding, and the influence eachhas on measured frictional forces[14]. Persson andcoworkers, for example, have predicted that the contri-bution of electronic drag to friction between incom-mensurate solids is roughly comparable to frictional

forces measured experimentally with a quartz crystalmicrobalance[22]. This is in apparent disagreement withsimulations involving only energy dissipation to phononmodes, which also claim reasonable agreement withexperiment. This remains an area of controversy[23].

An interesting example of the novel tribology ofnanostructures was recently uncovered in a study com-bining AFM and atomistic simulations of fullerenetubules on graphite. Fullerene tubules are essentiallygraphite sheets rolled into cylinders. They have beenproduced with radii as small as about a nanometer, and may have lengths of up to several microns or larger. While manipulating a fullerene tubule ongraphite using AFM, Superfine and coworkers observedthat tubules initially slide about a pivot point relativelyeasily before locking into a position in which the tubuleand graphite lattices apparently line up[5]. After ‘lock-ing-in’, it was concluded from surface images thattubules prefer to roll rather than slide while beingpushed with an AFM tip. The rolling motion itself, however, could not be imaged. This interpretation of the experimental data was tested using moleculardynamics[24] and quasi-static simulations[25].

In the molecular dynamics simulations, a single-shelltubule was placed on a graphite substrate (see Figure 2).While in the quasi-static calculations, a multi-shell nestedtubule, (which is closer to that used in the experiment)was modeled. Both sets of calculations confirmed an ener-getically preferred configuration, in which the lattices oftubules and graphite were aligned. To examine dynamicbehavior in the molecular dynamics studies, tubules wereplaced either in or out of registry with the graphite sub-strate. An impulse was applied to eachtubule in turn, and the subsequentdynamics were followed as each tubulemoved. For the out of registry case,the tubule simply slid along thesurface, with frictional forcesslowing the structure. Whenin registry, however, it was observed that thetubule initially slid,and then under-went an alter-nating rolling-sliding motionas it sloweddown. The netresult was arolling of thetubule as it moved along the substrate, but with a com-plicated mechanism that could not be discerned from theexperiment alone. An identical mechanism was independ-ently identified from the quasi-static calculations.

One of the more intriguing results from atomic sim-ulations was that as the thickness of lubricating liquidsapproached atomic scales, friction between slidinginterfaces may increase, and in some cases, may be high-

The AMPTIAC Newsletter, Volume 5, Number 34

Figure 2: Illustration from a Simulation of a Short Sectionof a Single-Walled Fullerene Nanotube on a GraphiteLattice.

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er than the sliding of non-lubricated, incommensurateinterfaces[14]. This result is contrary to macroscopic scalelubrication, and is a result of the interesting properties offluids as their containment dimensions approach molecu-lar scales. It has been inferred from experiment anddemonstrated through simulation and theory that smoothsurfaces can induce two types of ordering in liquids - a layering of the liquid parallel to the surface, and anordering in the layers due to the periodicity of the surface[14,26,27]. The former ordering results in densityfluctuations normal to the surface that decay into the liq-uid, and that are indiscernible after a few atomic spacings.

Random nanometer scale surface roughness, consistingof surface asperities that are larger than the liquid mole-cules, smears out this order. For macroscale lubrication,both types of ordering do not influence friction, and con-tinuum models appropriately describe relevant propertiesof the liquid lubricant. As the separation between the sliding surfaces decreases, such that the regions of wall-induced ordering begin to overlap, oscillations in energy,intersurface forces, and viscosity, all with respect to surfaceseparation, occur. As the separation is further reduced, theliquid layer can undergo a phase transition to a glassy state,or in some cases to a crystalline structure with an orderingthat reflects the regular potential energy of the surface.

In the glassy case, relaxation times increase dramatically,resulting in relatively large friction and quasi-stick-slipbehavior. Similarly, when the crystalline state is commen-surate with the solid, the resulting friction can be higherthan that for sliding of incommensurate solids, as discussed above.

Alternating melting and freezing transitions of molecu-larly thin lubricating layers induced by shear stress duringsliding have also been observed in simulations to exert a profound influence on frictional forces[14]. Similarbehavior has also been characterized for polymeric bound-ary lubricants.

There have also been simulations of tribochemistry(chemical reactions induced by sliding interfaces), albeitthese studies are much more limited in scope compared tothe types of friction studies discussed above. Harrison andBrenner, for example, used atomic scale simulations tocharacterize chemistry occurring at a hydrogen-terminateddiamond surface that was slid along a second diamond surface terminated by hydrogen, methyl or ethylgroups[28]. Interface sliding for the hydrogen and methylterminations did not result in any observable chemicalreactions. For the ethyl termination case, however, severalinteresting chemical reactions were observed in the simu-lations. In one simulation, for example, hydrogen atomswere sheared from the tail portion of two terminating ethylgroups and became trapped at the interface. One of thehydrogen atoms abstracted a third hydrogen atom fromthe opposite surface, creating a trapped H2 molecule andleaving radicals on each of the two surfaces. During con-tinued sliding, the radicals at the end of one of the ethylchains (created when a hydrogen atom was sheared off )formed a bond with the radical at the surface (which was

created by the abstraction reaction). As the shear forceexceeded the bond strength, the carbon-carbon bonds tothe two interfaces broke almost simultaneously, creatingan ethylene molecule trapped at the interface and radicalson the top and bottom surfaces. The second hydrogenatom created by the initial shearing event then formed abond with one of these surface radicals.

Simulations of sliding in different directions produceddifferent chemical reaction mechanisms and resulting weardebris. Although there were too few events to draw anyquantitative conclusions, the simulations did indicate anisotropic wear rate in agreement with experimental studies.

