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Opportunities in Protection Materials Science and Technology for Future Army Applications (2011)

Chapter: 4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities

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Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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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 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-

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×

havior is pushed to the extreme. This is particularly true for simulations of ballistic penetration. Much of what is covered in this chapter applies to both ballistic and blast assaults, but for the most part the discussion will be cast in the context of ballistic assaults owing to the extreme demands they place on the theoretical and experimental knowledge of material response and on numerical simulation.

After presenting three examples of current capabilities, the committee discusses present-day experimental methods. Its discussion underscores the importance of understanding and characterizing the basic mechanisms of deformation and fracture in advancing protection materials. The committee goes on to address opportunities and challenges in experimental and computational methods.

THREE EXAMPLES OF CURRENT CAPABILITIES FOR MODELING AND TESTING

Three examples illustrate current capabilities for simulating the actual test performance of protection materials and highlight opportunities for further advances. They are (1) projectile penetration of an aluminum plate; (2) projectile penetration of ceramic plates; and (3) blast loading of steel sandwich plates. These exemplary cases demonstrate that a rational approach to armor design based on computational and experimental methods is feasible. It is not the committee’s intention to cover all possible armor systems or to bound armor performance characteristics.

Projectile Penetration of High-Strength Aluminum Plates

Accurate simulation of projectile penetration of metal plates is being worked on using all three tools, and several groups have achieved predictive success. A recent study by Børvik et al.1 addresses the penetration of plates of 7075 aluminum by two types of projectiles. The authors are from a research group in Norway noted for its emphasis on each of these three tools.

FIGURE 4-1 shows a blunt projectile and an ogive-nosed projectile, both of hardened steel (projectiles such as these are often used in unclassified studies) exiting a 20-mm-thick plate of AA7075-T651 aluminum. Figure 4-2 presents a plot of the exit velocity of the projectile as a function of its initial velocity before impact. As mentioned in Chapter 2, the initial velocity at which the projectile just manages to penetrate the plate with zero residual velocity is known as the ballistic limit V0; Figure 4-3 presents the results of numerical simulations of these tests.

The constitutive relation used to characterize plastic deformation of AA7075 in the simulations of Børvik et al.2 is the Johnson-Cook3 relation, which has been used in many recent simulations of this type. There are six constants in this constitutive law that must be chosen to give the best possible fit to the data on the material. Supplementing the Johnson-Cook relation is an equation relating the temperature increase to plastic deformation. In addition to accounting for the effect of stress state, the constitutive model accounts for the effects of the strain rate and thermal softening on plastic deformation and can capture some aspects of adiabatic shear localization. To calibrate the constitutive laws for a given material, an extensive suite of tests must be performed, from tensile and compressive stress-strain tests up to tests at large strains in differing material orientations and temperatures, with strain rates as high as 104 s–1. The Johnson-Cook deformation relation is supplemented by a material fracture criterion that usually employs a critical value of the equivalent plastic strain, dependent on the stress triaxiality. Stress triaxiality is the ratio of hydrostatic tension to the von Mises effective stress. A series of notched-bar tensile ductility tests was used by Børvik et al.4 to calibrate the critical effective plastic strain at fracture as a function of stress triaxiality. As this outline makes clear, the characterization of a material for input into constitutive models is a considerable task in its own right.

To simulate the penetration of a hard, ductile metal target, the numerical method must account for large plastic strains, for dynamic effects, including inertia and material 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. For several decades, finite-element codes have been able to model large strains, but the intense deformations encountered in penetration are challenging because they involve the difficult problem of remeshing to avoid overly distorted elements. It is also important to model the material failure response after the critical plastic strain has been attained. Current procedures usually erode an element during the final failure process, stepping down its stress to zero and finally deleting the element. In addition, it is essential to account for the pressure and friction exerted by the projectile on the plate.

The simulation challenge presented by projectile penetration owing to distortion of the meshes is evident in Figure 4-4. The blunt-nosed projectile produces shear localization through the thickness of the plate, followed by shear-off, which creates a plug of material that is pushed ahead of the projectile. In contrast, the ogive-nosed projectile pushes

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1Børvik, T., O.S. Hopperstad, and K.O. Pedersen. 2010. Quasi-brittle fracture during structural impact of AA7075-T651 aluminum plates. International Journal of Impact Engineering 37(5): 537-551.

2Ibid.

3Johnson, G.R., and W.H. Cook. 1983. A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures. Pp. 541-547 in Proceedings of the 7th International Symposium on Ballistics, The Hague, The Netherlands. Available online at http://www.lajss.org/HistoricalArticles/A%20constitutive%20model%20and%20data%20for%20metals.pdf. Last accessed April 5, 2011.

4Børvik, T., O.S. Hopperstad, and K.O. Pedersen. 2010. Quasi-brittle fracture during structural impact of AA7075-T651 aluminum plates. International Journal of Impact Engineering 37(5): 537-551.

5See http://www.lstc.com.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
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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.

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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, V0. 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.

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FIGURE 4-3 Numerical finite-element simulations of the ballistic behavior shown in Figure 4.2 depicting the effects of mesh refinement 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 Engineering 37(5): 537-551.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
image

FIGURE 4-4 Simulations of penetration of a plate of AA7075-T651 showing finite-element mesh for a blunt-nosed (a) and an ogive-nosed (b) hard steel projectile. In both cases the projectile 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 127 m/s. 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.

material radially outward, dissipating more energy. The numerical results in Figure 4-3 reproduce both sets of data in Figure 4-2 quite accurately, including the ballistic limits.

While AA7075 aluminum is not the most important material for projectile defeat, these 2008 simulations represent the state of the art. All the material parameters required as inputs to the constitutive and failure models have been independently measured, including those of the steel projectiles. Only the finite-element mesh layout and the element size are selected by the analyst. The predictions in Figure 4-3 depend on element size, because the constitutive model used in these simulations can predict the onset of shear localization and/or the fracture process but cannot predict the thickness of the associated failure zone. The thickness of a shear localization band is determined by a combination of factors, including microstructural length scales (see Chapter 3). These factors are not accounted for in commonly employed constitutive laws such as the Johnson-Cook relation, so they cannot set the size of these zones. As a result, the calculations give rise to a shear zone whose thickness is the width of one element. Thus, the energy dissipated in a zone of shear localization, or within any fracture process zone where the material is weakening, is proportional to the element size. Consequently, a systematic refinement of the mesh size to smaller and smaller elements will not converge to the correct physical 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 500μ in the three-dimensional case. Either element size calibration or a constitutive length parameter will continue to be an essential, non-straightforward requirement in penetration simulations.

