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Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities

There are two important challenges to be considered in improving protection systems. The first is to develop materials that are more efficient than existing materials, and the second is to design protection systems that optimally exploit existing or improved materials and in which the materials are physically arranged to optimize their protective properties. Advanced simulations and experimental methods are important for meeting both challenges.

Protection materials must be modeled on the atomic and microstructural levels such that their crystalline structure and microstructure can be computationally modeled to determine how changes at those levels affect their macrostructural (continuum) properties. Although there is no particular prescribed way to design materials with improved performance, computational methods enhance our understanding and give us insights into the synthesis and fabrication processes.

In addition to improving nano- and microstructural modeling techniques, researchers must ensure that the models can feed into new continuum models such that the net effect of the new materials can be assessed at the macroscopic level, which is the level of interest for an application. These multiscale, multiphysics computations could take the form of separate computations on the micro and macro levels or they could be integrated and performed in a single computation. Finally, the computational capabilities for complex material systems must be improved as well, such that system designs can be optimized quickly, accurately, and confidently with uncertainties quantified.

Protection materials and material systems made up of combinations of materials have attracted attention for many years. A substantial community of experimentalists, analysts, and armor designers is dedicated to improving existing protection capabilities and to discovering new materials and material combinations. This chapter takes a broad view of the underlying science base and reviews current activities with an eye to identifying opportunities in materials science and mechanics (theoretical, experimental, and computational) that could significantly advance protection performance.

The range of materials in use today for protection applications is quite remarkable, spanning metals, ceramics, and polymers. Materials for protection are combined in various ways, including ceramics constrained by metals or polymers and layered metal/ceramic/polymer systems. Some of the materials can be used as composite systems while others are protective structures in their own right. This chapter opens with a brief survey of the status of simulation capabilities for several of the most important systems, including simulations for the penetration of ceramic and metallic targets by projectiles and for the blast resistance of metallic plate structures. It should be noted at the outset that in spite of decades of concerted research efforts to develop simulation methods, the design of protection systems today still relies heavily on the make-it-and-shoot-it empirical approach. Meanwhile, simulations have reached the point where they can provide insight into system behavior and be used to point to promising possibilities. One objective of this report is to identify scientific opportunities that will elevate simulation methods to an equal partnership with empirical methods for advancing protection systems.

The following tools are needed for accurate simulation for most applications of structural materials:

  • Knowledge of material response described by sound constitutive models characterizing both the deformation and failure over a wide range of strain rates, temperatures, and multiaxial stresses.
  • Computational methods capable of capturing deformation and fracture under intense dynamic loads.
  • Experimentation to supply basic material inputs to the constitutive models implemented in the computational codes and to provide performance data against which the simulations can be checked.

These three tools—constitutive models, computational methods, and experimentation—underlie simulation fidelity and are critical for protection materials because their be-



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4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities There are two important challenges to be considered in The range of materials in use today for protection appli- improving protection systems. The first is to develop mate- cations is quite remarkable, spanning metals, ceramics, and rials that are more efficient than existing materials, and the polymers. Materials for protection are combined in various second is to design protection systems that optimally exploit ways, including ceramics constrained by metals or polymers existing or improved materials and in which the materials and layered metal/ceramic/polymer systems. Some of the are physically arranged to optimize their protective proper- materials can be used as composite systems while others are ties. Advanced simulations and experimental methods are protective structures in their own right. This chapter opens important for meeting both challenges. with a brief survey of the status of simulation capabilities for Protection materials must be modeled on the atomic and several of the most important systems, including simulations microstructural levels such that their crystalline structure and for the penetration of ceramic and metallic targets by projec- microstructure can be computationally modeled to determine tiles and for the blast resistance of metallic plate structures. how changes at those levels affect their macrostructural It should be noted at the outset that in spite of decades of (continuum) properties. Although there is no particular pre- concerted research efforts to develop simulation methods, scribed way to design materials with improved performance, the design of protection systems today still relies heavily on computational methods enhance our understanding and give the make-it-and-shoot-it empirical approach. Meanwhile, us insights into the synthesis and fabrication processes. simulations have reached the point where they can provide In addition to improving nano- and microstructural mod- insight into system behavior and be used to point to promis- eling techniques, researchers must ensure that the models can ing possibilities. One objective of this report is to identify feed into new continuum models such that the net effect of scientific opportunities that will elevate simulation methods the new materials can be assessed at the macroscopic level, to an equal partnership with empirical methods for advancing which is the level of interest for an application. These mul- protection systems. tiscale, multiphysics computations could take the form of The following tools are needed for accurate simulation separate computations on the micro and macro levels or they for most applications of structural materials: could be integrated and performed in a single computation. Finally, the computational capabilities for complex material • Knowledge of material response described by sound systems must be improved as well, such that system designs constitutive models characterizing both the defor- can be optimized quickly, accurately, and confidently with mation and failure over a wide range of strain rates, uncertainties quantified. temperatures, and multiaxial stresses. Protection materials and material systems made up of • Computational methods capable of capturing defor- combinations of materials have attracted attention for many mation and fracture under intense dynamic loads. years. A substantial community of experimentalists, analysts, • Experimentation to supply basic material inputs to and armor designers is dedicated to improving existing the constitutive models implemented in the computa- protection capabilities and to discovering new materials and tional codes and to provide performance data against material combinations. This chapter takes a broad view of the which the simulations can be checked. underlying science base and reviews current activities with an eye to identifying opportunities in materials science and These three tools—constitutive models, computational mechanics (theoretical, experimental, and computational) methods, and experimentation—underlie simulation fidelity that could significantly advance protection performance. and are critical for protection materials because their be- 35

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36 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS is the Johnson-Cook3 relation, which has been used in many havior is pushed to the extreme. This is particularly true for simulations of ballistic penetration. Much of what is covered recent simulations of this type. There are six constants in this in this chapter applies to both ballistic and blast assaults, but constitutive law that must be chosen to give the best possible for the most part the discussion will be cast in the context of fit to the data on the material. Supplementing the Johnson- ballistic assaults owing to the extreme demands they place Cook relation is an equation relating the temperature increase on the theoretical and experimental knowledge of material to plastic deformation. In addition to accounting for the ef- response and on numerical simulation. fect of stress state, the constitutive model accounts for the After presenting three examples of current capabilities, effects of the strain rate and thermal softening on plastic the committee discusses present-day experimental methods. deformation and can capture some aspects of adiabatic shear Its discussion underscores the importance of understanding localization. To calibrate the constitutive laws for a given and characterizing the basic mechanisms of deformation and material, an extensive suite of tests must be performed, from fracture in advancing protection materials. The committee tensile and compressive stress-strain tests up to tests at large goes on to address opportunities and challenges in experi- strains in differing material orientations and temperatures, with strain rates as high as 104 s–1. The Johnson-Cook de- mental and computational methods. formation relation is supplemented by a material fracture criterion that usually employs a critical value of the equiva- THREE EXAMPLES OF CURRENT CAPABILITIES FOR lent plastic strain, dependent on the stress triaxiality. Stress MODELING AND TESTING triaxiality is the ratio of hydrostatic tension to the von Mises Three examples illustrate current capabilities for simu- effective stress. A series of notched-bar tensile ductility tests was used by Børvik et al.4 to calibrate the critical effective lating the actual test performance of protection materials and highlight opportunities for further advances. They are (1) plastic strain at fracture as a function of stress triaxiality. As projectile penetration of an aluminum plate; (2) projectile this outline makes clear, the characterization of a material penetration of ceramic plates; and (3) blast loading of steel for input into constitutive models is a considerable task in sandwich plates. These exemplary cases demonstrate that a its own right. rational approach to armor design based on computational To simulate the penetration of a hard, ductile metal and experimental methods is feasible. It is not the com- target, the numerical method must account for large plastic mittee’s intention to cover all possible armor systems or to strains, for dynamic effects, including inertia and material bound armor performance characteristics. rate dependence, and for material failure in the form of shear-off or separation. The simulations reported here use the finite-element code LS-DYNA5 for the computations. Projectile Penetration of High-Strength Aluminum Plates For several decades, finite-element codes have been able to Accurate simulation of projectile penetration of metal model large strains, but the intense deformations encountered plates is being worked on using all three tools, and several in penetration are challenging because they involve the diffi- groups have achieved predictive success. A recent study by cult problem of remeshing to avoid overly distorted elements. Børvik et al.1 addresses the penetration of plates of 7075 It is also important to model the material failure response aluminum by two types of projectiles. The authors are from after the critical plastic strain has been attained. Current a research group in Norway noted for its emphasis on each procedures usually erode an element during the final failure of these three tools. process, stepping down its stress to zero and finally deleting Figure 4-1 shows a blunt projectile and an ogive-nosed the element. In addition, it is essential to account for the projectile, both of hardened steel (projectiles such as these pressure and friction exerted by the projectile on the plate. are often used in unclassified studies) exiting a 20-mm-thick The simulation challenge presented by projectile pen- plate of AA7075-T651 aluminum. Figure 4-2 presents a plot etration owing to distortion of the meshes is evident in of the exit velocity of the projectile as a function of its initial Figure 4-4. The blunt-nosed projectile produces shear local- velocity before impact. As mentioned in Chapter 2, the initial ization through the thickness of the plate, followed by shear- velocity at which the projectile just manages to penetrate the off, which creates a plug of material that is pushed ahead of plate with zero residual velocity is known as the ballistic the projectile. In contrast, the ogive-nosed projectile pushes limit V0; Figure 4-3 presents the results of numerical simula- 3Johnson, G.R., and W.H. Cook. 1983. A constitutive model and data for tions of these tests. metals subjected to large strains, high strain rates, and high temperatures. The constitutive relation used to characterize plastic Pp. 541-547 in Proceedings of the 7th International Symposium on Bal- deformation of AA7075 in the simulations of Børvik et al.2 listics, The Hague, The Netherlands. Available online at http://www.lajss. org/HistoricalArticles/A%20constitutive%20model%20and%20data%20 for%20metals.pdf. Last accessed April 5, 2011. 1Børvik, 4Børvik, T., O.S. Hopperstad, and K.O. Pedersen. 2010. Quasi-brittle T., O.S. Hopperstad, and K.O. Pedersen. 2010. Quasi-brittle fracture during structural impact of AA7075-T651 aluminum plates. Inter- fracture during structural impact of AA7075-T651 aluminum plates. Inter- national Journal of Impact Engineering 37(5): 537-551. national Journal of Impact Engineering 37(5): 537-551. 2Ibid. 5See http://www.lstc.com.