Challenges to be Addressed by Theory and ModelingWhile computational methods have contributed tremen-dously to our understanding of friction and wear at thenanometer scale, corresponding contributions to our fun-damental understanding of friction and wear at engineer-ing scales have not yet been made. There have reportedlybeen more than 300 equations related to friction and wearof engineering materials published over the last 40years[29]. Most of these expressions, however, are largelyphenomenological in nature, with little or no input fromfundamental computational studies.

The biggest challenge in using atom-based com-putational methods (as opposed to continuum-basedapproaches) to understand friction and wear in traditionalengineering applications is scale; with respect to both sizeand time. Practical considerations limit atomic simulationsto sliding speeds that are typically orders of magnitudelarger than most experimental studies (and engineeringapplications), and at present sizes up to hundreds of millions of atoms for analytic potentials[30] and hundreds(up to a few thousand) atoms for first-principles forces.This size scale is barely large enough to adequately modelsingle asperity contact conditions, and well below thatneeded to model multiple asperity contacts.

Recent advances in computational approaches, however,show promise for overcoming some of these limitations.Hybrid approaches that mix continuum and atomic-scalemodels[31,32,33,34] have recently been applied to crackpropagation[33] and nanoindentation[34] with impressivesuccess, and a similar approach could presumably be usedto model asperity contact during sliding[32].

Similarly, hybrid approaches combining mesoscale continuum defect theory with results from atomic-scalecalculations are being developed to accurately model ener-gies and stresses of materials with grain boundaries andrelated defect structures characteristic of polycrystallinematerials[35]. This approach, in principle, could also beextended to model the elastic and plastic response of engi-neering materials under shear stress during sliding, includ-ing formation of wear debris and transfer films.

There have also been impressive advances in the devel-opment of methods that efficiently model forces in mate-rials with relatively complicated bonding. Mintmire andStreitz, for example, have developed an efficient methodfor modeling charge transfer in Al-O systems, that allows

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The AMPTIAC Newsletter, Volume 5, Number 36

Don’t Let Your Work Become Part of a Landfill!The value of good materials data only appreciates with time. It cost a lot of time, effort, and money to produce yourquality data – it would be a shame if it were all for nothing! If you’re retiring, changing careers, transferring, runningout of storage space, or just want to get rid of data you no longer need, then please don’t trash it! Donate it to AMPTIAC, where the valuable products of your career will continue to be of use.

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large-scale simulations of these systems with relatively accu-rate forces[36]. Similarly, advances in computational algo-rithms in density functional theory, like the multi-gridmethods being developed by Bernholc et al[37], holdpromise for capturing the details of tribological processes.

Author’s Notes and Acknowledgements:‘This article highlights some of the contributions that compu-tational materials science (CMS) has made in the last ten yearsto our fundamental understanding of tribology. It is notintended as a comprehensive literature review, as that is avail-able elsewhere[38]. Nonetheless, it is hoped that the conceptsdiscussed here will help to illustrate how computational scien-tists have approached this field, the types of contributions thatthey are able to make, and a few of the challenges that will beaddressed in the next few years.’ - D.W. Brenner

The author would like to recognize the Tribology Program ofthe Office of Naval Research, which currently funds theauthor’s work. The author would also like to thank the pro-gram monitor, Dr. P.P. Schmidt, for his invaluable discussionsand support.

References:[1] D. Dowson, ‘The History of Tribology’ (Longman,

London, 1979); B. Bushan ‘Introduction - Measure-ment Techniques and Applications’, Chapter 1 in the CRC Handbook of Micro/Nanotribology, Second Edition, Bushan, ed. (CRC Publishers, 1998),pp. 3-80.

[2] See for example J.N. Israelachvili, Intermolecular andSurface Forces, Second Edition, (Academic Press,London, 1991).

[3] S.M. Hsu, ‘Fundamental Mechanisms of Friction andLubrication of Materials,’ Langmuir 12, 4482 (1996).

[4] See for example O. Marti, ‘AFM Instrumentation andTips,’ Chapter 2 in the CRC Handbook of Micro/Nanotribology, Second Edition, Bushan, ed. (CRC

Publishers, 1998), pp. 81-144 and references therein.[5] M.R. Falvo, R.M. Taylor, A. Helser, V. Chi, F.P.

Brooks, S. Washburn, and R. Superfine, ‘Nanometre-Scale Rolling and Sliding of Carbon Nanotubes.’Nature 397, 236 (1999).

[6] J.F. Wang, K.C. Rose and C.M. Lieber, ‘Load-Independent Friction: MoO3 Nanocrystal Lubricants,’J. Phys. Chem. B 103, 8405 (1999).

[7] J.N. Israelachvili, ‘Techniques for Direct Measure-ments of Forces Between Surfaces in Liquids at theAtomic Scale,’ Chemtracts Anal. Phys. Chem. 1, 1(1989).

[8] J. Krim and R. A. Widom, ‘Damping of a CrystalOscillator by an Adsorbed Monolayer and Its Relationto Interfacial Viscosity,’ Phys. Rev. B 38, 12184(1988).

[9] See for example D.W. Brenner and B.J. Garrison,‘Gas-Surface Reactions: Molecular DynamicsSimulations of Real Systems,’ Adv. Chem. Phys.,(Wiley, New York) 76, 281 (1989); D.W. Brenner,O.A. Shenderova and D.A. Areshkin, ‘Quantum-Based Analytic Interatomic Forces and MaterialsSimulation,’ Reviews in Computational Chemistry,K.B. Lipkowitz and D.B. Boyd, Eds., (VCHPublishers, New York, 1998), pp 213-245.