The simulation of penetration represented by the results in Figure 4-3 must be pushed further to demonstrate the robustness 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 impacting the plate at an oblique angle? More sophisticated constitutive 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 demonstrated, the payoff in material protection simulations has yet to be realized.

Projectile Penetration of Bilayer Ceramic-Metal Plates

The simulation of projectile penetration of bilayer ceramic-metal plates further illustrates the need to combine good work on computation with sound experiments to investigate material and system properties in extreme conditions of strain, strain rate, and pressure. Holmquist and Johnson6 published the results of such simulations for a bilayer plate of boron carbide backed by 6061-T6 aluminum alloy, where the simulations utilized the ceramic constitutive law of Johnson, Holmquist, and Beissel,7known as JHB. These simulations represent the state of the art in computations for the ballistic performance of ceramic armor components.

Experiments carried out many years ago by Wilkins8 for the same system provide data on the ballistic limit that may be compared with the simulation results in Holmquist and Johnson.9 Wilkins fired blunt and pointed projectiles at targets consisting of a 7.24-mm-thick boron carbide plate bonded to a 6.35-mm-thick piece of aluminum alloy as the backing plate, and the projectiles were made of very hard

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6Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide subjected to high-velocity impact. International Journal of Impact Engineering 35(8): 742-752.

7Johnson, G.R., T.J. Holmquist, and S.R. Beissel. 2003. Response of aluminum nitride (including phase change) to large strains, high strain rates, and high pressures. Journal of Applied Physics 94(3): 1639-1646.

8Wilkins, M.L. 1967. Second Progress Report of the Light Armor Program, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence Livermore National Laboratory.

9Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide subjected to high-velocity impact. International Journal of Impact Engineering 35(8): 742-752.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×

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 plate to break. In the case of the cylindrical projectile, the full impact of the hit is felt by the target immediately. The bilayer begins to bend almost at once, and the ceramic plate fractures due to tensile stresses at a relatively early stage of the impact. On the other hand, the sharp nose of the pointed projectile does not immediately fully load the impact onto the target. Instead, the forces applied by the projectile to the bilayer 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, which shows ceramic strength versus applied pressure. In this context, “strength” is the ability of the material to support shear stress without extensive deformation. Such deformation may occur as the material yields and flows like a very viscous liquid owing to rearrangements within its internal lattice structure as it fractures and comminutes into small particles, which then flow collectively like sand. The relationships in Figure 4-5 are shown for intact material and failed material, each at two different strain rates, denoted by image The connections between ceramic strength and applied pressure depicted in Figure 4-5 are used in the JHB model to represent the fact that a ceramic is strong in compression (i.e., at high pressure) and weak in tension (i.e., at negative pressure). The plot for intact material indicates that at high pressure, strength is almost insensitive to pressure. Under these conditions, a ceramic cannot fracture. Instead, at a critical level of shear stress (equal to the ceramic strength) it flows by the motion of dislocations that rearrange the internal structure of the ceramic lattice. In negative pressure (i.e., weak tension) the strength of the intact ceramic is very low and vanishes at a critical pressure, negative T. This situation reflects the fact that in tension, ceramic cracks and fractures at a low tensile stress. As the pressure applied to the ceramic is increased, it is less likely to crack and its strength increases. The plots for intact ceramic (Figure 4-5) interpolate this behavior between the extremes of tensile stress and very high pressure. The plots also indicate that the strengths will be slightly different at high and low strain rates.

image

FIGURE 4-5 Ceramic strength versus applied pressure for the JHB constitutive model. The relationship is shown for intact material and failed material, each at two different strain rates, denoted by image NOTE: D stands for damage. D = 1, fully damaged; D < 1 not fully damaged; D = 0 would mean no damage. As is illustrated, the damage weakens the material. SOURCE: Reprinted with permission from Johnson, G.R., T.J. Beissel, and S.R. Beissel, Journal of Applied Physics, 94, 1639, (2003). Copyright 2003, American Institute of Physics.

It is obvious that when the ceramic cracks and fractures, it will be irreversibly damaged as it comminutes into granular material. This situation is captured in Figure 4-5, which shows that failed material has lower strengths at the same pressure than an intact material. Furthermore, the comminuted material cannot support tensile stresses, and so the plot of strength versus pressure for failed material terminates at the origin in Figure 4-5. The JHB constitutive law encompasses detailed rules for transitioning the state of the ceramic from intact to failed, and, broadly speaking, these rules implement the concept that as the material experiences deformation by flow of the fracturing material, the strength is steadily degraded. Therefore, as extensive deformation of the ceramic takes place, its strength steadily changes from the initial level appropriate for intact ceramic to that for failed ceramic.

Another feature of the JHB model as implemented in simulations of projectiles hitting the bilayer of boron carbide and aluminum alloy11 is that once the material has failed and is subsequently, or simultaneously, placed under tension, the original continuum material is converted into a collection of individual free-flying particles. Such a condition represents the situation observed in experiments12 where much of the

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10Wilkins, M.L. 1967. Second Progress Report of the Light Armor Program, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence Livermore National Laboratory.

11Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide subjected to high-velocity impact. International Journal of Impact Engineering 35(8): 742-752.

12Wilkins, M.L. 1967. Second Progress Report of the Light Armor Program, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence Livermore National Laboratory.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×

ceramic material is removed from the crater created by the penetration of projectile when clouds of comminuted ceramic particles form.

Constitutive laws such as the JHB model have many material parameters in them that characterize the elastic, acoustic, yielding, and fracturing behavior of the material being simulated. Holmquist and Johnson13 calibrated most of the material parameters in their model using the results of plate impact experiments14 involving a solid disc launched at high speed against a flat surface of the material being investigated. They augmented the information from these tests with spall data from experiments.15These observations reinforce the notion that successful simulation depends on the availability of experimental data to (1) characterize the parameters in the models being used, (2) validate and test the quality of the computational results, and (3) provide insights into how computational simulation should be conducted for a given material in a given situation.