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37 INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS FIGURE 4-1 Blunt-nosed (a) and ogive-nosed (b) projectiles exiting a 20-mm-thick aluminum plate. SOURCE: Børvik, T., O. Hopperstad, and K. Pedersen. 2010. Quasi-brittle fracture during structural impact of AA7075-T651 aluminum plates. International Journal of Impact Engineering 37(5): 537-551. b a 350 350 Experimental data Experimental data Best fit (a = 0.89 and p = 2.15) Best fit (a = 0.87 and p = 2.54) 300 300 Residual velocity [m/s] Residual velocity [m/s] 250 250 200 200 150 150 100 100 50 50 Blunt projectiles Ogival projectiles vbl = 183.8 m/s vbl = 208.7 m/s 0 0 150 200 250 300 350 400 150 200 250 300 350 400 Initial velocity [m/s] Initial velocity [m/s] FIGURE 4-2 Experimental results for final exit (residual) velocity as a function of initial velocity for blunt-nosed (a) and ogive-nosed (b) projectiles. The smallest initial velocity producing full penetration is known as the ballistic limit, V 0. SOURCE: Børvik, T., O. Hopperstad, Figure 4-3.eps and K. Pedersen. 2010. Quasi-brittle fracture during structural impact of AA7075-T651 aluminum plates. International Journal of Impact Engineering 37(5): 537-551. a b 350 350 Numerical result (3D - fine mesh) Numerical result (3D - fine mesh) Numerical result (3D - coarse mesh) Numerical result (3D - coarse mesh) 300 300 Residual velocity [m/s] Fit ( a = 1 and p = 2) Numerical result (2D - coarse mesh) Residual velocity [m/s] Fit ( a = 0.87 and p = 2.32) 250 250 200 200 vblc (2D) = 180 m/s 150 150 vblf (3D) = 181 m/s 100 100 vblc (3D) = 185 m/s vblf = 268 m/s vblc = 271 m/s 50 50 Blunt projectiles Ogival projectiles 0 0 150 200 250 300 350 400 150 200 250 300 350 400 Initial velocity [m/s] Initial velocity [m/s] FIGURE 4-3 Numerical finite-element simulations of the ballistic behavior shown in Figure 4.2 depicting the effects of mesh refinement Figure 4-3.eps and the contrast between three-dimensional and two-dimensional (axisymmetric) meshing. SOURCE: Børvik, T., O. Hopperstad, and K. Pedersen. 2010. Quasi-brittle fracture during structural impact of AA7075-T651 aluminum plates. International Journal of Impact Engineer - ing 37(5): 537-551.

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38 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS result associated with shear localization and fracture zones having finite thicknesses. Although the thickness of the shear localization zone is estimated as 100 μ, the element size used in the simulations was 200 μ in the two-dimensional case and 500 μ in the three-dimensional case. Either element size calibration or a constitutive length parameter will continue to be an essential, non-straightforward requirement in pen- etration simulations. The simulation of penetration represented by the results in Figure 4-3 must be pushed further to demonstrate the ro- bustness of the predictive capability. Would the agreement between simulation and experiment continue to hold if plate thickness was doubled or if the target was two air-separated plates? Would the agreement hold up for projectiles impact- ing the plate at an oblique angle? More sophisticated con- stitutive models that incorporate the evolution of damage prior to failure and a material length based on mechanisms of deformation and failure hold promise for simulations that are more closely tied to fundamental material mechanisms and properties and freed from element size calibration. While the potential of such added sophistication has been FIGURE 4-4 Simulations of penetration of a plate of AA7075- demonstrated, the payoff in material protection simulations T651 showing finite-element mesh for a blunt-nosed (a) and an ogive-nosed (b) hard steel projectile. In both cases the projectile has yet to be realized. velocity prior to impact is 300 m/s; the exit speed of the blunt- nosed projectile is 221 m/s while that of the ogival projectile is Projectile Penetration of Bilayer Ceramic-Metal Plates 127 m/s. SOURCE: Børvik, T., O. Hopperstad, and K. Pedersen. 2010. Quasi-brittle fracture during structural impact of AA7075- The simulation of projectile penetration of bilayer T651 aluminum plates. International Journal of Impact Engineering ceramic-metal plates further illustrates the need to combine 37(5): 537-551. good work on computation with sound experiments to inves- tigate material and system properties in extreme conditions of strain, strain rate, and pressure. Holmquist and Johnson6 material radially outward, dissipating more energy. The published the results of such simulations for a bilayer plate of numerical results in Figure 4-3 reproduce both sets of data boron carbide backed by 6061-T6 aluminum alloy, where the in Figure 4-2 quite accurately, including the ballistic limits. simulations utilized the ceramic constitutive law of Johnson, While AA7075 aluminum is not the most important ma- Holmquist, and Beissel,7 known as JHB. These simulations terial for projectile defeat, these 2008 simulations represent represent the state of the art in computations for the ballistic the state of the art. All the material parameters required as performance of ceramic armor components. inputs to the constitutive and failure models have been inde- Experiments carried out many years ago by Wilkins8 pendently measured, including those of the steel projectiles. for the same system provide data on the ballistic limit that Only the finite-element mesh layout and the element size are may be compared with the simulation results in Holmquist selected by the analyst. The predictions in Figure 4-3 depend and Johnson.9 Wilkins fired blunt and pointed projectiles at on element size, because the constitutive model used in these targets consisting of a 7.24-mm-thick boron carbide plate simulations can predict the onset of shear localization and/or bonded to a 6.35-mm-thick piece of aluminum alloy as the the fracture process but cannot predict the thickness of the backing plate, and the projectiles were made of very hard associated failure zone. The thickness of a shear localization band is determined by a combination of factors, including 6Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide microstructural length scales (see Chapter 3). These factors subjected to high-velocity impact. International Journal of Impact Engineer- are not accounted for in commonly employed constitutive ing 35(8): 742-752. laws such as the Johnson-Cook relation, so they cannot set 7Johnson, G.R., T.J. Holmquist, and S.R. Beissel. 2003. Response of the size of these zones. As a result, the calculations give rise aluminum nitride (including phase change) to large strains, high strain rates, to a shear zone whose thickness is the width of one element. and high pressures. Journal of Applied Physics 94(3): 1639-1646. 8Wilkins, M.L. 1967. Second Progress Report of the Light Armor Pro - Thus, the energy dissipated in a zone of shear localization, gram, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence or within any fracture process zone where the material is Livermore National Laboratory. weakening, is proportional to the element size. Consequent- 9Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide ly, a systematic refinement of the mesh size to smaller and subjected to high-velocity impact. International Journal of Impact Engineer- smaller elements will not converge to the correct physical ing 35(8): 742-752.

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39 INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS steel. Ballistic limits of about 800 m/s and 700 m/s were obtained for the two kinds of projectiles. It is notable that the ballistic limit for the cylinder is lower than that for the pointed projectile, indicating that for this target as well as the aluminum plate target discussed earlier, the cylinder is the better penetrator. However, it should be noted that this result is specific to the target and projectile configuration. An ogive-nosed projectile will penetrate considerably deeper into a thick aluminum target. Wilkins10 observed that both projectiles cause the bilayer to bend at impact, an effect that tends to generate tensile stress at the far side of the ceramic plate. As ceramics are very poor at coping with tensile stress, the bending causes the ceramic FIGURE 4-5 Ceramic strength versus applied pressure for the JHB plate to break. In the case of the cylindrical projectile, the constitutive model. The relationship is shown for intact material full impact of the hit is felt by the target immediately. The and failed material, each at two different strain rates, denoted by bilayer begins to bend almost at once, and the ceramic plate ε * . NOTE: D stands for damage. D = 1, fully damaged; D < 1 not  fractures due to tensile stresses at a relatively early stage of fully damaged; D = 0 would mean no damage. As is illustrated, the the impact. On the other hand, the sharp nose of the pointed damage weakens the material. SOURCE: Reprinted with permis- sion from Johnson, G.R., T.J. Beissel, and S.R. Beissel, Journal projectile does not immediately fully load the impact onto the of Applied Physics, 94, 1639, (2003). Copyright 2003, American target. Instead, the forces applied by the projectile to the bi- Institute of Physics. layer build up gradually as the point of the projectile flattens, enabling the ceramic to remain intact for longer and to serve as better armor against the threat of the pointed projectile. The JHB constitutive law is summarized in Figure 4-5, high pressure. The plots also indicate that the strengths will which shows ceramic strength versus applied pressure. be slightly different at high and low strain rates. In this context, “strength” is the ability of the material to It is obvious that when the ceramic cracks and frac- support shear stress without extensive deformation. Such tures, it will be irreversibly damaged as it comminutes into deformation may occur as the material yields and flows like granular material. This situation is captured in Figure 4-5, a very viscous liquid owing to rearrangements within its which shows that failed material has lower strengths at the internal lattice structure as it fractures and comminutes into same pressure than an intact material. Furthermore, the small particles, which then flow collectively like sand. The comminuted material cannot support tensile stresses, and so relationships in Figure 4-5 are shown for intact material and the plot of strength versus pressure for failed material termi- failed material, each at two different strain rates, denoted by nates at the origin in Figure 4-5. The JHB constitutive law ε * . The connections between ceramic strength and applied  encompasses detailed rules for transitioning the state of the pressure depicted in Figure 4-5 are used in the JHB model ceramic from intact to failed, and, broadly speaking, these to represent the fact that a ceramic is strong in compression rules implement the concept that as the material experiences (i.e., at high pressure) and weak in tension (i.e., at negative deformation by flow of the fracturing material, the strength pressure). The plot for intact material indicates that at high is steadily degraded. Therefore, as extensive deformation of pressure, strength is almost insensitive to pressure. Under the ceramic takes place, its strength steadily changes from these conditions, a ceramic cannot fracture. Instead, at a the initial level appropriate for intact ceramic to that for critical level of shear stress (equal to the ceramic strength) it failed ceramic. flows by the motion of dislocations that rearrange the internal Another feature of the JHB model as implemented in structure of the ceramic lattice. In negative pressure (i.e., simulations of projectiles hitting the bilayer of boron carbide weak tension) the strength of the intact ceramic is very low and aluminum alloy11 is that once the material has failed and and vanishes at a critical pressure, negative T. This situation is subsequently, or simultaneously, placed under tension, the reflects the fact that in tension, ceramic cracks and fractures original continuum material is converted into a collection of at a low tensile stress. As the pressure applied to the ceramic individual free-flying particles. Such a condition represents is increased, it is less likely to crack and its strength in- the situation observed in experiments12 where much of the creases. The plots for intact ceramic (Figure 4-5) interpolate this behavior between the extremes of tensile stress and very 11Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide subjected to high-velocity impact. International Journal of Impact Engineer- ing 35(8): 742-752. 10Wilkins, M.L. 1967. Second Progress Report of the Light Armor Pro - 12Wilkins, M.L. 1967. Second Progress Report of the Light Armor Pro - gram, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence gram, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence Livermore National Laboratory. Livermore National Laboratory.