[10] See for example W. Zhong and D. Tomanek, ‘First-Principles Theory of Atomic-Scale Friction,’ Phys. Rev.Lett. 64, 3054 (1990).

[11] G.A. Tomlinson, ‘A Molecular Theory of Friction,’Philos. Mag. 7, 905 (1929).

[12] Y.I. Frenkel. and T. Kontorova, ‘On the Theory ofPlastic Deformation and Twinning,’ Zh. Eksp. Teor.Fiz. 8, 1340 (1938).

[13] J. Krim, D.H. Solina and R. Chiarello, ‘Nanotri-bology of a Kr Monolayer: A Quartz-CrystalMicrobalance Study of Atomic-Scale Friction,’ Phys.Rev. Lett. 66, 181 (1991).

continues, page 12

relationships between how the independent variables;stress, strain rate, strain, and temperature independent-ly affect the constitutive behavior of materials[1].

Robust material models capturing the physics ofhigh-rate material response are required for large-scalefinite-element simulations of complex engineer-ing problems. Some examples are:• Automotive crash-worthiness,• Aerospace impacts, including foreign-object

damage such as during bird ingestion in jetengines and meteorite impact on satellites,

• Dynamic structural loading such as thatoccurring during an earthquake,

• High-rate manufacturing processes includinghigh-rate forging and machining, and

• Conventional ordinance behavior andarmor/anti-armor interactions.Simulations of large-scale dynamic events

such as ballistic impact, foreign-object damage,or crash-worthiness are challenging engineeringproblems, where material properties underextreme conditions (large strain, high strainrates, and high temperatures) are criticallyimportant. Mathematical representation ofthese requirements is a part of the developmentof constitutive relations that are based on estab-lished physical mechanisms and extensive exper-imental testing. Models of material strength, includingtexture evolution, and damage and failure of engineer-ing materials over a wide range of temperature, strain,strain rates and stress states are needed for integrationinto continuum mechanics codes to predict thesedynamic deformation processes.

Measurement of the mechanical properties of materi-als is normally conducted via loading test samples incompression, tension, or torsion. Mechanical testingframes can be utilized to achieve nominally constantloading rates for limited plastic strains and thereby aconstant engineering strain rate. Typical screw-driven orservo-hydraulic testing machines are routinely utilizedto measure the stress-strain response of materials tostrain rates as high as 5 s-1. Specially-designed testingmachines, typically equipped with high capacity servo-hydraulic valves and high-speed control and data acqui-sition instrumentation can be used during compressiontesting to achieve strain rates as high as 200 s-1.

Above this strain rate regime, ε. > 200 s-1, alternatetechniques employing projectile driven impacts toinduce stress wave propagation in a sample materialhave been developed.

Chief among these techniques is the split-Hopkinsonpressure bar (SHPB)[2], which is capable of achievingthe highest uniform uniaxial stress loading of a specimenin compression at nominally constant strain rates (of theorder of 103 s-1). Using a SHPB, the dynamic stress-strain response of materials at strain rates up to 2 x 104

s-1 and true strains of 0.3 can be readily achieved in a sin-

gle test. Utilization of several of the aforementionedcharacterization techniques allows quantification of theconstitutive response of a material over a wide range ofstrain rates and temperatures, such as those shown inFigure 1 for unalloyed tantalum metal[1].

Incorporating constitutive material responses intolarge-scale application codes (for use in simulating engineering problems) is accomplished using a phenom-enologically analytic description, capturing the consti-tutive response in a constitutive strength model. A number of engineering strength constitutive models arefrequently used in both the industrial and defense sectors[1]. Figure 2 presents an example of theMechanical Threshold Strength (MTS) Model consti-tutive fit[1] to the unalloyed tantalum data in Figure 1.While derivation of a strength model based upon constitutive stress-strain data is sufficient for modeldevelopment, it is limited to the regime or regimes overwhich the constitutive data was quantified.

Accordingly, to assess the “robustness” of a materialstrength model to accurately predict constitutiveresponse (yielding and strain-hardening) over a widerange of loading conditions, it is critical to conduct val-idation integral testing that probes the range of variableapplicability, and therefore the physics captured by themodel. The strain rate dependence of the strength of amaterial is indirectly modeled at intermediate strainrates, i.e., 104 s-1 to 106 s-1, which is precisely the rangeof critical importance to many engineering simulations,including foreign-object damage and ballistic impact.The Taylor impact test represents a readily conductedaxisymmetric, integrated validation test which probesboth a wide range of plastic strains (deformations up toseveral hundred percent) and strain rates in excess of105 s-1.

continues, page 8

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The AMPTIAC Newsletter, Volume 5, Number 3 7

Figure 1: Compressive Stress-Strain Curves of Unalloyed Tantalum under Dynamic and Quasi-StaticDeformation at Various Temperatures.

Strain, εSt

ress

, σ (M

pa)