Results from Holmquist and Johnson’s simulations16 show that for the initial velocities—V = 790 m/s for the pointed projectile and 700 m/s for the cylinder. At 100 µs after first hitting the bilayer at velocity V, the projectile has a residual velocity Vr. This velocity is 200 m/s for the pointed projectile and 257 m/s for the cylinder, and the projectiles will not slow down much more because the target is then offering no resistance. These results match those of Wilkins17 in multiple ways, including appearance of the crater and the value of the ballistic limit.

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 in the now destroyed segment of the aluminum immediately below the penetrator. Although the ceramic layer in its residual shape is largely unbent due to the lack of a bond between the materials in the bilayer in the simulations, the ceramic will have bent like the aluminum in the early stage of projectile penetration, though to a lesser extent than the bending of the aluminum layer. Nevertheless, the results of the simulation clearly point out the importance of bending in the projectile penetration of relatively thin ceramic targets. A feature of the concave upward bending of the ceramic immediately below the projectile as it penetrates the target is a significant tensile stress at the bottom surface of the ceramic, leading to its fragmentation and comminution. In this state, the ceramic will retain the ability to resist the penetrator as long as the comminuted granular material is well contained by the aluminum backing and the penetrator itself. However, if such constraint is lost, the ceramic becomes ineffective in resisting the penetrator as it simply turns into a freely flying granular cloud. This consideration is an important element in the proper design of ceramic armor.

Note that Holmquist and Johnson18 simulated two other types of experiment in addition to the penetration of a thin bilayer target: the impact on boron carbide plates19and the deep penetration of steel-jacketed boron carbide blocks.20,21 Each of these experiments was successfully simulated with use of the JHB constitutive law, showing that the state of the art of simulation for the ballistic response of ceramic targets is quite far advanced. However, Holmquist and Johnson found it necessary to use a different set of material parameters for each distinct type of experiment. Therefore no single material model is yet able to capture the penetration and material response phenomena occurring in the cases of, for example, a ceramic under plate impact, deep penetration by a long heavy rod, and perforation of a thin bilayer target. As the authors note, this limitation of the results they obtained suggests that some important mechanisms of ceramic response are not being modeled accurately in the JHB constitutive law and that further work will be necessary to improve the constitutive laws for the response of ceramic under ballistic conditions of high strain, high strain rate, and high pressure.

All-Steel Sandwich Plates for Enhanced Blast Protection: Design, Simulation, and Testing

Traditionally, plate structures designed to withstand blast loads have employed monolithic plates. Within the past decade, the Office of Naval Research has supported efforts to explore whether all-metal sandwich plates comprised of the same material and having the same mass per area can be more effective against blasts than monolithic metal plates. Studies completed to date have considered various core types, such as honeycombs, corrugated plates, and lattice

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13Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide subjected to high-velocity impact. International Journal of Impact Engineering 35(8): 742-752.

14Vogler, 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 Program, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence Livermore National Laboratory.

16Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide subjected to high-velocity impact. International Journal of Impact Engineering 35(8): 742-752.

17Wilkins, M.L. 1967. Second Progress Report of the Light Armor Program, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence Livermore National Laboratory.

18Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide subjected to high-velocity impact. International Journal of Impact Engineering 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.

20Orphal, D.L., R.R. Franzen, A.C. Charters, T.L. Menna, and A.J. Piekutowski. 1997. Penetration of confined boron carbide targets by tungsten long rods at impact velocities from 1.5 to 5.0 km/s. International Journal of Impact Engineering 19(1): 15-29.

21Lundberg, P., L. Holmberg, and B. Janzon. 1998. An experimental study of long rod penetration into boron carbide at ordnance and hypervelocities. Pp. 251-258 in Proceedings of the 17th International Symposium on Ballistics. Midrand, South Africa: South African Ballistics Organization.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×

trusses, with attention to design and ease of manufacturing.22Both air and water blast environments have been investigated, and an understanding is now in place of when fluid-structure interaction effects are important. The advancement of understanding that has been achieved is due to tightly coupled numerical simulation and experimental testing. In this section a brief overview is given of recent work by Dharmasena et al.,23 which illustrates current capabilities and limitations along with possible opportunities.

The sequence of events occurring when a sandwich plate is struck by a blast wave is depicted in simplified form in Figure 4-6, where three relatively separate stages in the sequence can be visualized. For meter-size plates subject to intense blasts, the entire process lasts about 10 ms. In the scenario sketched in the figure, fluid-structure interaction occurs in Stage I. If the mass of the face toward the blast is sufficiently large, the blast wave bounces off the plate in much the way a rubber ball would be reflected, transmitting almost twice its incident momentum to the plate before the plate has time to displace. This is a reasonable way of viewing most air blasts striking a metal face of more than a few millimeters thick. However, a 1-cm thick metal plate struck by a water blast wave interacts with the wave in such a way that the reflection is reduced and therefore a smaller fraction of the incident wave momentum is transferred to the plate. This basic fluid-structure interaction effect for water blasts was discovered in World War II and has recently been extended to air blasts.24

Various core geometries have been investigated experimentally and by simulations, including hexagonal and square honeycomb cores; corrugated or folded-plate cores; and cores made of truss elements. These have generally been plates fashioned from relatively ductile steels. A folded-plate core has the advantage that it is readily manufactured. This is also true of several truss-core geometries, which have the added advantage that the core is an open structure useful for multifunctional applications.25Which core yields the best performance depends on the type and level of blast, whether the blast is in air or water, and whether the standoff is close or remote. A sandwich plate can be designed to capitalize on the fluid-structure interaction effect because the mass per area of the face sheet toward the blast will be less than half that of its monolithic competitor. For this effect to come into play, the core must not be overly strong, so that only the face sheet acquires momentum during the period it is impacted by the water blast.26 For air blasts, decoupled calculations can supply a good approximation. In such cases, the pressure history is computed in the first step by treating the plate structure as rigid; this history is then applied to the structure in the second step to obtain its response. While fluid-structure effects are not usually significant in air blasts, interaction effects can be important for air blasts that entrain sand or gravel, such as those experienced by vehicles exposed to buried improvised explosive devices.

Figure 4-7 displays the deformation of clamped square-honeycomb-core sandwich plates made from stainless steel and subject to three explosive levels at close standoff in air. At the lowest level shown, the back face undergoes relatively little deformation; the high bending stiffness of the sandwich plate is very effective. At the two higher levels of blast, significant stretching of the face sheets occurs in addition to core crushing. Both core crushing and face sheet stretching absorb substantial energy. While severely deformed, these plates have not fractured.