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40 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS significant tensile stress at the bottom surface of the ceramic, ceramic material is removed from the crater created by the leading to its fragmentation and comminution. In this state, penetration of projectile when clouds of comminuted ce- the ceramic will retain the ability to resist the penetrator as ramic particles form. long as the comminuted granular material is well contained Constitutive laws such as the JHB model have many by the aluminum backing and the penetrator itself. However, material parameters in them that characterize the elastic, if such constraint is lost, the ceramic becomes ineffective in acoustic, yielding, and fracturing behavior of the material being simulated. Holmquist and Johnson13 calibrated most resisting the penetrator as it simply turns into a freely flying granular cloud. This consideration is an important element of the material parameters in their model using the results of plate impact experiments14 involving a solid disc launched in the proper design of ceramic armor. Note that Holmquist and Johnson18 simulated two other at high speed against a flat surface of the material being types of experiment in addition to the penetration of a thin investigated. They augmented the information from these bilayer target: the impact on boron carbide plates19 and the tests with spall data from experiments.15 These observations deep penetration of steel-jacketed boron carbide blocks.20,21 reinforce the notion that successful simulation depends on Each of these experiments was successfully simulated with the availability of experimental data to (1) characterize the use of the JHB constitutive law, showing that the state of the parameters in the models being used, (2) validate and test the art of simulation for the ballistic response of ceramic targets quality of the computational results, and (3) provide insights is quite far advanced. However, Holmquist and Johnson into how computational simulation should be conducted for found it necessary to use a different set of material param- a given material in a given situation. Results from Holmquist and Johnson’s simulations16 eters for each distinct type of experiment. Therefore no single material model is yet able to capture the penetration and show that for the initial velocities—V = 790 m/s for the pointed projectile and 700 m/s for the cylinder. At 100 ms material response phenomena occurring in the cases of, for example, a ceramic under plate impact, deep penetration by a after first hitting the bilayer at velocity V, the projectile has a long heavy rod, and perforation of a thin bilayer target. As the residual velocity Vr. This velocity is 200 m/s for the pointed authors note, this limitation of the results they obtained sug- projectile and 257 m/s for the cylinder, and the projectiles gests that some important mechanisms of ceramic response will not slow down much more because the target is then of- fering no resistance. These results match those of Wilkins17 are not being modeled accurately in the JHB constitutive law and that further work will be necessary to improve the in multiple ways, including appearance of the crater and the constitutive laws for the response of ceramic under ballistic value of the ballistic limit. conditions of high strain, high strain rate, and high pressure. A further feature of the results from the simulation is the distinct bending of the bottom aluminum layer, with prior concave upward bending of the plate being apparent All-Steel Sandwich Plates for Enhanced Blast Protection: in the now destroyed segment of the aluminum immedi- Design, Simulation, and Testing ately below the penetrator. Although the ceramic layer in Traditionally, plate structures designed to withstand its residual shape is largely unbent due to the lack of a bond blast loads have employed monolithic plates. Within the past between the materials in the bilayer in the simulations, the decade, the Office of Naval Research has supported efforts ceramic will have bent like the aluminum in the early stage to explore whether all-metal sandwich plates comprised of of projectile penetration, though to a lesser extent than the the same material and having the same mass per area can be bending of the aluminum layer. Nevertheless, the results of more effective against blasts than monolithic metal plates. the simulation clearly point out the importance of bending in Studies completed to date have considered various core the projectile penetration of relatively thin ceramic targets. types, such as honeycombs, corrugated plates, and lattice A feature of the concave upward bending of the ceramic im- mediately below the projectile as it penetrates the target is a 13Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide 18Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide subjected to high-velocity impact. International Journal of Impact Engineer- ing 35(8): 742-752. subjected to high-velocity impact. International Journal of Impact Engineer- 14Vogler, T.J., W.D. Reinhart, and L.C. Chhabildas. 2004. Dynamic ing 35(8): 742-752. 19Vogler, T.J., W.D. Reinhart, and L.C. Chhabildas. 2004. Dynamic behavior of boron carbide. Journal of Applied Physics 95(8): 4173-4183. 15Wilkins, M.L. 1967. Second Progress Report of the Light Armor Pro - behavior of boron carbide. Journal of Applied Physics 95(8): 4173-4183. 20Orphal, D.L., R.R. Franzen, A.C. Charters, T.L. Menna, and A.J. Pie - gram, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence Livermore National Laboratory. kutowski. 1997. Penetration of confined boron carbide targets by tungsten 16Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide long rods at impact velocities from 1.5 to 5.0 km/s. International Journal of subjected to high-velocity impact. International Journal of Impact Engineer- Impact Engineering 19(1): 15-29. 21Lundberg, P., L. Holmberg, and B. Janzon. 1998. An experimental study ing 35(8): 742-752. 17Wilkins, M.L. 1967. Second Progress Report of the Light Armor Pro - of long rod penetration into boron carbide at ordnance and hyperveloci - gram, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence ties. Pp. 251-258 in Proceedings of the 17th International Symposium on Livermore National Laboratory. Ballistics. Midrand, South Africa: South African Ballistics Organization.

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41 INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS trusses, with attention to design and ease of manufacturing.22 its monolithic competitor. For this effect to come into play, the core must not be overly strong, so that only the face sheet Both air and water blast environments have been investi- acquires momentum during the period it is impacted by the gated, and an understanding is now in place of when fluid- water blast.26 For air blasts, decoupled calculations can sup- structure interaction effects are important. The advancement ply a good approximation. In such cases, the pressure history of understanding that has been achieved is due to tightly is computed in the first step by treating the plate structure as coupled numerical simulation and experimental testing. rigid; this history is then applied to the structure in the second In this section a brief overview is given of recent work by Dharmasena et al.,23 which illustrates current capabilities and step to obtain its response. While fluid-structure effects are not usually significant in air blasts, interaction effects can be limitations along with possible opportunities. important for air blasts that entrain sand or gravel, such as The sequence of events occurring when a sandwich those experienced by vehicles exposed to buried improvised plate is struck by a blast wave is depicted in simplified form explosive devices. in Figure 4-6, where three relatively separate stages in the Figure 4-7 displays the deformation of clamped square- sequence can be visualized. For meter-size plates subject to honeycomb-core sandwich plates made from stainless steel intense blasts, the entire process lasts about 10 ms. In the and subject to three explosive levels at close standoff in air. scenario sketched in the figure, fluid-structure interaction At the lowest level shown, the back face undergoes relatively occurs in Stage I. If the mass of the face toward the blast little deformation; the high bending stiffness of the sandwich is sufficiently large, the blast wave bounces off the plate in plate is very effective. At the two higher levels of blast, much the way a rubber ball would be reflected, transmit- significant stretching of the face sheets occurs in addition to ting almost twice its incident momentum to the plate before core crushing. Both core crushing and face sheet stretching the plate has time to displace. This is a reasonable way of absorb substantial energy. While severely deformed, these viewing most air blasts striking a metal face of more than plates have not fractured. a few millimeters thick. However, a 1-cm thick metal plate Accurate simulations of blast-loaded structures re - struck by a water blast wave interacts with the wave in such quire input material properties for the constitutive relation, a way that the reflection is reduced and therefore a smaller knowledge of the temporal and spatial pressure pulse on fraction of the incident wave momentum is transferred to the the structure, and a finite element code that can cope with plate. This basic fluid-structure interaction effect for water highly nonlinear material and geometric behavior, includ- blasts was discovered in World War II and has recently been extended to air blasts.24 ing internal contacting surfaces. As no fracture occurred in the test specimens, no attempt was made to model damage Various core geometries have been investigated ex- or fracture in the simulations.27 Finite-strain plasticity was perimentally and by simulations, including hexagonal and employed along with input of tensile data for the stainless square honeycomb cores; corrugated or folded-plate cores; steel as a function of strain and strain rate. and cores made of truss elements. These have generally been Comparisons of the simulations with the experimental plates fashioned from relatively ductile steels. A folded-plate results are displayed in Figure 4-8. Nearly all the experi- core has the advantage that it is readily manufactured. This mental details are replicated. Even the buckling of the webs is also true of several truss-core geometries, which have the can be captured accurately. The back face of these sandwich added advantage that the core is an open structure useful for multifunctional applications.25 Which core yields the best plates deflects less than the equivalent mass of solid plate even in an air blast. The performance of the sandwich plate performance depends on the type and level of blast, whether relative to a monolithic plate would be better in water blasts the blast is in air or water, and whether the standoff is close or due to fluid-structure interaction that favors sandwich plates. remote. A sandwich plate can be designed to capitalize on the There are no “adjustable” parameters in the simulations fluid-structure interaction effect because the mass per area of presented above. Thus, one can conclude it is possible to the face sheet toward the blast will be less than half that of carry out calculations to improve the design of plate struc- tures against blast loads of various types. This optimistic as - 22Wadley, H.N.G. 2006. Multifunctional periodic cellular metals. Philo- sessment must be tempered by the following considerations: sophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364(1838): 31-68. • The ultimate blast resistance of these structures has 23Dharmasena, K.P., H.N.G. Wadley, Z. Xue, and J.W. Hutchinson. 2008. not been determined. To do so would require subject- Mechanical response of metallic honeycomb sandwich panel structures to high-intensity dynamic loading. International Journal of Impact Engineer- ing 35(9): 1063-1074. 24Kambouchev, N., L. Noels, and R. Radovitzky. 2006. Nonlinear 26Liang, Y., A.V. Spuskanyuk, S.E. Flores, D.R. Hayhurst, J.W. Hutchin - compressibility effects in fluid-structure interaction and their implications son, R.M. McMeeking, and A.G. Evans. 2007. The response of metallic on the air-blast loading of structures. Journal of Applied Physics 100(6): sandwich plates to water blast. Journal of Applied Mechanics 74(1): 81-99. 27Dharmasena, K.P., H.N.G. Wadley, Z. Xue, and J.W. Hutchinson. 2008. Article number 063519. 25Wadley, H.N.G. 2006. Multifunctional periodic cellular metals. Philo - Mechanical response of metallic honeycomb sandwich panel structures to sophical Transactions of the Royal Society A: Mathematical, Physical and high-intensity dynamic loading. International Journal of Impact Engineer- Engineering Sciences 364(1838): 31-68. ing 35(9): 1063-1074.