Unalloyed Ta

The Taylor Impact Test – A Means to Validate aConstitutive Strength ModelThe Taylor cylinder impact test, named after G.I. Taylor[3] who developed the test to screen materials for use inballistic applications during WW II, entails firing a solidcylinder rod of a material (typically 7.5 to 12.5 mm indiameter by 25 to 40-mm in length) at high velocityagainst a massive and rigid target as schematically shownin Figure 3. The deformation induced in the Taylor roddue to the impact shortens the rod as radial flow occurs atthe impact surface. The fractional change in the rodlength (difference between the final length Lf and the ini-tial length L0) can then, by assuming one-dimensionalrigid-plastic analysis, be correlated to the dynamic yieldstrength. Taylor cylinder impact testing has previouslybeen utilized to probe both the deformation responses ofmetals and alloys in the presence of large gradients of

stress, strain, and strain-rate and as a means tovalidate constitutive models. This axisymmetricintegrated test provides a straight-forwardexperimental method to examine the large-strain, high-strain-rate mechanical behavior ofmaterials, while simultaneously evaluating theaccuracy and correctness of the physics incor-porated into the constitutive models.Taylor cylinder impact tests represent integrat-ed tests rather than unique quantificationexperiments at uniform stress states or strainrates, as does the SHPB. Consequently, theTaylor test tends to be most utilized as a valida-tion experiment in concert with two- or three-dimensional application calculations.[4,5,6,] Inthis approach, the final length, cylinder profile,and bottom footprint of the Taylor sample iscompared with code simulations to validate thematerial constitutive model implemented in theapplication code. Comparisons with the recov-ered Taylor sample provide a check on howaccurately the code can calculate the gradient in

deformation stresses and strain rates leading to the finalspatial gradients of strain imparted to the cylinder duringthe impact event.

Taylor cylinder impact samples tested over a range ofimpact velocities for a variety of materials (such as Cu, Ta,Al, W-Ni-Fe, and steels relevant to armor at Los AlamosNational Laboratory) have been shown to be sensitive toaccurately capturing the influence of strain hardening,crystallographic texture, strain-rate and temperature sensi-tivity for the large-strain constitutive response of thesemetals.[5,6]

Figure 4 presents an illustration of the characterizationand modeling used to validate the constitutive response ofcrystallographically textured, unalloyed tantalum.[5,6]Processing of the tantalum plate studied has led to a pro-nounced through-thickness {111} fiber texture† leading toanisotropic constitutive response of the tantalum duringloading[5]. After testing, geometric profile data for Taylorcylinders of impacted unalloyed tantalum was generatedusing an optical comparitor. The data consist of three dig-itized side profiles for the minor and major dimension (seeFigure 4b for the major profile), and three digitized foot-prints that give the x-y cross-sectional area at the impactinterface (see Figure 4a). Validation of the tantalum con-stitutive behavior was accomplished by simulating theTaylor impact test with the explicit LaGrangian finite ele-ment code EPIC[5] in a 3D mode under the assumptionsof negligible impact-interface friction and anvil compli-ance. The cylinder was spatially modeled using 4185nodes and 17,280 single-integration-point tetrahedral ele-ments (in symmetrical arrangement). The impact eventwas simulated for 90 µs of problem time after which plas-tic deformation has reached quiescence. Calculationresults (meshes) are shown in Figure 4c in terms of late-time cylindrical major side profile and an impact-interfacefootprint.

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The AMPTIAC Newsletter, Volume 5, Number 38

Figure 3: Schematic of Taylor Impact Test Showing the Initial and FinalStates of the Cylindrical Sample.[3]

continues, page 14

Strain, ε

Stre

ss, σ

(Mpa

)Unalloyed Ta

Figure 2: The Stress-Strain Curves (Dashed Lines) of Unalloyed Tantalum Showing the Fit to theMTS Model as Open Symbols.

Rigid Anvil

Lo

X

Lf

BeforeImpact

AfterImpact

The AMPTIAC Newsletter, Volume 5, Number 3 9

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4th BCC Conference on Fine, Ultrafine and Nano Particles 2001October 14 - 17, 2001 Chicago, ILBusiness Communications Co., Inc.25 Van Zant StreetNorwalk, CT 06855 USAPhone: (203) 853-4266Fax: (203) 853-0348Email: sales@bccresearch.comWeb Link: www.bccresearch.com

Carbon Fiber 2001October 16 - 18, 2001Bordeaux, FranceIntertech Conferences19 Northbrook Office ParkPortland, MA 04105 USAPhone: (207) 781-9603Fax: (207) 781-2150Email: dboucher@intertechusa.com

Infrared Technology, Theory andApplications October 22 - 26, 2001Rockville, MDUniv. of Michigan/Ctr, for Professional Dev2121 Bonisteel, 273 Chrysler CenterAnn Arbor, MI 48109-2092 USAFax: (734) 647-7182Web Link: cpd.engin.umich.edu

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Materials Solutions Conference & Expo - 2001November 5 - 8, 2001Indianapolis, INContact: Lana ShapowalASM International9639 Kinsman RoadMaterials Park, OH 44073-0002 USAPhone: (440) 338-5151Fax: (440) 338-4634Email: lshapowa@asminternational.orgWeb Link: www.asm-intl.org

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Integrating Materials Science intoEngineering Structures and Devices November 11 - 16, 2001Lake Arrowhead, CAContact: Professor Krishna RajanRensselaer Polytechnic InstituteEmail: rajank@rpi.edu / zadors@rpi.edu (sec.)

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Ceramic materials have been considered for armor appli-cations for over 30 years. These materials are very strongin compression, but weak in tension. They are also verybrittle, but can have significant strength after fracturewhen under compression. They also tend to be light-weight when compared to other armor materials such asmetals. These characteristics make ceramics well suitedfor armor applications, but also make them very complexand difficult to understand.

Effective armor design can be enhanced, its cost reduced,and its behavior better understood by the use of computa-

tions, if such computations adequately represent theceramic’s behavior. Recently, a coordinated effort involvingresearchers at the Army High Performance ComputingResearch Center (AHPCRC), the Weapons and MaterialsResearch Directorate at the U.S. Army ResearchLaboratory (ARL), and the U.S. Army Tank-AutomotiveResearch, Development, and Engineering Center(TARDEC) was initiated to improve the Army’s computa-tional capability to simulate ceramic armor systems.