Accurate simulations of blast-loaded structures require input material properties for the constitutive relation, knowledge of the temporal and spatial pressure pulse on the structure, and a finite element code that can cope with highly nonlinear material and geometric behavior, including internal contacting surfaces. As no fracture occurred in the test specimens, no attempt was made to model damage or fracture in the simulations.27Finite-strain plasticity was employed along with input of tensile data for the stainless steel as a function of strain and strain rate.

Comparisons of the simulations with the experimental results are displayed in Figure 4-8. Nearly all the experimental details are replicated. Even the buckling of the webs can be captured accurately. The back face of these sandwich plates deflects less than the equivalent mass of solid plate even in an air blast. The performance of the sandwich plate relative to a monolithic plate would be better in water blasts due to fluid-structure interaction that favors sandwich plates.

There are no “adjustable” parameters in the simulations presented above. Thus, one can conclude it is possible to carry out calculations to improve the design of plate structures against blast loads of various types. This optimistic assessment must be tempered by the following considerations:

  • The ultimate blast resistance of these structures has not been determined. To do so would require subject-

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22Wadley, H.N.G. 2006. Multifunctional periodic cellular metals. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364(1838):31-68.

23Dharmasena, 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.

24Kambouchev, N., L. Noels, and R. Radovitzky. 2006. Nonlinear compressibility effects in fluid-structure interaction and their implications on the air-blast loading of structures. Journal of Applied Physics 100(6): Article number 063519.

25Wadley, H.N.G. 2006. Multifunctional periodic cellular metals. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364(1838): 31-68.

26Liang, Y., A.V. Spuskanyuk, S.E. Flores, D.R. Hayhurst, J.W. Hutchinson, R.M. McMeeking, and A.G. Evans. 2007. The response of metallic 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. Mechanical response of metallic honeycomb sandwich panel structures to high-intensity dynamic loading. International Journal of Impact Engineering 35(9): 1063-1074.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
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FIGURE 4-6 Schematic depicting the response of a clamped sandwich plate to blast loading: (a) Impulsive loading (Stage I); (b) core crushing (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 of fracture in the simulations. Reliable models for such simulations are not yet established for either monolithic plates or sandwich plates.

  • Plate structures are susceptible to failures along welds and joints, and simulations of these events are not yet reliable. Existing continuum models can be calibrated to reproduce fractures in tension or in
  • shear, but they cannot reliably predict both types of fractures under a wide range of stress states. Mechanistic-based fracture models are needed to expand predictive capabilities.
  • Highly refined meshes were employed in the sandwich plate simulations reported above—far more refined than would be feasible for-large scale structures. New constitutive models and computational
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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FIGURE 4-7 Half-sectional square honeycomb core test panels. 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 clamped around their edges subjected to three levels of air blast. The plates were sectioned after deformation to display the core and the relative position of the faces. The core webs are 0.76 mm thick 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 the plate. The equivalent thickness of a solid plate with the same mass per area is 13.1 mm. 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.

image

FIGURE 4-8 Comparison of experimental test specimens (on the left) deformed at the three levels of air blast shown, with simulations carried out for the same plates and level of blasts (on the right). 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.

methods are required to capture the main deformational features of the core with relatively coarse meshing.

THE STATE OF THE ART IN EXPERIMENTAL METHODS

As the discussion of the three examples above illustrates, 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 current experimental methods relevant to protection materials and points to opportunities for advancing their capabilities.

Definition of the Length Scales and Timescales of Interest

The committee has focused on developing lightweight protective materials for future Army applications and interpreted its mandate broadly to include providing protection from threats that involve the rapid deposition of energy directly into a material or structure. Examples of threats of this type include direct impact by (1) an incoming projectile and (2) explosive, or blast, loading. The timescales associated with these events are of paramount importance, and the characteristic velocities associated with propagating waves, projectiles, or failure processes generate associated 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 millimeter 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 controlling phenomena operate at much smaller timescales (microseconds 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

Experimental methods must be able to access the appropriate regimes in the length scale and timescale space in order to investigate any particular behavior or phenomenology. A critical issue here is that these scales should be investigated simultaneously. Because the events are transient and involve complex loading paths, it is difficult to pin down real-time

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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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.

behavior through postmortem analysis of the material or structure. This does not imply that there are no relevant phenomena at the larger timescales (multiple milliseconds and larger). Such timescales are relevant to a number of threats, particularly those related to blast and explosive loading, and they are tightly coupled to structural dynamics, which can involve both material and geometric nonlinearity. Broadly speaking, however, the challenges in understanding and observation at these longer timescales and length scales consist largely of correctly exploring the coupling of the dynamics to the design space.

In this section, state-of-the-art experimental methods capable of exploring various regimes in the length scale–timescale space are described. To begin, experimental methods will be classified in terms of their intended applications. First, however, a broad comment is in order. One approach to understanding the interaction between threat and material is to perform a highly instrumented version of the actual threat event. Although this approach is very useful, and is indeed the most definitive metric for the effectiveness of a protective material within a specific protected system, it does not necessarily provide significant guidance for the development of radically improved protective systems. The focus of this section is, accordingly, on the more fundamental experiments associated with developing a basic understanding of the mechanisms, behaviors, and processes associated with the threat-material interaction that can lead to improved constitutive characterizations, including those for failure processes.

Classification of Experimental Methods28

Experimental techniques commonly called “impact experiments” often have very different objectives. Since the design of an experimental technique depends on the goal of the experiment, it must first be decided what information one wants to extract from the experiment. Typically, what are called “impact” (or “dynamic”) experiments fall into one of four categories, listed here according to the complexity of the dynamics:

  1. High-strain-rate experiments. These measure the high-strain-rate characteristics of a material;
  2. Shock physics experiments. These aim at understanding shock wave propagation in a material or structure; they may also develop high strain rates, but the high-rate deformations vary as a function of space and time;
  3. Impact phenomenology experiments. These experiments endeavor to understand or discover impact phenomena such as cratering efficiency or fragmentation; and
  4. Dynamic failure experiments. These would help us to understand the processes of dynamic failure within a material or structure.

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28Except as noted in the text, this section drawn from Ramesh, K.T. 2008. High strain rate and impact experiments. Chapter 33 in Handbook of Experimental Solid Mechanics. W.N. Sharpe, Jr., ed. New York, N.Y.: Springer.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×

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) deformations 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, image, 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 the specimen rather than techniques that develop high strain rates just behind a propagating wave front.