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42 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS FIGURE 4-6 Schematic depicting the response of a clamped sandwich plate to blast loading: (a) Impulsive loading (Stage I); (b) core crush - ing (Stage II); and (c) overall bending and stretching (Stage III). SOURCE: Dharmasena, K.P., H.N.G. Wadley, Z. Xue, and J.W. Hutchinson. 2008. Mechanical response of metallic honeycomb sandwich panel structures to high-intensity dynamic loading. International Journal of Impact Engineering 35(9): 1063-1074. ing the structures to larger blasts and taking account shear, but they cannot reliably predict both types of fracture in the simulations. Reliable models for of fractures under a wide range of stress states. such simulations are not yet established for either Mechanistic-based fracture models are needed to monolithic plates or sandwich plates. expand predictive capabilities. • Plate structures are susceptible to failures along • Highly refined meshes were employed in the sand- welds and joints, and simulations of these events wich plate simulations reported above—far more are not yet reliable. Existing continuum models can refined than would be feasible for-large scale struc- be calibrated to reproduce fractures in tension or in tures. New constitutive models and computational

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43 INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS methods are required to capture the main defor- mational features of the core with relatively coarse meshing. THE STATE OF THE ART IN EXPERIMENTAL METHODS As the discussion of the three examples above illus- trates, experimental methods are at the heart of any effort to observe and characterize material behavior. This is especially true for protection materials, which experience extreme rates of loading and for which both deformation and failure must be understood and characterized. This section outlines cur- rent experimental methods relevant to protection materials and points to opportunities for advancing their capabilities. FIGURE 4-7 Half-sectional square honeycomb core test panels. Definition of the Length Scales and Timescales of Interest The impulse load is (a) 21.5 kPa s, (b) 28.4 kPa s, and (c) 33.7 kPa s. Stainless steel sandwich plates with square honeycomb cores The committee has focused on developing lightweight clamped around their edges subjected to three levels of air blast. protective materials for future Army applications and inter- The plates were sectioned after deformation to display the core and preted its mandate broadly to include providing protection the relative position of the faces. The core webs are 0.76 mm thick from threats that involve the rapid deposition of energy with spacing 30.5 mm. The core thickness is 51 mm. Each face sheet is 5 mm thick. The core comprises 24 percent of the mass of directly into a material or structure. Examples of threats of the plate. The equivalent thickness of a solid plate with the same this type include direct impact by (1) an incoming projectile mass per area is 13.1 mm. SOURCE: Dharmasena, K.P., H.N.G. and (2) explosive, or blast, loading. The timescales associ- Wadley, Z. Xue, and J.W. Hutchinson. 2008. Mechanical response ated with these events are of paramount importance, and of metallic honeycomb sandwich panel structures to high-intensity the characteristic velocities associated with propagating dynamic loading. International Journal of Impact Engineering waves, projectiles, or failure processes generate associated 35(9): 1063-1074. length scales. These scales can be envisioned in the two- dimensional space shown in Figure 4-9, where the inclined straight lines represent the domains in space and time that are affected by phenomena at each of the defined speeds. Typical components and structures in Army applications will be of the sizes represented in the blue shaded region, usually a mil- limeter to several centimeters. Given these sizes, the longest timescales associated with threat events are of the order of a millisecond (in the case of blast loading). Most of the con- trolling phenomena operate at much smaller timescales (mi- croseconds down to nanoseconds). The characteristic length scales that control material response to threat are of the order of nanometers to hundreds of micrometers. The experimental challenges associated with this field largely arise from the need to resolve phenomena at these timescales and length scales. As shall be seen in this section, the vast majority of available experimental methods provide either high time resolution or high spatial resolution, but few provide both. Relation to Experimental Methods FIGURE 4-8 Comparison of experimental test specimens (on the Experimental methods must be able to access the appro- left) deformed at the three levels of air blast shown, with simulations priate regimes in the length scale and timescale space in order carried out for the same plates and level of blasts (on the right). to investigate any particular behavior or phenomenology. A SOURCE: Dharmasena, K.P., H.N.G. Wadley, Z. Xue, and J.W. critical issue here is that these scales should be investigated Hutchinson. 2008. Mechanical response of metallic honeycomb simultaneously. Because the events are transient and involve sandwich panel structures to high-intensity dynamic loading. Inter- complex loading paths, it is difficult to pin down real-time national Journal of Impact Engineering 35(9): 1063-1074.

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44 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS Timescale FIGURE 4-9 Length scales and timescales associated with typical threats to Army fielded materials and structures. The lines represent the velocities associated with specific phenomena observed in impact events, such as the blast wave, cracks, and stress waves. The choice of structural length scale and the particular phenomenon of interest then determines a characteristic timescale for the problem. Classification of Experimental Methods28 behavior through postmortem analysis of the material or structure. This does not imply that there are no relevant phe- Experimental techniques commonly called “impact nomena at the larger timescales (multiple milliseconds and experiments” often have very different objectives. Since the larger). Such timescales are relevant to a number of threats, design of an experimental technique depends on the goal of particularly those related to blast and explosive loading, and the experiment, it must first be decided what information they are tightly coupled to structural dynamics, which can one wants to extract from the experiment. Typically, what involve both material and geometric nonlinearity. Broadly are called “impact” (or “dynamic”) experiments fall into one speaking, however, the challenges in understanding and ob- of four categories, listed here according to the complexity servation at these longer timescales and length scales consist of the dynamics: largely of correctly exploring the coupling of the dynamics to the design space. 1. High-strain-rate experiments. These measure the In this section, state-of-the-art experimental methods high-strain-rate characteristics of a material; capable of exploring various regimes in the length scale– 2. Shock physics experiments. These aim at under- timescale space are described. To begin, experimental meth- standing shock wave propagation in a material or ods will be classified in terms of their intended applications. structure; they may also develop high strain rates, First, however, a broad comment is in order. One approach but the high-rate deformations vary as a function of to understanding the interaction between threat and material space and time; is to perform a highly instrumented version of the actual 3. Impact phenomenology experiments. These experi- threat event. Although this approach is very useful, and is ments endeavor to understand or discover impact indeed the most definitive metric for the effectiveness of phenomena such as cratering efficiency or fragmen- a protective material within a specific protected system, it tation; and does not necessarily provide significant guidance for the 4. Dynamic failure experiments. These would help development of radically improved protective systems. us to understand the processes of dynamic failure The focus of this section is, accordingly, on the more fun - within a material or structure. damental experiments associated with developing a basic understanding of the mechanisms, behaviors, and processes associated with the threat-material interaction that can lead 28Except as noted in the text, this section drawn from Ramesh, K.T. 2008. to improved constitutive characterizations, including those High strain rate and impact experiments. Chapter 33 in Handbook of Experi- for failure processes. mental Solid Mechanics. W.N. Sharpe, Jr., ed. New York, N.Y.: Springer.

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45 INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS A detailed consideration of the state of the art for each of these types of experiments, based on examples from the literature, follows. Evaluating Material Behavior at High Strain Rates Most of the inelastic (and particularly the plastic) de- formations due to impacts at rapid velocities occur at high strain rates. The deformations may lead to large strains and high temperatures. The high-strain-rate behavior of many materials (often defined as the dependence σf ( ε, ε , T ) of the flow stress on the strain, strain rate, and temperature) is not, however, well understood, particularly at high strains and high temperatures. Some experimental techniques have been developed to measure material properties at high strain rates. Here, the committee considers experimental techniques that develop controlled high rates of deformation in the bulk of FIGURE 4-10 Experimental techniques used for the development the specimen rather than techniques that develop high strain of controlled high-strain-rate deformations in materials. rates just behind a propagating wave front. The main experimental techniques for measuring the rate-dependent properties of various materials are described technique was developed by Kolsky,34 the term Kolsky bar in Figure 4-10 (the stress states developed by the various will be used here. Kolsky bar experiments may include com- techniques may not necessarily be identical). One outstand- pression, tension, torsion, or combinations of all of these.35 ing recent review of these methods is that of Field et al.29 The Kolsky bar consists of two long bars, called the Here, strain rates above 102 s–1 are classified as high strain input and output bars, that are designed to remain elastic rates, those above 104 s–1 are called very high strain rates, and throughout the test. These bars sandwich a small specimen, those above 106 s–1 are ultrahigh strain rates. Strain rates at or usually cylindrical, which is expected to develop inelastic below 10–3 s–1 are usually considered to represent quasi-static deformations. The bars are typically made of high-strength deformations, and strain rates below 10–6 s–1 are considered steels, such as maraging steel, with a very high yield strength to represent “creep.” The emphasis here is on experimental and substantial toughness. Other bar materials that have techniques for strain rates greater than 102 s–1—that is, high been used include 7075-T6 aluminum, magnesium alloys (102-104 s–1), very high (104-106 s–1) and ultrahigh (>106 s–1). and poly(methyl methacrylate) (for testing very soft ma- terials), and tungsten carbide (for testing ceramics). One end of the input bar is impacted by a projectile made of a Kolsky Bars material identical to that of the bars; the resulting compres- The now-classical experimental technique in the high- sive pulse propagates down the input bar to the specimen. strain-rate domain is the Kolsky bar, or split-Hopkinson Several reverberations of the loading wave occur within the pressure bar, experiment30 for determining the mechanical specimen; a transmitted pulse is sent into the output bar and properties of various materials (e.g., metals,31 ceramics,32 a reflected pulse is sent back into the input bar. Typically, and polymers33) in the strain rate range 102 through 8 × 103 resistance strain gages are placed on the input and output s–1 (see Figure 4-11). This technique is now in use throughout bars for measuring (1) the incident pulse generated by the the world. Since the fundamental concept involved in this impacting projectile; (2) the reflected pulse from the input bar/specimen interface; and (3) the transmitted pulse through the specimen to the output bar. The strain gage signals are 29Field, J.E., S.M. Walley, W.G. Proud, H.T. Goldrein, and C.R. Siviour. typically measured using high-speed digital oscilloscopes 2004. Review of experimental techniques for high rate deformation and with at least 10-bit accuracy and preferably with differential shock studies. International Journal of Impact Engineering 30(7): 725-775. inputs to reduce noise. 30Nicholas, T., and A.M. Rajendran. 1990. Material characterization at high strain-rates. Pp. 127-296 in High Velocity Impact Dynamics. J.A. Many extensions and modifications to the traditional Zukas, ed. New York, N.Y.: John Wiley & Sons. Kolsky bar system have been developed over the last five 31Nemat-Nasser, S., and J.B. Isaacs. 1997. Direct measurement of iso - thermal flow stress of metals at elevated temperatures and high strain rates 34Kolsky, with application to Ta and Ta-W alloys. Acta Materialia 45(3): 907-919. H. 1949. An investigation of the mechanical properties of 32Chen, W., G. Subhash, and G. Ravichandran. 1994. Evaluation of ce - materials at very high rates of loading. Proceedings of the Physical Society: ramic specimen geometries used in a split Hopkinson pressure bar. DYMAT Section B 62(11): 676-700. 35Gray III, G.T. 2000. Classic split-Hopkinson pressure bar testing. Pp. Journal 1: 193-210. 33Walley, S., and J. Field. 1994. Strain rate sensitivity of polymers in 462-476 in ASM Handbook Volume 8: Mechanical Testing and Evaluation. compression from low to high strain rates. DYMAT Journal 1: 211-228. H. Kuhn and D. Medlin, eds. Materials Park, Ohio: ASM International.