Of particular interest to the Army is the ability to sim-ulate and understand the effect of layered ceramic armor.TARDEC has demonstrated experimentally that a singlelayer of ceramic, as opposed to many layers, dramaticallyincreases armor effective-ness. Figure 1 presents across-section of two armordesigns that were impactedby a projectile traveling atapproximately 1200 m/s.The armor designs consist-ed of aluminum nitride(AlN) ceramic placed ontop of an aluminum base.The design on the left usesa solid layer of AlN whilethe design on the right usesthree layers of AlN, bothwith the same total thick-ness of ceramic material.The projectile impacted the

target from the top. The three-layer design allowed theprojectile to penetrate completely through all three layersof AlN and into the aluminum base. The single-layerdesign stopped the projectile well before reaching the alu-minum base.

The computer code used to study these phenomena isthe EPIC LaGrangian finite element code[1]. Using anumerical technique identified by the author, along witha material model to describe the aluminum nitride behav-ior, excellent progress has been made to simulate theseevents[2]. Computations investigating the effect of layer-

ing, including a comparison to experi-mental results, are presented in Figure 2.AlN targets of one, two, three, and sixlayers were used. For all cases, the totalAlN thickness equaled 38.1mm. All tar-gets were impacted by a tungsten projec-tile at a nominal impact velocity of 1150m/s. The computations were performedin the 2D axisymmetric configuration.The right side of Figure 2 summarizes thecomputed and experimental results forthe four target configurations. The resultsare presented in terms of total penetrationnormalized by the projectile length. Forthe two-, three- and six-layer targets,multiple experiments were performed.

For the single-layer target only one experiment was per-formed. The computed results compare well to the exper-iments and both clearly show the degradation in targetresistance as the number of layers is increased.

The left side of Figure 2 shows the computational results forthe one-layer and six- layer AlN ceramic targets at 20 µs andat completion. The shaded region indicates completely frac-tured material. Careful examination of the computations iden-tify why layering reduces the ceramic resistance. In the six-layertarget, ceramic fracture initiates at the rear surface of the indi-vidual tiles and propagates upward through the tile. The frac-turing that occurs by this process is dominated by tensile fail-ure. Conversely, in the one-layer target, most of the fracture

Figure 1: Impact results for a tungsten projectile impacting one-layer and three-layer aluminum nitrideceramic targets.

The AMPTIAC Newsletter, Volume 5, Number 310

Modeling Ceramic Armor

Figure 2: Comparison of the computational results and experiments for layered targets.

Penetration Penetration

a) One-Layer AIN Target b) Three-Layer AIN Target

1 Layert=20 µs

6 Layers Numbers of Layers of Ceramic1 2 3 6

t=computation complete

L/D=6 (L=50mm) Tungsten ProjectileImpact Velocity = 1150 m/s

Ptotal Penetration DepthL Projectile LengthD Projectile Diameter

Air

Ceramic

Aluminum

ExperimentComputation

Projectile did notpenetrate into aluminum

0

0.5

1.0

1.5

P tot

al/LD = 1.0

Aluminum

AlN

The AMPTIAC Newsletter, Volume 5, Number 3 11

occurs from compression. This is because ceramic is weakerin tension than compression, thus it takes less energy to frac-ture ceramic in tension. A target that is dominated by ten-sile fracture will absorb less energy and be less resistant topenetration. This effect is most apparent when comparingthe response of the one-layer target to the six-layer target, asshown on the left in Figure 2.

The results in Figure 2 also identify the shape of thefractured zone that occurs from the damage process.The fractured zone typically takes the shape of a cone,as is shown for the six-layer target at 20 µs. This coneof fractured material has been observed experimentallyand is often referred to as the “fracture conoid”[3].Another observation of the computed results is theapparent reduction in the area of the fractured materi-al region when the ceramic is layered. This behavior hasalso been observed experimentally[4]. This work is veryencouraging to the AHPCRC and Army researchers, inthat the computations not only provide concurrencewith the experimental penetration depths, but also withobserved characteristics of the penetration process.

While the work discussed to this point has been eval-uated in two dimensions, the most interesting andimportant capabilities are in three dimensions. Currentefforts at the AHPCRC and TARDEC include extend-ing present capabilities to model ceramic behavior tothree dimensions. Figure 3 demonstrates current 3Dcapabilities by presenting a computation of a projectileimpacting a ceramic-metal target laminate. The ceram-ic is on the top and the metal is on the bottom. Theprojectile impacts at a 45-degree obliquity. The com-putation shows the complex fracture pattern thatoccurs from impact and penetration. Although 3Deffects can be modeled computationally for idealizedarmor systems, eventually it will be necessary to model

ceramic armor systems on actual vehicles. These com-putations will be extremely large and will require thehigh performance computing capabilities available atthe AHPCRC. Current and future work at theAHPCRC is focusing on evaluating and improving thecapabilities to model ceramic armor such that compu-tations will become a more integral part of the armordesign process.

Timothy HolmquistStaff Scientist: Computational Solid Mechanics, Army High Performance Computing Research

Center/Network Computing Services, Inc. 1200Washington Ave.