The main experimental techniques for measuring the rate-dependent properties of various materials are described in Figure 4-10 (the stress states developed by the various techniques may not necessarily be identical). One outstanding recent review of these methods is that of Field et al.29 Here, strain rates above 102 s–1 are classified as high strain rates, those above 104 s–1 are called very high strain rates, and those above 106 s–1 are ultrahigh strain rates. Strain rates at or below 10–3 s–1are usually considered to represent quasi-static deformations, and strain rates below 10–6 s–1 are considered to represent “creep.” The emphasis here is on experimental techniques for strain rates greater than 102 s–1—that is, high (102-104 s–1), very high (104-106 s–1) and ultrahigh (>106 s–1).

Kolsky Bars

The now-classical experimental technique in the high-strain-rate domain is the Kolsky bar, or split-Hopkinson pressure bar, experiment30 for determining the mechanical properties of various materials (e.g., metals,31 ceramics,32 and polymers33) in the strain rate range 102 through 8 × 103 s–1 (see Figure 4-11). This technique is now in use throughout the world. Since the fundamental concept involved in this technique was developed by Kolsky,34 the term Kolsky bar will be used here. Kolsky bar experiments may include compression, tension, torsion, or combinations of all of these.35

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FIGURE 4-10 Experimental techniques used for the development of controlled high-strain-rate deformations in materials.

The Kolsky bar consists of two long bars, called the input and output bars, that are designed to remain elastic throughout the test. These bars sandwich a small specimen, usually cylindrical, which is expected to develop inelastic deformations. The bars are typically made of high-strength steels, such as maraging steel, with a very high yield strength and substantial toughness. Other bar materials that have been used include 7075-T6 aluminum, magnesium alloys and poly(methyl methacrylate) (for testing very soft materials), and tungsten carbide (for testing ceramics). One end of the input bar is impacted by a projectile made of a material identical to that of the bars; the resulting compressive pulse propagates down the input bar to the specimen. Several reverberations of the loading wave occur within the specimen; a transmitted pulse is sent into the output bar and a reflected pulse is sent back into the input bar. Typically, resistance strain gages are placed on the input and output bars for measuring (1) the incident pulse generated by the 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 typically measured using high-speed digital oscilloscopes with at least 10-bit accuracy and preferably with differential inputs to reduce noise.

Many extensions and modifications to the traditional Kolsky bar system have been developed over the last five

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29Field, J.E., S.M. Walley, W.G. Proud, H.T. Goldrein, and C.R. Siviour. 2004. Review of experimental techniques for high rate deformation and shock studies. International Journal of Impact Engineering 30(7): 725-775.

30Nicholas, T., and A.M. Rajendran. 1990. Material characterization at high strain-rates. Pp. 127-296 in High Velocity Impact Dynamics. J.A. Zukas, ed. New York, N.Y.: John Wiley & Sons.

31Nemat-Nasser, S., and J.B. Isaacs. 1997. Direct measurement of isothermal flow stress of metals at elevated temperatures and high strain rates with application to Ta and Ta-W alloys. Acta Materialia 45(3): 907-919.

32Chen, W., G. Subhash, and G. Ravichandran. 1994. Evaluation of ceramic specimen geometries used in a split Hopkinson pressure bar. DYMAT Journal 1: 193-210.

33Walley, S., and J. Field. 1994. Strain rate sensitivity of polymers in compression from low to high strain rates. DYMAT Journal 1: 211-228.

34Kolsky, H. 1949. An investigation of the mechanical properties of materials at very high rates of loading. Proceedings of the Physical Society: Section B 62(11):676-700.

35Gray III, G.T. 2000. Classic split-Hopkinson pressure bar testing. Pp. 462-476 in ASM Handbook Volume 8: Mechanical Testing and Evaluation. H. Kuhn and D. Medlin,eds. Materials Park, Ohio: ASM International.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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FIGURE 4-11 High-strain-rate behavior of 6061-T6 aluminum determined through servohydraulic testing, compression and torsional Kolsky bars, and high-strain-rate pressure-shear plate impact.

decades. Most of these are listed in Table I of a review36 by Field et al., which includes an exhaustive literature set. Very high strain rates (up to 5 × 104 s–1) can be attained in miniaturized systems while retaining the ability to study materials at strain rates as low as 1.0 × 103 s–1 (the maximum achievable strain rate is limited by an inertial correction and varies with the material being tested). Both computational and experimental results have shown that this extended capability can be attained not only without violating the requirements for valid high-rate testing but also while improving the precision and accuracy of the experimental results.37

High-Strain-Rate, Pressure-Shear Plate Impact

Researchers have developed techniques called high-strain-rate, pressure-shear plate impact techniques to study shearing behavior in materials experiencing homogeneous shearing deformations at exceedingly high shear rates (104 to 106 s−1) and superimposed hydrostatic pressures of several gigapascals.38 Although this approach39 assesses a wider range of responses, it is not used as much as the Kolsky bar experiment since it necessitates much higher investment in lab equipment and personnel whose training is time-consuming. The experiment involves the impact of plates that are flat and parallel but inclined relative to their direction of approach. The specimen is a very thin (say, 100 m), very flat plate of the material being investigated. This specimen is adhered to a hard plate (the “flyer”), which is itself mounted on a projectile that is launched through the barrel of a gas gun at an immobile target (“anvil” plate). The target is positioned in a special fixture, known as the target holder, within an evacuated chamber. The flyer and the anvil plates are aligned before impact using an optical technique. Rotation of the projectile is prevented by a key in the projectile, which glides within a matching keyway machined in the barrel.

At impact, plane longitudinal (compressive) and transverse (shear) waves are generated in the specimen and the target plate propagating at the longitudinal wave speed cland the shear wave speed cs. These waves reverberate within the specimen, causing the normal stress and the shear stress to

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36Field, J.E., S.M. Walley, W.G. Proud, H.T. Goldrein, and C.R. Siviour. 2004. Review of experimental techniques for high rate deformation and shock studies. International Journal of Impact Engineering 30(7): 725-775.

37Jia, D., and K.T. Ramesh. 2004. A rigorous assessment of the benefits of miniaturization in the Kolsky bar system. Experimental Mechanics 44(5): 445-454.

38Clifton, R.J., and R.W. Klopp. 1985. Pressure-shear plate impact testing. Pp. 230-239 in ASM Handbook Volume 8: Mechanical Testing. Materials Park, Ohio: ASM International.