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58 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS Figure 4-18.eps FIGURE 4-18 Prediction of conical, radial, and lateral crack patterns in ceramic plate impact by the recent cohesive zone/discontinuous 2 bitmaps Galerkin method. only a few have taken root in the application to protection model,91 the Zerilli-Armstrong models,92 the Steinberg- materials. These models have ranged from those for simple Guinan-Lund models,93 the Bodner-Partom models,94 and dynamic flow stress and dynamic failure strain to very com- plex models that include microstructural details. Currently, some models for materials are advanced enough to provide 91Johnson, G.R., and W.H. Cook. 1983. A constitutive model and data for helpful and meaningful results, such as those illustrated in metals subjected to large strains, high strain rates and high temperatures. the first section of this chapter, but details of failure are not Available online at http://www.lajss.org/HistoricalArticles/A%20constitu - tive%20model%20and%20data%20for%20metals.pdf. Last accessed April sufficiently robust to allow the predictive design of material 7, 2011. systems to protect against specific threats. 92Zerilli, F.J., and R.W. Armstrong. 1987. Dislocation-mechanics-based For projectile-target interaction computations, the ma- constitutive relations for material dynamics calculations. Journal of Applied terials are usually modeled using phenomenological models Physics 61(5): 1816-1825. that compute strength and failure as a function of strain, 93Steinberg, D.J., S.C. Cochran, and M.W. Guinan. 1980. A constitutive model for metals applicable at high-strain rate. Journal of Applied Physics strain rate, temperature, and pressure. For metals the most 51(3): 1498-1504. commonly used strength models are the Johnson-Cook 94Bodner, S.R., and Y. Partom. 1975. Constitutive equations for elastic- viscoplastic strain-hardening materials. Journal of Applied Mechanics, Transactions ASME 42 Ser E(2): 385-389.

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59 INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS the Mechanical Threshold Stress model.95 The Johnson- such as fracture toughness, crack growth rates, flaw size, and densities.104 This new work sets an important direction for Cook model is a phenomenological model, and the others the development of constitutive models of material failure are more physically based. Generally these models require a for other protection materials. characterization of a specific material, and it is not possible to predict the strength from a microstructural description of Issues with Models of Material Damage and Failure Ma- the material. There are fewer failure models available, with the Johnson-Cook failure model96 being the most widely terial damage and failure in existing M&S codes is described at the constitutive model via so-called continuum damage used. Although this is primarily a phenomenological model, models. In these approaches, damage is considered a state it includes some physically based features of the ductile fracture mechanism.97 More mechanistic constitutive models variable of the material, whose history evolves according to of damage and fracture based on ductile void growth,98 such prescribed phenomenological laws. Either the elastic or plas- as the Gurson model,99 have been proposed. However, they tic response of the material is “softened” as material damage progresses in an irreversible manner. These laws describe the are still to be incorporated and widely adopted in produc- effect of the operative driving forces and mechanisms such as tion codes for ballistic analyses. Recent contributions have stress intensity and triaxiality, which depend on the material proposed improvements to the characterization of failure in the Johnson-Cook model100 and the Gurson model.101 type (brittle or ductile) and characteristics such as defect size and porosity. Damage models require additional parameters For ceramics there are fewer models available. A unique that must be calibrated to experiments or that sometimes feature of ceramics, compared to other materials (such as have physical meaning, such as initial porosity, defect size metals), is that they have such high compressive strengths and distribution, toughness, and so forth. that they cannot be tested with typical laboratory stress-strain tests.102 Instead, their material properties must be inferred Damage is characterized by a reduction in the mate- rial’s load-carrying capacity after reaching damage threshold from plate impact tests and/or penetration tests. This char- conditions. This is always accompanied by a localization of acteristic has made it difficult to directly obtain failure data the deformation in narrow regions, which is a precursor to under high (compressive) pressures and to obtain the (shear) failure. There is a fundamental mathematical problem with strength of failed ceramic under high pressures. The JHB phenomenological model103 used in the illustrative example continuum damage models and any other model describing weakening material response—for example, the models of in the beginning of the chapter has an intact strength, a de Borst and Sluys105 and Sluys et al.106 In the region where failed strength, a failure component based on plastic strain softening occurs, the governing equations of the dynamic and pressure, and bulking. Recently Deshpande and Evans problem change their mathematical character in a fundamen- proposed a mechanism-based model to compute damage tal way, from hyperbolic to elliptic. For elliptic equations, and failure in ceramics based on microstructural parameters waves cannot propagate as their speeds become imaginary, and the softening region collapses to a vanishing width. This, 95Follansbee, P.S., and U.F. Kocks. 1988. A constitutive description of the in turn, implies that no energy is dissipated by the softening deformation of copper based on the use of the mechanical threshold stress material, which is far from the real material response. What as an internal state variable. Acta Metallurgica 36(1): 81-93. happens in reality is that there is always a physical process 96Johnson, G.R., and W.H. Cook. 1985. Fracture characteristics of three that limits the localization process and introduces a charac- metals subjected to various strains, strain rates, temperatures and pressures. teristic length scale in the problem, which is not considered Engineering Fracture Mechanics 21(1): 31-48. 97Hancock, J.W., and A.C. Mackenzie. 1976. On the mechanism of in the classical continuum equations. ductile failure in high-strength steels subjected to multi-axial stress states. In the presence of softening, the numerical solution of Journal of the Mechanics and Physics of Solids 24(2-3): 147-160. the conventional continuum problem provides an erroneous 98McClintock, F.A. 1968. A criterion for ductile fracture by the growth resolution of the physical phenomenon. The element or grid of holes. Journal of Applied Mechanics 35(2): 363-371. 99Gurson, A.L. 1977. Continuum theory of ductile rupture by void nucle - size effectively sets the length scale necessary to regularize ation and growth: Part I, yield criteria and flow rules for porous ductile the problem as it imposes a lower bound for the localization media. Journal of Engineering Materials and Technology, Transactions of zone width. However, this is just an illusion, because the the ASME 99 Ser H(1): 2-15. solution does not converge as the mesh is refined. In the limit 100Bao, Y., and T. Wierzbicki. 2004. On fracture locus in the equivalent strain and stress triaxiality space. International Journal of Mechanical Sci - ences 46(1): 81-98. 101Nahshon, K., and J.W. Hutchinson. 2008. Modification of the Gurson 104Deshpande, V.S., and A.G. Evans. 2008. Inelastic deformation and Model for shear failure. European Journal of Mechanics-A/Solids 27(1): energy dissipation in ceramics: A mechanism-based constitutive model. 1-17. Journal of the Mechanics and Physics of Solids 56(10): 3077-3100. 102Johnson, G.R. 2011. Numerical algorithms and material models for 105de Borst, R., and L.J. Sluys. 1991. Localisation in a Cosserat con - high-velocity impact computations. International Journal of Impact Engi - tinuum under static and dynamic loading conditions. Computer Methods neering 38(6): 456-472. in Applied Mechanics and Engineering 90(1-3): 805-827. 103Johnson, G.R., T.J. Holmquist, and S.R. Beissel. 2003. Response of 106Sluys, L.J., R. de Borst, and H.-B. Muhlhaus. 1993. Wave propagation, aluminum nitride (including phase change) to large strains, high strain rates, localization and dispersion in a gradient-dependent medium. International and high pressures. Journal of Applied Physics 94(3): 1639-1646. Journal of Solids and Structures 30(9):1153-1171.