South Minneapolis, MN 55415. Office: 612-337-3561, Fax: 612-337-3400

References[1] G. R. Johnson, R. A. Stryk, T. J. Holmquist, and S. R.Beissel, “Numerical Algorithms in a LaGrangianHydrocode,” Report No. WL-TR-1997-7039, WrightLaboratory, June, 1997.[2] T. J. Holmquist, D. W. Templeton, and K. D. Bishnoi,“Constitutive Modeling of Aluminum Nitride for LargeStrain, High-Strain Rate, and High-Pressure Aplications,”Int. J. Impact Eng., 25 (2001) 211-231.[3] M. Wilkins, “Third Progress Report of Light ArmorProgram,” UCRL-50460, Lawrence Livermore NationalLaboratory, 1968.[4] K. Weber, M. El-Raheb and V. Hohler, “ExperimentalInvestigation on the Ballistic Performance of Layered AlNCeramic Materials and Pyrex,” Proceedings of the 18th Int.Symposium on Ballistics, San Antonio, TX, 1999, p. 1247-54. ■

(Reprinted from the AHPCRC Bulletin, Vol. 11, No. 2, 2001)

Figure 3: 3D computation of a bullet impacting aceramic-metal target. The results are shown at 5 µs,10 µs, and 30 µs after bullet impact.

t = 30 µs

t = 5 µs

t = 10 µs

Ceramic/metal target

The AMPTIAC Newsletter, Volume 5, Number 312

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[14] M.O. Robbins and E.D. Smith, ‘Connecting Molecular-Scale and Macroscopic Tribology,’ Langmuir 12, 4543(1996) and references therein.

[15] M. Hirano and K. Shinjo, ‘Atomistic Locking andFriction,’ Phys. Rev. B 41, 11837 (1984).

[16] J.A. Harrison, C.T. White, R.J. Colton and D.W.Brenner, ‘Molecular-Dynamics Simulations of Atomic-Scale Friction of Diamond Surfaces,’ Phys. Rev. B 46,9700 (1992).

[17] J.A. Harrison, C.T. White, R.J. Colton and D.W.Brenner, ‘Effects of Chemically-Bound, FlexibleHydrocarbon Species on the Frictional Properties ofDiamond Surfaces’ J. Phys. Chem. 97, 6573 (1993).

[18] J.N. Glosli and G.M. McClelland, ‘Molecular DynamicsStudy of Sliding Friction of Ordered Organic Molecules’Phys. Rev. Lett. 70, 1960 (1993).

[19] K.J. Tupper and D.W. Brenner, ‘Molecular DynamicsSimulations of Friction in Self-Assembled Monolayers,’Thin Solid Films 253, 185 (1994).

[20] A. Koike and M. Yoneya, ‘Molecular DynamicsSimulations of Sliding Friction of Langmuir-BlodgettMonolayers,’ J. Chem. Phys. 105, 6060 (1996).

[21] A.B. Tutein, S.J. Stuart, and J.A. Harrison, ‘Role ofDefects in Compression and Friction of AnchoredHydrocarbon Chains on Diamond,’ Langmuir 16, 291(2000).

[22] B.N. Persson, D. Schumacher and A. Otto, ‘SurfaceResistivity and Vibrational Damping in AdsorbedLayers,’ Chem. Phys. Lett. 178, 204 (1991).

[23] C. Daly and J. Krim, ‘Sliding Friction of Solid XenonMonolayers and Bilayers on Ag(111),’ Phys. Rev. Lett.76, 803 (1996).

[24] J.D. Schall and D.W. Brenner, ‘Molecular DynamicsSimulations of Carbon Nanotubule Rolling and Slidingon Graphite,’ Molecular Simulation 25, 73 (2000).

[25] A. Buldum and J. P. Lu, ‘Atomic Scale Sliding andRolling of Carbon Nanotubes,’ Phys. Rev. Lett. 83, 5050(1999).

[26] P.A. Thompson and M.O. Robbins, ‘Shear Flow NearSolids: Epitaxial Order and Flow Boundary Conditions,’Phys. Rev. A 41, 6830 (1990)

[27] U. Landman, W.D. Luedtke, M.W. Ribarsky, ‘Structural

and Dynamical Consequences of Interactions inInterfacial Systems,’ J. Vac. Sci. Technol. A 7, 2829 (1989).

[28] J.A. Harrison and D.W. Brenner, ‘SimulatedTribochemistry: An Atomic-Scale View of the Wear ofDiamond,’ J. Am. Chem. Soc. 116, 10399 (1995).

[29] K.C. Ludema, ‘Mechanism Based Modeling of Frictionand Wear,’ Wear 200, 1 (1996).

[30] P. Vashishta, et al. ‘Multimillion Atom Simulations ofNanostructured Materials on Parallel Computers -Sintering and Consolidation, Fracture, and Oxidation,’Progress of Theoretical Physics Supplement 138, 175 (2000).

[31] S. Kohlhoff, P. Gumbsch and H.F. Fischmeister, ‘CrackPropagation in BCC Crystals Studies with a CombinedFinite-Element and Atomistic Model,’ Phil. Mag. 64A,851 (1991).

[32] E.B. Tadmor and R. Phillips, Mixed Atomistic andContinuum Models of Deformation in Solids,’ Langmuir12, 4529 (1996).

[33] J.Q. Broughton, F.F. Abraham, N. Bernstein and E.Kaxiras, ‘Concurrent Coupling of Length Scales:Methodology and Application,’ Phys. Rev. B 60, 2391(1999).

[34] G.S. Smith, E.B. Tadmor and E. Kaxiras, ‘MultiscaleSimulation of Loading and Electrical Resistance inSilicon Nanoindentation,’ Phys. Rev. Lett. 84, 1260(2000).

[35] O. Shenderova, D.W. Brenner, A. Nazarov, A. Romanov,L. Yang, ‘Multiscale Modeling Approach for CalculatingGrain Boundary Energies from First Principles,’ Phys.Rev. B 57, R3181(1998).

[36] F.H. Streitz and J.W. Mintmire, ‘Molecular DynamicsSimulations of Elastic Response and Tensile Failure ofAlumina,’ Langmuir 12, 4609 (1996).

[37] J.L. Fattebert and J. Bernholc, ‘Towards Grid-BasedO(N) Density-Functional Theory Methods: OptimizedNonorthogonal Orbitals and Multigrid Acceleration,’Phys. Rev. B 62, 1713 (2000).