39Other, similar approaches include the shear-compression test (SCS test) developed by Ravichandran and co-workers, which is simpler to perform but more difficult to analyze.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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FIGURE 4-12 Schematic of the high-strain-rate, pressure-shear plate impact experiment. The specimen thickness is greatly exaggerated for clarity. TDI, transverse-displacement interferometer; NVI, normal velocity interferometer.

build up in the specimen material. As Yadev notes, information on the stress levels sustained by the specimen material is carried by the normal and transverse waves propagating into the target plate.40 The target remains elastic, so there is a linear correspondence between the stresses and the particle velocities in the target plate. It is therefore good enough to measure the normal and transverse particle velocities in the target plate in order to obtain the specimen’s stress state and deformation state. The whole experiment is over before any unloading waves from the periphery of the plates reach the point of observation. Thus only plane waves are involved, and a one-dimensional analysis is not only sufficient but also rigorously correct. Like most plate impact experiments, this is a uniaxial strain experiment in that no transverse normal strains can occur during the time of interest.

Measurements of particle velocities at the free surface of the target plate are made using laser interferometry off a diffraction grating that is photodeposited onto the rear surface.41 The normal velocity and the transverse displacement at the center of the rear surface of the target are measured. The high-strain-rate, pressure-shear plate impact technique is capable of achieving shear rates of 8 × 104 to 106 s–1, depending on the specimen thickness.42 A version of this experiment that is designed to allow recovery of the specimen (for microstructural examination) after a single high-strain-rate shear loading has also been developed.43

The superimposed hydrostatic pressures that can be exerted during the high-strain-rate, pressure-shear plate impact experiment may be as high as 10 GPa, depending on the impedances of the flyer and target plates and the projectile velocity. The superimposed hydrostatic pressures must always be remembered when comparing high-strain-rate, pressure-shear plate impact data with data obtained using the other techniques shown in Figure 4-12, since all of the other techniques can generate essentially uniaxial stress states, typically corresponding to low hydrostatic pressures. In particular, while the effect of pressure on the flow stress of most metals is negligible in comparison with the effect of strain rate, the effect of pressure on the strength of polymers, ceramics, glasses, and amorphous materials may be substantial, even in comparison with the effect of strain rate.

Investigating Shock Physics

Experiments designed to study the propagation of large-amplitude stress waves within materials constitute a very broad class of impact experiments. The interest here is in experiments that examine the interactions of waves with materials, particularly exciting inelastic modes such as plasticity, cracking, or other kinds of damage. In contrast to the experiments in the preceding section, the experiments in this section all generate strain rates and stress states that vary in both space and time, and the wave propagation is fundamentally dispersive (i.e., the waveform changes as the wave propagates) because of material behavior.

In broad terms, wave-propagation experiments of this

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40Yadev, S. 1995. The mechanical response of a 6061-T6 A1/A1 “2O” 3 metal matrix composite at high rates of deformation, Acta Metallurgica Et Materialia.

41Except as noted in the text, this section is drawn from Ramesh, K.T. 2008. High strain rate and impact experiments. Chapter 33 in Handbook of Experimental Solid Mechanics. W.N. Sharpe, Jr., ed. New York, N.Y.: Springer.

42See, for example, Frutschy, K.J., and R.J. Clifton. 1998. High-temperature pressure-shear plate impact experiments on ofhc copper. Journal of the Mechanics and Physics of Solids 46(10): 1723-1744.

43Jia, D., A.M. Lennon, and K.T. Ramesh. 2000. High-strain-rate pressure-shear recovery:A new experimental technique. International Journal of Solids and Structures 37(12):1679-1699.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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type fall into two categories: bar wave experiments44 and plate impact experiments, or more specifically, uniaxial-stress-wave propagation experiments and uniaxial-strain-wave propagation experiments. The plate impact experiments are far more common since they can explore a wider range of the phenomena that arise in impact events. In the timescales associated with ultrahigh-strain-rate experiments, uniaxial strain conditions are sampled. Such results are difficult to compare with results obtained at high and very high strain rates (typically obtained with uniaxial stress experiments), particularly if the material has pressure-dependent properties.

The strain rates developed in large-amplitude wave propagation experiments, where shocks are developed, can be on the order of 106 to 108 s–1, but they only exist for a short time behind a propagating wave front, and because of inelastic dissipation, as well as reflections from surfaces, the strain rates will vary with position in the impact plate. The temperatures behind the wave front may be substantial and must be accounted for as well. Comparisons of material properties estimated using wave propagation experiments and high-strain-rate experiments (the distinction made in this chapter) can therefore require careful parsing of experimental conditions.

A shock wave generated during a plate-impact experiment propagates at a shock speedUS that varies with the particle velocity up, and it is commonly observed that these two variables are related linearly or nearly so: US = U0 + sup, where U0 and s are material-specific parameters, with the first being essentially the sound wave speed in the material. Large numbers of experiments have been performed to determine these parameters in various materials. A summary of such data is presented in Meyers45; another useful reference is Gray.46 The shock wave propagation literature is extensive and includes a large number of conference proceedings from the biannual meetings of the American Physical Society Topical Group on Shock Compression of Condensed Matter published by the American Institute of Physics and a series on the shock compression of solids. Experimental details are often emphasized in these conference proceedings.

The main experimental issues associated with shock wave plate impact experiments are (1) the development of gun-launching facilities at the appropriate velocities; (2) the accurate measurement of projectile velocity; (3) the measurement of the stress state within the specimen, typically through the use of stress gauges; and (4) the measurement of the particle velocities in the targets, typically through the use of interferometers such as the velocity interferometry system for any reflector (VISAR). Shock wave experiments at very high velocities, pressures, and strain rates can also be accomplished using a “laser shock” apparatus, where the interaction of a metal film with a high-power laser pulse generates the wave.47Such experiments are of very short duration (typically only a few nanoseconds) and are very hard to control when it is desired to generate a planar shock.

The gun-launch facilities associated with shock physics experiments are typically extremely specialized facilities run by a small number of companies and the national laboratories, and extraordinary precautions must be taken to ensure safety. Most of these facilities offer gas guns, light gas guns, or powder guns; for the higher velocities, multistage guns are typically required. Since kinetic energy increases with the square of the velocity, reaching higher velocities typically requires the use of lower-mass sabots and flyers. Velocities greater than 10 km/s have been achieved with ~1 g flyers using multistage guns.