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60 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS of the material’s microstructure or for the associated micro- when the mesh size goes to zero, the dissipated energy in the mechanical responses that affect global behavior. The ability localization zone is zero. This numerical manifestation of the to consistently incorporate the effect of micromechanical ill-posedness of the mathematical problem is what is usually features on material response would enable rational micro- referred to as “damage-induced mesh dependency.” A com- structure design. mon approach to circumvent this problem in existing codes There is therefore a critical need to develop descriptions is to calibrate the material model parameters for a given of material behavior directly rooted in the first principles of mesh size. In other words, not only the model parameters micromechanics, a long-standing aspiration of solid mechan- but also the mesh size are tied to a specific application. The ics. This requires new mathematical frameworks; multiscale, illustrative example in the introduction to this chapter for the multiphysics constitutive models; and numerical algorithms. projectile penetrating the aluminum plate was approached in Multiscale modeling is a rational and systematic way to this manner. This is clearly a significant limitation. construct hierarchical models for the behavior of complex A proper mathematical treatment of softening material material with the least amount of empiricism and uncertainty. response necessarily involves the modification of the classi- In this approach, the pertinent unit processes at every length cal governing equations in a way that the physically relevant scale in the hierarchy of material behavior are identified. The length scale is introduced. A number of generalizations of the processes at any scale are the average of the unit processes classical formulation have been proposed to this end. They taking place at the length scale just below. The modeling involve either the introduction of higher-order derivatives effort for systems in which these relations are well defined in the constitutive model (gradient models, as, for example, Aifantis107 and Fleck and Hutchinson108) or the spatial aver- simply involves analyzing each unit mechanism in turn and aging of strains (nonlocal models such as Bazant et al.109). computing the averages, which eventually results in a full description of the material’s macroscopic behavior. This Both generalizations reflect the fact that micromechanical inductive process ceases at the atomic scale, at which point processes in the localization zone have an inherently non- the fundamental theories describing atomic bonds take over. local character. In the particular case of gradient-type soft - For instance, as part of the Caltech advanced simulation ening or damage models, it can be shown that an internal and computing program, a full multiscale model of mate- length scale exists and that the resulting set of governing rial response was developed for tantalum.110 The multiscale equations is well posed, having wave speeds that remain hierarchy that underlies metal plasticity is shown schemati- real in the softening regime. The immediate computational cally in Figure 4-19. The foundational theory on which the consequence of this reformulation is that softening-induced hierarchy rests is quantum mechanics and, in particular, the mesh dependence is eliminated. electronic structure of metals. Quantum mechanics encap- These models have not permeated production compu- sulates the fundamental laws that govern the behavior of tational frameworks, primarily for two reasons: (1) new materials at the angstrom scale. In their density-functional- (high-order) algorithms and computer codes are required theory approximation, quantum mechanical calculations can because the existing algorithmic frameworks cannot accom- characterize the structure and properties of crystal lattices modate the higher-order derivatives and their field continuity and isolated crystal defects, especially when coarse-graining requirements and (2) additional constitutive parameters have techniques are employed.111 Fundamental properties of dislo- emerged that in many cases do not have a clear physical cations such as kink structure and mobility can be evaluated meaning or a discerning experiment that can be used to using molecular dynamics and empirical potentials.112 These calibrate them. Multiscale modeling might be one way to properties can be used to formulate theories of linear-elastic address this issue. dislocation dynamics. Dislocation dynamics models—for example, the models of van der Giessen and Needleman113 Multiscale Modeling: Issues with Phenomenological Models and the Need to Incorporate Microstructural Information The difficulty of correlating material properties with armor performance can often be explained by the inability of 110Cuitiño, A.M., L. Stainier, G. Wang, A. Strachan, T. Cain, W.A. God - macroscopic constitutive descriptions to account for details dard III, and M. Ortiz. 2001. A multiscale approach for modeling crystalline solids. Journal of Computer-Aided Materials Design 8(2-3): 127-149. 111Gavini, V., K. Bhattacharya, and M. Ortiz. 2007. Quasi-continuum 107Aifantis, E.C.. 1984. On the microstructural origin of certain inelastic orbital-free density-functional theory: A route to multi-million atom non- models. Journal of Engineering Materials and Technology, Transactions of periodic DFT calculation. Journal of the Mechanics and Physics of Solids the ASME 106(4): 326-330. 55(4): 697-718. 108Fleck, N.A., and J.W. Hutchinson. 1993. A phenomenological theory 112Cuitiño, A.M., L. Stainier, G. Wang, A. Strachan, T. Cain, W.A. God - for strain gradient effects in plasticity. Journal of the Mechanics and Physics dard III, and M. Ortiz. 2001. A multiscale approach for modeling crystalline of Solids 41(12): 1825-1857. solids. Journal of Computer-Aided Materials Design 8(2-3): 127-149. 109Bazant, Z.P., T.B. Belytschko, and T.-P. Chang. 1984. Continuum 113Van Der Giessen, E., and A. Needleman. 1995. Discrete dislocation theory for strain-softening. Journal of Engineering Mechanics 110(12): plasticity: A simple planar model. Modelling and Simulation in Materials 1666-1692. Science and Engineering 3(5): 689-735.

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61 INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS FIGURE 4-19 Multiscale hierarchy for metal plasticity. The arrows indicate upscaling directions across length scales. Figure 4-19.eps bitmap and Arsenlis et al.114—have the potential for characterizing reproduced the observed effective response of polycrystal- the work-hardening characteristics of metals. However, to line metals but also captured local details of the deformation date, such models are restricted to small deformations and and grain interactions. impossibly high dislocation densities and deformation rates. It is, however, easier to expound the multiscale paradigm The deformation of individual grains is often strongly het- than to carry it out. Today, the unit mechanisms can be ana- erogeneous and entails the formation of lamellar dislocation lyzed and the effective behavior characterized based either structures. Variational formulations of plasticity based on on numerical schemes or on a motley assortment of analyti- incremental energy minimization have proven effective at cal tools, such as mean-field theories, statistical mechanics, predicting such structures and characterizing the effective transition-state theory, or homogenization. The great breadth behavior of the material, including well-established scaling of the field and its current state of development mean that relations such as those of Hall-Petch and Taylor.115 Finally, multiscale modeling generally cannot be easily formalized the direct simulation of polycrystalline behavior, in which as a self-contained, unified theory and therefore remains as the polycrystalline structure is resolved by the mesh, is much art as a science. As a result, there is a tendency to base within the reach of present petascale computing power.116,117 multiscale modeling on purely numerical schemes such as Large-scale simulations and a detailed experimental valida- molecular dynamics, kinetic Monte Carlo, quasicontinuum, tion process showed that this multiscale approach not only and direct numerical simulation of polycrystals. One com- mon multiscale paradigm is “information-passing”—that is, computing material constants that are then used to inform 114Arsenlis, A., W. Cai, M. Tang, M. Rhee, T. Oppelstrup, G. Hommes, upscale models. An important limitation of this type of T.G. Pierce, and V.V. Bulatov. 2007. Enabling strain hardening simulations with dislocation dynamics. Modelling and Simulation in Materials Science multiscale analysis is that it does not provide insight into, and Engineering 15(6): 553-595. nor does it supply, the functional form of the models gov- 115Ortiz, M., and E.A. Repetto. 1999. Nonconvex energy minimization erning material behavior at the various scales of interest. A and dislocation structures in ductile single crystals. Journal of the Mechanics competing paradigm consists of running several schemes, and Physics of Solids 47(2): 397-462. 116Zhao, Z., R. Radovitzky, and A. Cuitino. 2004. A study of surface each operating on a different length scale and feeding av- roughening in fcc metals using direct numerical simulation. Acta Materialia erage information to the upper scales, as part of the same 52(20): 5791-5804. calculation, which is referred to as “concurrent multiscale 117Zhao, Z., M. Ramesh, D. Raabe, A.M. Cuitiño, and R. Radovitzky. computing.” However, this paradigm is self-limiting owing 2008. Investigation of three-dimensional aspects of grain-scale plastic to the inordinate volume of computing that it generates, and surface deformation of an aluminum oligocrystal. International Journal of Plasticity 24 (12): 2278-2297.

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62 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS to the difficulty in interpreting and learning from the vast Clearly, for this important effort to be effective, stronger amounts of numerical data that it generates. Thus, whereas coordination and collaboration between experimentalists and much of multiscale computing is driven by the rapid pace of modelers must be encouraged. In summary, mathematical development of computational platforms, the goal of “full analysis could give simulations a great competitive advan- physics”—that is, of employing solely fundamental theories tage and should be an important part of a balanced approach in calculations and brute computational force—remains to multiscale modeling. Efforts are under way at the Army elusive at present. Research Laboratory to apply this paradigm to protection An appealing alternative to computational multiscale materials. schemes is to derive models of effective behavior across length scales analytically. In recent years, powerful tech- Model Verification and Validation niques for characterizing such effective, or macroscopic, behavior, including relaxation and gamma convergence, Verification and validation are defined in the DoE plan have been developed in the context of the “modern calculus for the Strategic Computing & Simulation Validation & of variations” by, among others, Müller.118 What these meth- Verification Program as follows: ods do is to exhaustively evaluate all the possible subscale behaviors, or microstructures, that may develop in the mate- • Verification. The process of determining that a com- rial in response to macroscopic deformation and to determine puter simulation correctly represents the conceptual the optimal, or “softest,” material response enabled by those model and its solution. microstructures. Examples of a material with microstructures • Validation. The process of determining the degree to that can be treated in this manner include martensite, sub- which a computer simulation is an accurate represen- grain dislocation structures, dislocation walls and networks, tation of the real world. ferroelectric domains, shear bands, spall planes, and others. By using the relaxed, or macrocoscopic, material model in The DoE Accelerated Strategic Computing Initiative has calculations, the microstructural length scale is effectively defined V&V requirements for the computer codes used as pushed down to the subgrid level and need not be accounted part of the national nuclear Stockpile Stewardship Program. for in the calculations explicitly, at enormous computational One of the requirements is to develop a well-defined plan for savings.119 Remarkably, the calculations still capture the V&V for each code. The idea is that a successfully executed exact macroscopic behavior exactly, since the effect of all V&V plan will certify the suitability of a computer code for possible microstructures has in effect been precomputed in a particular application. This paradigm is now commonplace the course of determining the relaxed model. Finally, the for large-scale simulation efforts at DOE Defense Programs upscaling of the material behavior happens without a loss of laboratories. information, since the optimal microstructures can always be Although the idea has taken hold that some form of reconstructed from the macroscopic solution. This ability to V&V is required in protection material simulation codes reconstruct microstructures from the macroscopic response and some efforts have been made, a rigorous formalism and may be critical in applications where the extreme values of framework such as those established at DOE would greatly the microscopic deformation and temperature fields, and not benefit the DoD research community (see Figure 4-20). just their average values, are of consequence. The next step beyond V&V is UQ to determine the un- Unfortunately, explicit relaxations are known for only a certainties that affect not only simulations but experiments as handful of material models, although the list of such models well. It is widely accepted that experimental results are ac- continues to grow. Despite this paucity of explicit results, companied by systematic and random errors. UQ attempts to relaxation and related methods illustrate the important role quantify these errors in a meaningful way. Each computation that analytical methods can play in the field of multiscale involves both numerical and physical parameters that have analysis. Indeed, when used in simulations, each material ranges, and distributions, of values. UQ techniques quantify model that is added to the list of explicitly known relaxations, the effect on the simulation outcomes of these parameter or homogenizations, saves vast volumes of computation variations. Such sensitivity information is directly relevant and, perhaps more importantly, makes feasible calculations to design. that would otherwise be intractable using sheer brute force. Production Runs—Large-Scale Simulations of Problems of Interest 118Müller, S. 1999. Variational models for microstructure and phase transitions. Pp. 85-210 in Calculus of Variations and Geometric Evolution Simulations of protective material performance are Problems, Springer Lecture Notes in Math 1713. F. Bethuel, G. Huisken, S. commonly conducted on multiprocessor parallel computers Mueller, K. Steffen, S. Hildebrandt, and M. Struwe, eds. Berlin, Germany: available in DoD as part of the High Performance Comput- Springer-Verlag. ing Modernization Program. The DoD platforms belong to 119Conti, S., P. Hauret, and M. Ortiz. 2007. Concurrent multiscale computing of deformation microstructure by relaxation and local enrich - the so-called teraflop generation (1012 flops, where a flop is ment with application to single-crystal plasticity. Multiscale Modeling and the number of floating point operations per second) (www. Simulation 6(7): 135-157.