[38] See for example J.A. Harrison, S.J. Stuart and D.W.Brenner, ‘Atomic-Scale Simulation of Tribological andRelated Phenomena,’ Chapter 10 in the CRC Handbookof Micro/Nanotribology, Second Edition, Bushan, ed.(CRC Publishers, 1998), pp. 525-596. "

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NEW FROM AMPTIAC!

Codes, models, data visualization, model validation…What do all these terms mean?

Looking to learn more about the exciting field of Computational Materials Science?

AMPTIAC is pleased to introduce its first specialized product in this area:Computational Materials Science, a Critical Review and TechnologyAssessment (CRTA). As a bonus with your order of this product, youwill also receive a complimentary copy of the proceedings from theDOD’s recent workshop on computational materials science. TheCD-ROM contains the report, all the speakers’ presentationsand the attendee list.

CRTA: At the request of Dr. Lewis Sloter, StaffSpecialist, Materials and Structures, in the Office ofthe Deputy Under Secretary of Defense forScience & Technology, AMPTIAC surveyedDOD, government, and academic efforts currently studying materials sciencethrough the use of computational methods,and from this research compiled the CRTA:Computational Materials Science. The report provides anin-depth examination of the field, and describes many of the programs, tech-niques, and methodologies in use and under development today. The report is a stand-aloneintroduction and primer to CMS nomenclature, tools, and methodologies, as they are applied tomaterials engineering, and is now available from AMPTIAC in a CD-ROM format.

Proceedings: Dr. Sloter also requested AMPTIAC to organize a workshop to bring togethersome of the nation’s leaders in CMS. They were invited to discuss their programs and where theythink CMS is headed in the future. Dr. Sloter wished to compile their input into strategies and ini-tiatives that will influence future DOD and Government efforts to lend support and direction tothis field.

The proceedings of the workshop, including speakers’ presentations and the strategy/initiativesummary are included free of charge with purchase of the CMS CRTA. For information or order-ing, please contact Gina Nash, AMPTIAC product sales, at (315) 339-7047, or by email atgnash@iitri.org.

The AMPTIAC Newsletter, Volume 5, Number 3 13

The AMPTIAC Newsletter, Volume 5, Number 314

These results are compared with the experimental shapes(circular points). The calculated elliptical footprint shown inFigure 4c has an eccentricity (ratio of major to minor diame-ters) of about 1.20, which compares well with the experimen-tal footprints which ranged from 1.18 - 1.23 (von Misesisotropy would produce a round footprint with an eccentricityof 1). The major side profile compared in Figure 4d indicatesthat the final length agrees well with the experimental length,and that the axial distribution of plastic strain also tracks verywell with the experimental profiles. This study demonstratesthat for unalloyed tantalum and using the MTS strengthmodel previously derived for tantalum,[1,5] that very goodagreement was realized between the calculated and experimen-tal plastic deformation field for the final shapes of the Taylorimpact test cylinders, including the anisotropic shape of thecylinders due to texture. This example demonstrates the stateof the art of constitutive modeling coupled with a 3-D descrip-tion of the yield anisotropy of a material, as probed using anintegrated impact test. The direction of future constitutivemodel development will dictate that further materials effortscharacterize increasingly complicated deformation mecha-nisms as part of their constitutive behavior.

ConclusionsRobust material strength models capturing the physics of high-rate material response are required to support large-scale finite-element simulations. These models must be capable of predict-

ing the loading in many complex engineeringproblems. The realization of the importance andneed of efforts to link experiments and modelingthrough validation and verification activitieswithin the computational mechanics communityis reflected by the recent establishment ofVerification and Validation Committees withinAIAA and ASME. Due to its ability to probelarge gradients of stress, strain, and strain-rate,the Taylor cylinder test offers an axisymmetric,readily conducted experimental method. By thismethod, one may examine the large-strain, high-strain-rate mechanical behavior of materials.Simultaneously, the Taylor test exhibits a largedegree of sensitivity when evaluating the effec-tiveness and correct “physics” incorporation inconstitutive models.

References[1] Shuh Rong Chen and G.T. Gray III,

“Constitutive Behavior of Tantalum and Tantalum-TungstenAlloys,” Metallurgical and Materials Transactions A, 27A, pp.2994-3006, (1996).

[2] G.T. Gray III, “Classic Split-Hopkinson Pressure Bar Technique,”ASM – Handbook Volume 8 “Mechanical Testing andEvaluation, edited by H. Kuhn and D. Medlin, (ASMInternational, Metals Park, Ohio 44073-0002), pp. 462-476.(2000).

[3] G.I. Taylor, “The Use of Flat-Ended Projectiles for DeterminingDynamic Yield Stress, I. Theoretical Considerations,” Porch. Roy.Soc. London, A-194, 289 (1948).

[4] P.J. Maudlin, J.C. Foster, Jr. and S. E. Jones, “On the Taylor Test,Part III: A Continuum Mechanics Code Analysis of Steady PlasticWave Propagation,” Int. J. Impact Engng., 19, No. 3, pp. 231-256 (1997).

[5] P.J. Maudlin, J.F. Binge, J.W. House and S.R. Chen, “On theModeling of the Taylor Cylinder Impact Test for OrthotropicTextured Materials: Experiments and Simulations,” Int. J.Plasticity, 15, pp. 139-166 (1999).

[6] P.J. Maudlin, G.T. Gray III, C.M. Cady, and G.C. Kaschner,“High-Rate Material Modeling and Validation Using the TaylorCylinder Impact Test,” Phil. Trans. Royal Soc., Series A, Vol. 357,(1999).