The typical results obtained from shock experiments include the determination of the Hugoniot elastic limit (this is essentially a uniaxial strain version of the traditional elastic limit), the determination of the Hugoniot curve itself, and (depending on the instrumentation) the determination of the hydrostat and possibly of the shear strength. Note that there are independent methods (such as the diamond anvil cell) for measuring hydrostat response. Another problem with shock experiments is that it is quite difficult, although not impossible, to do recovery experiments. Additionally, it is difficult to separate strength and failure from overall thermodynamic response (lateral gages can be introduced but have their own attendant issues), because diagnostics typically provide only the longitudinal stress, which is a combination of the spherical and deviatoric stresses.

A sophisticated capability exists within the national laboratories for analyzing the results of shock wave experiments in fine detail, and much of the current understanding of the high-pressure behavior of materials comes from such experiments. These methods are generally incapable of determining the rate-dependent shear strength of materials, except under very special conditions. This leads to one of the primary difficulties in understanding material behavior under the extreme conditions developed in the armor problem: The experimental techniques available are generally either most sensitive to material behavior under high pressure or under high strain rate, but they rarely provide accurate information under combined high pressure and ultrahigh strain rate. As the shock is passing a material point, the stress increases very

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44Cazamias, J.U., W.D. Reinhart, C.H. Konrad, and L.C. Chhabildas. 2001. Bar impact tests on alumina (AD995). Pp. 787-790 in Shock Compression of Condensed Matter—2001:Proceedings of the Conference of the American Physical Society, Topical Group on Shock Compression of Condensed Matter, Atlanta, Ga., June 25-29. AIP Conference Processing volume 620. M.D. Furnish, N.N. Thadhani, and Y. Horie, eds. New York, N.Y.: Springer.

45Meyers, M.A. 1994. Dynamic Behavior of Materials. New York, N.Y.: John Wiley &Sons.

46Gray III, G.T. 2000. Shock wave testing of ductile materials, Pp. 530-538 in ASM Handbook Volume 8: Mechanical Testing and Evaluation. H. Kuhn and D. Medlin, eds.Materials Park, Ohio: ASM International.

47Kimberley, J., J. Lambros, I. Chasiotis, J. Pulskamp, R. Polcawich, and M. Dubey. 2010. Mechanics of energy transfer and failure of ductile microscale beams subjected to dynamic loading. Journal of Mechanics and Physics of Solids 58(8): 1125-1138.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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rapidly (ultrahigh strain rates). Once the shock has passed, the material is under a state of high pressure but at relatively low strain rates since there is no relative particle motion. Upon release, however, the material again experiences high strain rates, but now starting at high pressures. Further, under uniaxial strain conditions, self-confinement conditions prevail. Efforts to bridge this gap are recommended.

A great deal can be learned about material behavior (the constitutive law rather than the failure process) by analyzing the results of a suite of experiments that include all of those discussed above, combined with a microscopic analysis of the deformation mechanisms active within the material before loading and postmortem. This capability would be significantly enhanced by in situ determination of the active mechanisms, an essential requirement for ceramics and polymers.

The Department of Defense (DoD) has traditionally been a user of armor analysis codes developed by the Department of Energy (DoE) (LS-DYNA, CTH, ALE3D, LAMMPS, and others) rather than a developer of new algorithms and production codes. There are individual exceptions where multiscale, multiphysics methods are being developed, but this is not a concerted effort that will furnish the tools needed to address the future of protection material systems. There have been significant advances in the models and algorithms addressing the limitations of existing armor codes, which must be integrated into existing or completely new codes to achieve the next level of understanding of armor material response.

Investigating Dynamic Failure Processes

Turning now to the experimental study of dynamic failure processes, many are active mechanisms within the impact events, as discussed earlier. In a broad sense, failure processes consist of brittle fracture at various length scales, void growth associated with ductile fracture, void collapse, the development of adiabatic shear bands, and a variety of structural instabilities such as necking.

For the case of the dynamic brittle fracture process in ceramics, an example of the state of the art in the understanding of the dynamic failure process is that provided in Paliwal et al.48 High-speed photography with a modified compression Kolsky bar technique was used to observe the dynamic failure of uncoated and Cr-coated, transparent polycrystalline aluminum oxynitride (AlON) undergoing uniaxial high-strain-rate compression. High-speed photographs were correlated in time with stress measurements in the specimen (Figure 4-13).

In the fully transparent samples, dynamic activation, growth, and coalescence of cracks and resulting damage zones from spatially separated internal defects were directly observed and correlated with the macroscopic loss of load-carrying capacity and the ultimate catastrophic failure of this material. Identical experiments on the coated material showed only the dynamic progressive failure on the specimen surface, not the origin of the failure images at the internal defects. Therefore, the actual failure mode differs from what is suggested by the photographs of the opaque ceramic undergoing dynamic compression. By means of high-speed photographs on transparent AlON, these authors obtained real-time data on the damage kinetics, which suggest that the cause of the final failure for AlON under dynamic loading was the formation of a damage zone that propagates unstably, not splitting parallel to the loading axis.

This is an example of the value of using a model material—the transparency of the AlON allows determination of internal failure processes that would be otherwise inaccessible—and demonstrates that modeling approaches that only generate axial splitting modes do not properly describe the dynamic failure processes, even though they may capture surface features. Nor would the postmortem examination of fragments in such experiments provide this critical information on dynamic failure processes in the material.

An excellent example of an experimental technique that provides critical information on the dynamic failure process of void growth is provided by the work of Chhabildas and co-workers, who use a line VISAR to examine the process of spallation.49 Spallation is the process of dynamic void growth within a “spall plane” generated by converging rarefaction fans in a shock experiment designed to generate local tension. Experiments designed to generate such a spall plane normally use a VISAR—which measures the particle velocity at a single point on the rear surface of the target—to determine the “spall strength” of the target material. This spall strength is used in a number of armor design approaches as a measure of when the material will fail under hydrostatic tension. Furnish et al.50 used a line VISAR—which measures the particle velocity of a number of points (rather than a single point) along a line on the rear surface of the target—instead of a single-point VISAR to make the measurement. Their results show (Figure 4-14) that there is a stochastic character to the spall process, and that the spall strength of the material is not a single number but a result of the specific microstructural defect distribution within the target. This latter idea was articulated in Wright and Molinari51 and Wright and Ramesh52 in terms of a model of

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48Paliwal, B., K.T. Ramesh, and J.W. McCauley. 2006. Direct observation of the dynamic compressive failure of a transparent polycrystalline ceramic (AlON). Journal of the American Ceramic Society 89(7): 2128-2133.