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63 INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS DARPA, to “meet the relentlessly increasing demands for greater performance, higher energy efficiency, ease of pro- grammability, system dependability and security.”121 They will, among other things, offer unique opportunities for the simulation-based design of protective materials. Quantification of Margins and Uncertainties The extreme-scale computing world is quickly moving into the exascale, largely driven by the DoE (Figure 4-21). The unprecedented computing power is bringing about not just incremental improvements in capacity, fidelity, and resolution but also a paradigm shift in predictive science. The new main goal of this science is to make predictions with rigorously quantified uncertainties, so that the system can be certified or qualified. Specifically, in physics-based quantification of margins and uncertainties (QMU) the goal is to rigorously quantify means and uncertainties in the response of complex systems by maximizing the use of physical and computational models and minimizing use of experiments.122,123,124,125,126,127 The development of such approaches is driven by applications in which experimental data are prohibitively expensive or cannot be obtained in the laboratory under the operating conditions of the device. Sterling, R.S. Williams, and K. Yelick. 2008. ExaScale Computing Study: Technology Challenges in Achieving Exascale Systems, September 28. FIGURE 4-20 V&V process. SOURCE: Reprinted from ASME Available online at http://www.er.doe.gov/ascr/Research/CS/DARPA%20 V&V 10-2006, by permission of the American Society of Mechani- exascale%20-%20hardware%20%282008%29.pdf. Last accessed April cal Engineers. All rights reserved. 7, 2011. On June 20, 2010, DARPA announced the Omnipresent High Performance Computing Program (OHPC). See https://www.fbo.gov/ind ex?s=opportunity&mode=form&id=3ba522c52b23884843a6639c8cbd115 4&tab=core&_cview=0. top500.org) and have on the order of 104 cores (processing 121Dillow, C. 2010. DARPA Wants to Usher in the Age of Exaflop Com - units). Existing hydrocodes are reasonably scalable in the puting. Available at http://www.popsci.com/technology/article/2010-06/ darpa-wants-usher-age-exaflop-computing. Accessed May 2, 2011. range of hundreds to a few thousand processors. But produc- 122National Research Council. 2008. Evaluation of Quantification of tion armor simulations seldom need more than a few hundred Margins and Uncertainties Methodology for Assessing and Certifying processors. A typical large simulation involves a few million the Reliability of the Nuclear Stockpile. Washington, D.C.: The National degrees of freedom and requires tens of gigaflops. Although Academies Press. this resolution makes it possible to conduct the simulations 123Eardley, D., H. Abarbanel, J. Katz, J. Cornwall, S. Koonin, P. Dimo - takis, D. Long, S. Drell, D. Meiron, F. Dyson, R. Schwitters, R. Garwin, J. in three dimensions, in most cases much higher resolution is Sullivan, R. Grober, C. Stubbs, D. Hammer, P. Weinberger, R. Jeanloz, and J. necessary to obtain results that converge. Kammerdiener. 2005. Quantification of Margins and Uncertainties (QMU), Record-breaking platforms have recently achieved the JSR-04-330, March. Available online at http://www.stanford.edu/group/uq/ petaflop (1015 flops) scale and involve between 105 and 3 × docs/jason_qmu_margins.pdf. Last accessed April 7, 2011. 105 cores. After conducting a study of the key technology 124Helton, J.C. 2009. Conceptual and Computational Basis for the Q uantification of Margins and Uncertainty, SAND2009-3055, June. challenges for exascale computing, the Defense Advanced Available online at http://www.scribd.com/doc/27238941/Conceptual-and- Research Projects Agency (DARPA), announced the Om- Computational-Basis-for-the-Quantification-of-Margins-and-Uncertainty. nipresent High Performance Computing Program (OHPC), Last accessed April 7, 2011. aimed at building computers that exceed current petascale 125Pilch, M., T.G. Trucano, and J.C. Helton. 2006. Ideas Underlying computers to achieve the mind-boggling speed of one quin- Quantification of Margins and Uncertainties (QMU): A White Paper, SAND2006-5001, September. Available online at http://www.stanford.edu/ tillion (1,000,000,000,000,000,000) calculations per second group/uq/docs/qmu_ideas.pdf. Last accessed April 7, 2011. (1 exaflop).120 Such computers are needed, according to 126Sharp, D.H., and M.M. Wood-Schultz. 2003. QMU and nuclear weap - ons certification: What’s under the hood. Los Alamos Science 28: 47-53. 127Lucas, L., H. Owhadi, and M. Ortiz. 2008. Rigorous verification, vali - 120Kogge, P., K. Bergman, S. Borkar, D. Campbell, W. Carlson, W. Dally, dation, uncertainty quantification and certification through concentration- M. Denneau, P. Franzon, W. Harrod, K. Hill, J. Hiller, S. Karp, S. Keckler, of-measure inequalities. Computer Methods in Applied Mechanics and D. Klein, R. Lucas, M. Richards, A. Scarpelli, S. Scott, A. Snavely, T. Engineering 197(51-52): 4591-4609.

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64 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS FIGURE 4-21 Growth in supercomputer powers as a function of year. SOURCE: Courtesy of Ray Kurzweil and Kurzweil Technologies, Inc. Available online at http://www.kurzweilai.net/growth-in-supercomputing-power. the variability of the response of a protection system given QMU is also thought of as a tool for making high-conse- the randomness of inputs to the model and, potentially, the quence decisions about the design, certification, and deploy- stochasticity of the response. In general, providing a measure ment of high-value assets whose failure to perform safely of the maximum variability of the protection system over its and reliably could cause severe economic losses or loss of operating range as computed by the model would require life. QMU radically alters the picture of predictive science solving global optimization problems over input parameter and extreme-scale computing in many ways: by insisting on space. This variability in turn provides a measure for the rigorously quantified uncertainties in the predictions as a uncertainty in the response of the protection system—that measure of the confidence that decision makers can place in is, a measure of how well the response of the system can be such predictions; by injecting probability and statistics into pinned down under operating conditions given the random- the calculations; by insisting on a global view of the response ness of the system. Such global optimization calculations of the system over its entire operating range, thus breaking are inordinately intensive, hence the need for extreme-scale away from the “hero calculation” mode; and by the very computing. However, the model uncertainty is only one part tight coupling between simulations and validation or integral of the uncertainty budget: The level of confidence that can experiments that is required in order to establish confidence be placed in the physics and in the computations themselves, in the physics models. and the level of confidence that can be placed in the experi- In the context of protection materials, QMU, as enabled mental data, need to be rigorously evaluated. The evaluation by extreme-scale computing, holds the promise of physics- of both these terms in the uncertainty budget requires experi- based qualification of armor and protection systems. In this mental data, either data-on-demand or archival (legacy) data. approach, computational models would be used to compute

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65 INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS Finding 4-4. The formulation of rigorous quantification of should be considered, there is strong motivation to select margins and uncertainties (QMU) protocols leading to the among the multitude of combinations using simulation rather high-confidence certification of complex systems poses a than testing alone, since the latter is time consuming, expen- challenge. However, the benefits of the application of QMU sive, and not necessarily insightful. It was noted earlier in to the design and qualification of protective systems are this chapter that, to perform effectively, a block of ceramic potentially enormous. must be packaged in such a way that it deforms and fractures under a state of high compression. Metals and polymers, and combinations thereof, have been employed as packaging NEW PROTECTION MATERIALS AND MATERIAL materials for ceramic protection systems. SYSTEMS: OPPORTUNITIES AND CHALLENGES Finding 4-5. Accurate simulation of the performance of Polymeric materials such as some polycarbonates and Kevlar have demonstrated capabilities for certain protection armor protection systems under various ballistic threats and applications, including transparent face shields and body multiple hits necessitates advances in numerical methods, as armor. Polyethylene-based fiber materials such as Dyneema outlined in the section “Modeling and Simulation Tools,” as and Spectra have some properties, such as very high specific well as a better understanding of mechanisms of deformation strength, that make them very effective in ballistic and blast and fracture coupled with better constitutive descriptions. applications when they are employed either as a single mate- rial or in combination with ceramics and metals in the form Computational Materials Methods of a composite armor system. Preliminary ballistic tests have indicated their promise, especially for some of the higher The focus in this chapter has been on characterizing strength versions of these fibers that are not yet available materials with respect to their performance as protection commercially. Nor are the constitutive laws and property materials using observation and the experimental and com- inputs available that are needed to characterize these fibers putational methods of mechanics. These methods can be in the range of strains and strain rates relevant to ballistic or used to evaluate new materials, and they are essential for blast simulations. Even the constitutive laws and material establishing material properties that would enhance protec- properties needed to characterize an established fiber such tion performance; however, they cannot be used to design as Kevlar for these purposes are not fully in place. Thus far, new materials nor are they able to predict fundamental these materials have been assessed largely based on pro- material parameters such as modulus, hardness, or tough- jectile testing alone—make a target and shoot it. Efforts to ness. These more fundamental objectives are in the realm of employ constitutive models of fibers and yarns in simulations computational materials science. Computational materials of protection systems have been published in recent years, methods have been covered in a variety of reports, among including an assessment of lightweight fragment barriers for them Integrated Computational Materials Engineering: A commercial aircraft128,129 and a multiscale model of impacts Transformational Discipline for Improved Competitiveness on textile fabrics.130 and National Security, published by the NRC in 2008,131 and a report by DOE.132 In view of these widely available docu- Improving the properties of specific materials used in protection systems is one route to improved ballistic per- ments, the techniques of computational materials science, formance but may not open up opportunity for significant other than those already outlined above, will be described advances for some of the most widely employed protection only briefly in the current report. Integrated Computational materials given their maturity (some polymers are clear Materials Engineering is drawn on heavily for what is pro- exceptions). By contrast, there is almost certainly scope vided in the next few paragraphs, in many cases verbatim. for major advancement in the design of protection material That report also recommends a computationally enabled way systems made up of combinations of metals, ceramics, and forward for improving the development and insertion cycle polymers. Given the potential of polymer/ceramic/metal for new materials across the entire spectrum of materials sci- composite material protection systems and given the huge ence and engineering and is therefore an important forerun- number of material and architectural combinations that ner of the current document. Indeed, the field of protection materials is recognized by the committee as a good chance to implement many of the concepts described in Integrated 128Shockey, D.A., D.C. Erlich, and J.W. Simons. 1999. Lightweight fragment barriers for commercial aircraft, paper presented to the 18th In - Computational Materials Engineering. ternational Symposium on Ballistics, San Antonio, Tex. Available online at In addition to methods designed to simulate structural http://www.sri.com/psd/fracture/as_pdf/18th_int_symposium_ballistics99. pdf. Last accessed April 7, 2011. 129King, M.J., P. Jearanaisilawong, and S. Socrate. 2005. A continuum 131National Research Council. 2008. Integrated Computational Materials constitutive model for the mechanical behavior of woven fabrics. Interna- Engineering: A Transformational Discipline for Improved Competitiveness tional Journal of Solids and Structures 42(13): 3867-3896. and National Security. Washington, D.C.: The National Academies Press. 130Nilakantan, G., M. Keefe, T.A. Bogetti, and J.W. Gillespie, Jr. 2010. 132Department of Energy. 2005. Opportunities for Discovery: Theory Multiscale modeling of the impact of textile fabrics based on hybrid element and Computation in Basic Energy Sciences. Available online at http:// analysis. International Journal of Impact Engineering 37(10): 1056-1071. www.sc.doe.gov/bes/reports/files/OD_rpt.pdf. Last accessed April 7, 2011.