† Metals with many crystals oriented in the same direction are said to behighly textured. A {111} textured fiber is a polycrystalline fiber withmost crystals oriented along a similar direction (typically written as apercentage of grains whose orientations are within x degrees of thespecified direction). ■

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Figure 4: Photographs of the Post-Test Geometry for a Tantalum Taylor Specimen Showing the (a) Footprint,(b) Side-Profile, and a Comparison of the (c) Digitized Footprints and (d) Major Side Profiles of ThreePost-Test Geometries for Tantalum Taylor Specimens Compared to the EPIC 3-D Code Simulation of theTaylor Test.

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(a) Side Profile

(d)(c)

PlateThickness

Plastic Strain

5 mm

5 mm 2.83

2.26

1.70

1.13

0.57

0.00

AMPTIAC DirectoryGovernment Personnel IITRI Personnel

TECHNICAL MANAGER/COTRDr. Lewis E. Sloter IIStaff Specialist, Materials & StructuresODUSD(S&T)/Weapons Systems1777 North Kent St., Suite 9030Arlington, VA 22209-2110(703) 588-7418, Fax: (703) 588-7560Email: lewis.sloter@osd.mil

ASSOCIATE COTRS

CERAMICS, CERAMIC COMPOSITES

Dr. S. Carlos SandayNaval Research Laboratory4555 Overlook Ave., S.W. Code 6303Washington, DC 20375-5343(202) 767-2264, Fax: (202) 404-8009Email: sanday@anvil.nrl.navy.mil

ORGANIC STRUCTURES

& ORGANIC MATRIX COMPOSITES

Roger GriswoldDivision ChiefU.S. Air ForceAFRL/MLS2179 Twelfth St., Bldg. 652Wright-Patterson AFB, OH 45433-7702(937) 656-6052Email: roger.griswold@wpafb.af.mil

METALS, METAL MATRIX COMPOSITES

Dr. Joe WellsArmy Research LaboratoryWeapons & Materials Research DirectorateAMSRL-WM-MCAPG, MD 21005-5069(410) 306-0752, Fax: (410) 306-0736Email: jwells@arl.army.mil

ELECTRONICS, ELECTRO-OPTICS, PHOTONICS

Robert L. DenisonAFRL/MLPO, Bldg. 6513005 P Street, STE 6Wright-Patterson AFB, OH 45433-7707(937) 255-4474 x3250, Fax: (937) 255-4913Email: robert.denison@wpafb.af.mil

ENVIRONMENTAL PROTECTION

& SPECIAL FUNCTION MATERIALS

Dr. James MurdayNaval Research Laboratory4555 Overlook Ave., S.W. Code 6100Washington, DC 20375-5320(202) 767-3026, Fax: (202) 404-7139Email: murday@ccsalpha3.nrl.navy.mil

DEFENSE TECHNICAL INFORMATION CENTER

(DTIC) POCMelinda Rozga, DTIC-AI8725 John J. Kingman Road, STE 0944Ft. Belvoir, VA 22060-6218(703) 767-9120, Fax: (703) 767-9119Email: mrozga@dtic.mil

DIRECTOR, AMPTIACDavid Rose201 Mill StreetRome, NY 13440-6916(315) 339-7023, Fax: (315) 339-7107Email: drose@iitri.org

DEPUTY DIRECTOR, AMPTIACChristian E. Grethlein, P.E.201 Mill StreetRome, NY 13440-6916(315)-339-7009, Fax: (315) 339-7107Email: cgrethlein@iitri.org

TECHNICAL DIRECTORS

METALS, ALLOYS, METAL MATRIX

COMPOSITES (ACTING)Edward J. Vesely215 Wynn Drive, Suite 101Huntsville, AL 35805(256) 382-4778, Fax: (256) 382-4701Email: evesely@iitri.org

CERAMICS, CERAMIC COMPOSITES

Dr. Lynn Neergaard215 Wynn Drive, Suite 101Huntsville, AL 35805(256) 382-4773, Fax: (256) 382-4701Email: lneergaard@iitri.org

ORGANIC STRUCTURES & ORGANIC MATRIX COMPOSITES

Jeffrey Guthrie201 Mill StreetRome, NY 13440(315) 339-7058, Fax: (315) 339-7107Email: jguthrie@iitri.org

ELECTRONICS, ELECTRO-OPTICS, PHOTONICS

Kent Kogler3146 Presidential DriveFairborn, OH 45324(937) 431-9322, Fax: (937) 431-9325Email: kkogler@iitri.org

ENVIRONMENTAL PROTECTION & SPECIAL

FUNCTION MATERIALS (ACTING)Bruce E. SchulteIIT Research Institute2251 San Diego Ave., Suite A218(619) 260-6080, Fax: (619) 260-6084Email: bschulte@iitri.org

The AMPTIAC Newsletter, Volume 5, Number 3 15

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We greatly appreciate your help in keeping our records current. Yourupdates allow us to continue providing our readership with the best possible source of valuable materials news and information. Additions,deletions and corrections may be sent by email to amptiac@iitri.org, telephoned to (315) 339-7092, faxed to (315) 339-7107, or mailed toAMPTIAC, 201 Mill St., Rome, NY 13440-6916. ■

Inside this Issue …

Mysteries of Friction and Wear Unfolding: CMS Advances the Field of Tribology

Spotlight on Technology:Bridging The Experimental – Computational Gap:

The Taylor Test as an Effective Tool to Validate Constitutive Models

Modeling Ceramic Armor

And more …

Computational Materials Science…Part Two of a Two Part Special!

A D VA N C E D M AT E R I A L S A N D P R O C E S S E S T E C H N O L O G Y

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