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66 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS others strictly research tools. As noted in the source study materials behavior at the macroscopic level, as described from which it was taken, above, the computational materials scientist has a host of techniques for simulation for a variety of purposes. The . . . the table is not intended to be complete but rather to wide variety of tools available reflects the fact that materials exemplify the methods available for modeling materials response and behavior involve a multitude of physical and characteristics. This table indicates typical inputs and outputs chemical phenomena whose accurate treatment in models of the software and examples of widely used or recognized requires the spanning of many orders of magnitude in length codes. Electronic structure methods employ different ap- and time. Further, computational simulation is used to tackle proximate solutions to the quantum mechanics of atoms a wide variety of materials attributes and phenomena, in- and electrons to explore the effects of bonding, chemistry, cluding thermodynamic, kinetic, and structural properties, local structure, and dynamics on the mechanisms that affect to bring advances in areas such as materials processing, material properties. Typically, tens to hundreds of atoms are microstructural evolution, structure-property relationships, included in such a calculation and the timescales are on the materials stability and corrosion, and stiffness and strength. order of nanoseconds. In atomistic simulations, arrange- Moreover, ments and trajectories of atoms and molecules are calculated. Generally based on models to describe the interactions among atoms, simulations are now routinely carried out with . . . the length scales in materials response range from millions of atoms. Length scales and timescales are in the nanometers of atoms to the centimeters and meters of nanometer and nanosecond regime, and longer length scales manufactured products. Similarly, time scales range from and timescales are possible in the case of molecular system the picoseconds of atomic vibrations to the decades over coarse graining from “all-atom” to “united atom” models which a component will be in service. Fundamentally, prop- (that is, interacting clusters of atoms). Dislocation dynam- erties arise from the electronic distributions and bonding ics methods are used to study the evolution of dislocations at the atomic scale of nanometers, but defects that exist on (curvilinear defects in the lattice) during plastic deformation. multiple length scales, from nanometers to centimeters, may The total number of dislocations is typically less than a mil - in fact dominate properties. It should not be surprising that lion, and strain rates are large compared to those measured no single modeling approach can describe this multitude of in standard laboratory tests. Thermodynamic methods range phenomena or the breadth of scales involved. While many from first-principle predictions of phase diagrams to complex computational materials methods have been developed, each database integration methods using existing tabulated data to is focused on a specific set of issues and appropriate for a produce phase diagrams and kinetics data.135 given range of lengths and times. Consider length scales from 1 angstrom to 100 microns. At the smallest scales scientists use electronic structure methods to predict bond - Microstructural evolution methods predict material ing, magnetic moments, and transport properties of atoms stability and evolution at the microscopic level based on free- in different configurations. As the simulation cells get larger energy functions, elastic parameters, and kinetic databases. and the times scales longer, empirical interatomic potentials are used to approximate these interactions. Optimization Micromechanical and mesoscale property models include and temporal evolution of electronic structure and atomistic solid mechanics and FEA methods that use experimentally methods are achieved using conjugate gradients, molecular derived models of materials behavior to explore microstruc- dynamics, and Monte Carlo techniques. At still larger scales, tural influences on properties. The models may incorporate the information content of the simulation unit decreases until details of the microstructure (resolving scales at the relevant it becomes more efficient to describe the material in terms level). Results may be at full system scale. Mesoscale struc- of the defect that dominates at that length scale. These units ture models include models for solidification and solid state might be defects in the lattice (for example, dislocations), the deformation using combinations of the previous methods internal interfaces (for example, grain boundaries), or some to predict favorable processing conditions for specific mi- other internal structure, and the simulations use these defects crostructural characteristics. Methods for code and systems as the fundamental simulation unit in the calculation. 133 integration offer ways to connect many types of models and simulations and to apply systems engineering strategies. Table 3-1 (Table 4-1 in the current report) from the Statistical tools are often used to gain new understanding above-mentioned NRC report Integrated Computational through correlations in large data sets. Other important Materials Engineering134 lists a variety of computational ICME tools include databases, quantifiable knowledge rules, error propagation models, and cost and performance materials methods, some of them standard and already ad- models.136 opted in materials development and industry activities, and Finding 4-6. Computational methods have considerable 133National Research Council. 2008. Integrated Computational Materials potential for aiding the architectural design of composite Engineering: A Transformational Discipline for Improved Competitiveness and National Security. Washington, D.C.: The National Academies Press. protection packages, but they require robust constitutive P. 69. 134National Research Council. 2008. Integrated Computational Materials 135Ibid., Engineering: A Transformational Discipline for Improved Competitiveness p. 71. 136Ibid. and National Security. Washington, D.C.: The National Academies Press.

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67 INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS TABLE 4-1 Mode or Method, Required Input, Expected Output, and Typical Software Used in Materials Science and Engineering Class of Computational Materials Model/Method Inputs Outputs Software Examples Electronic structure methods Atomic number, mass, valence Electronic properties, elastic VASP, Wien2K, CASTEP, GAMES, (density functional theory, quantum electrons, crystal structure and constants, free energy vs. structure Gaussian, a=chem., SIESTA, chemistry) lattice spacing, Wyckoff positions, and other parameters, activation DACAPO atomic arrangement energies, reaction pathways, defect energies and interactions Atomistic simulations (molecular Interaction scheme, potentials, Thermodynamics, reaction CERIU2, LAMMPS, PARADYN, dynamics, Monte Carlo) methodologies, benchmarks pathways, structures, point defect DL-POLY and dislocation mobility, grain boundary energy and mobility, precipitate dimensions Dislocation dynamics Crystal structure and lattice Stress-strain behavior, hardening PARANOID, ParaDis, Dis-dynamics, spacing, elastic constants, boundary behavior, effect of size scale Micro-Megas conditions, mobility laws Thermodynamic methods Free-energy data from electronic Phase predominance diagrams, Pandat, ThermoCalc, Fact Sage (CALPHAD) structure, calorimetry data, free- phase fractions, multicomponent energy functions fit to materials phase diagram, free energies databases Microstructural evolution methods Free-energy and kinetic databases Solidification and dendritic OpenPF, MICRESS, DICTRA, 3DGG, (phase-field, front-tracking methods, (atom mobilities), interface structure, microstructure during Rex3D Potts models) and grain boundary energies, processing, deployment, and (anisotropic) interface mobilities, evolution in service elastic constants Micromechanical and mesoscale Microstructural characteristics, Properties of materials—for OOF, Voronoi Cell, JMatPro, FRANC- property models (solid mechanics properties of phases and example, modulus, strength, 3D, ZenCrack, DARWIN and finite-element analysis) constituents toughness, strain tolerance, thermal/electrical conductivity, permeability; possibly creep and fatigue behavior Microstructural imaging software Images from optical microscopy, Image quantification and digital Mimics, IDL, 3D Doctor, Amira electron microscopes, X-rays, etc. representations Mesoscale structure models Processing thermal and strain Microstructural characteristics PrecipiCalc, JMat Pro (processing models) history (for example, grain size, texture, precipitate dimensions) Part-level finite-element analysis, Part geometry, manufacturing Distribution of temperatures, ProCast, MagmaSoft, CAPCAST, finite difference, and other processing parameters, component stresses and deformation, electrical DEFORM, LS-Dyna, Abaqus continuum models loads, materials properties currents, magnetic and optical behavior, etc. Code and systems integration Format of input and output of Parameters for optimized design, iSIGHT/FIPER, QMD, Phoenix modules and the logical structure of sensitivity to variations in inputs or integration, initial input individual modules Statistical tools (neural nets, Composition, process conditions, Correlations between inputs and SPLUS, MiniTab, SYSTAT, FIPER, principal component analysis) properties outputs; mechanistic insights PatternMaster, MATLAB, SAS/STAT SOURCE: National Research Council. 2008. Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security. Washington, D.C.: The National Academies Press. characterizations of component materials. Experimental data tural feature sizes and the range of strains, strain rates, and and constitutive characterizations of some materials used in stress states relevant to blast and penetration events. Close composite armor systems are woefully inadequate. This is es- communication between experimentalists who measure the pecially true for some promising polymers. Properties must high-stress, high-strain-rate properties of materials and the be measured and characterized over the range of microstruc- modelers who use these data is strongly encouraged.

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68 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS Overall Recommendations microsecond resolution in time) capabilities for in situ visu- alization of deformation and failure mechanisms during the Recommendation 4-1. The Department of Defense should impact event. pursue an initiative for protection materials by design by exploiting the capabilities of advanced computational and Recommendation 4-4. As part of the initiative, a program experimental methods. The initiative will (1) enable im- should be established with primary focus on code validation proved understanding of fundamental material deformation and verification; multiscale, multiphysics material models; and fracture mechanisms governing protection materials integrated simulation/experimental protocols; prediction performance and (2) provide guidance for changes in mate- with quantified uncertainties; and simulation-based quali- rial processing. fication to help advance predictive science for protection materials and material systems. Recommendation 4-2. The protection materials by design initiative should also use advanced computational and ex- Recommendation 4-5. The initiative should identify a series perimental methods to simulate the ballistic and blast perfor- of unclassified protection material challenge problems com- mance of candidate material protection systems. prising simulation and experimental validation whose solu- tion would convincingly demonstrate the effectiveness of Recommendation 4-3. The protection materials by design protection materials by design. One such canonical problem initiative should include a concerted effort to develop the might be the characterization of the high-strain-rate response next generation of Department of Defense advanced pro- of brittle armor materials such as ceramics and glasses un- tection codes that incorporate experimentally validated, der combinations of high pressure and shear representative high-fidelity scientific models, as well as the necessary of ballistic penetration, followed by a demonstration of the high-performance computing infrastructure. Progress in effectiveness of the new characterization in simulating the this direction will require the development of high spatial performance of a particular ceramic armor package. and temporal resolution (with 10-μ resolution in space and