49Furnish, M.D., L.C. Chhabildas, W.D. Reinhart, W.M. Trott, and T.J. Vogler. 2009.Determination and interpretation of statistics of spatially resolved waveforms in spalled tantalum from 7 to 13 GPa. International Journal of Plasticity 25(4): 587-602.

50Ibid.

51Wright, T.W., and A. Molinari. 2005. A physical model for nucleation and early growth of voids in ductile materials under dynamic loading. Journal of the Mechanics and Physics of Solids 53(7): 1476-1504.

52Wright, T.W., and K.T. Ramesh. 2008. Dynamic void nucleation and growth in solids:A self-consistent statistical theory. Journal of the Mechanics and Physics of Solids56(2): 336-359.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
image

FIGURE 4-13 Photographs taken by a high-speed camera (interframe times of 1 μs and exposure times of 100 ns) of the dynamic failure process in uncoated transparent AlON. The stress-time and damage-time curve at the bottom corresponds to the photographs at the top (the times at which each photograph is taken are shown through the matched numbers on the stress-time plot). Note how the damage begins at internal flaws in the material; subsequent damage interactions lead to cooperative growth of a damage front.

dynamic void growth and interaction in a material containing a distribution of defects.

Investigating Impact Phenomenology

The experiment on the projectile impact of an aluminum plate described earlier in this chapter is an excellent example of an experiment designed to investigate impact phenomenology. Such experiments are highly instrumented and highly controlled versions of the real impact and are valuable for determining the sometimes unexpected couplings that can occur between material properties, failure processes, and system behavior. Such experiments, if they are designed to promote a detailed and specific understanding of the impact phenomenology, are particularly useful when performed on model material systems. A large fraction of the impact phenomenology experiments described in the literature has the different objective of providing a broad and generalized evaluation of the performance of the material system under a specific threat. While these performance evaluation experiments have a critical role to play in the evaluation of armor systems, it is difficult to use them to extract guidelines for the design of improved armor systems. The combination of a very experienced investigator and a large database of experimental data can be a powerful tool in armor development, but this should not be the primary approach to armor development.

Several recent developments in experimental methods hold great promise for addressing complex protection materials problems. These include improved temporal and spatial resolution, the development of high-speed cameras and associated triggering electronics, and the coupling of com-

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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FIGURE 4-14 Line VISAR figure showing spallation in polycrystalline tantalum. The critical recent development for two failure processes is the in situ real-time observation of the active mechanism. Postmortem evaluations require the assumption of a mechanism and then the use of circumstantial evidence to verify the assumed mechanism, which can lead to erroneous conclusions in impact problems. SOURCE: Furnish, M.D., L.C. Chhabildas, W.D. Reinhart, W.M. Trott, and T.J. Vogler. 2009. Determination and interpretation of statistics of spatially resolved waveforms in spalled tantalum from 7 to 13 GPa. International Journal of Plasticity 25(4): 587-602.

putational and experimental capabilities. A variety of very sophisticated experimental techniques has been developed for addressing major parts of the problem.

However, some important technical gaps remain. An example is the characterization of the high-strain-rate response of brittle armor materials such as ceramics and glasses under combinations of high pressure and shear representative of ballistic penetration. Currently available experimental techniques are generally most sensitive to material behavior under either high pressure or high strain rate, but they rarely provide accurate information under combined high pressure and ultrahigh strain rate. There is also a need to develop techniques that address the variety of paths taken by material elements in the pressure/strain rate space during impact events.

Finding 4-1. Several recent developments in experimental methods hold great promise for addressing complex protection materials problems. However, some important technical gaps remain, including the following:

  • The in situ and real-time determination of the active failure processes during the impact event.
  • Experimental techniques that provide accurate information under combined high pressure and ultrahigh strain rate.
  • Techniques that address the variety of paths taken by material elements in the pressure/strain rate space during the impact event.

MODELING AND SIMULATION TOOLS

Modeling and simulation (M&S) has long been considered an invaluable tool for analyzing engineering systems in a wide range of technology areas. The expected role of M&S is to provide a quantitative description of the physical system response that can be used to assess system performance and inform potential improvements. Such has been the case in protection materials technology, where, as discussed in this chapter, significant effort has been devoted in the last 50 years to developing the basic science, algorithms, simulation software, and hardware infrastructure to meet this goal. However, owing to the intricacies and unique physical complexities associated with the response of materials subject to extreme loading conditions, and to the dependence of protection materials performance on such details, the full potential of M&S has so far not been realized. In addition, the role of M&S is currently undergoing a significant revision as the result of efforts to develop rigorous M&S-based uncertainty quantification (UQ) methodology for the assessment and certification of complex systems. In this new view, the role of M&S is no longer to provide best-practices predictions of the response of the system, often in the form of isolated “hero calculations,” but to provide predictions with rigorously quantified uncertainties. This paradigm shift could lead to profound change in the way M&S is conducted, in its interaction with experimental science, and in the manner in which protection systems are assessed and qualified.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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One may review the state of the art in M&S technologies for the analysis of protection materials by identifying the main technology gaps and challenges. The committee suggests directions in which these technologies could be further developed so as to have a bigger impact on protection materials. A path forward is recommended to advance the simulation-aided design of the next generation of protection materials and systems.

Background and State of the Art

Why M&S Is Needed

The fundamental macroscopic properties of materials influencing armor performance—high strength, elastic stiffness, and ductility—are well known even if the manner in which they combine to create the most effective performance is still far from certain. A clear avenue for improving armor performance is thus to continue the quest for ever lighter, stronger, and stiffer yet more malleable materials (Chapter 5). The correlation of material properties with armor performance is usually difficult to establish exactly, as performance depends on specific details of the threat and the armor system and on their complex interactions. For example, for a given threat and a certain mass of protective material with predetermined macroscopic properties, armor performance is found to be strongly dependent on the layout of the material in the armor system—in other words, the material system. In addition, as discussed in the earlier section on mechanisms, the performance is influenced by more subtle properties of the material response such as strain hardening and rate dependency and by certain aspects of the material’s mesostructure—for example, topological, composite, or cellular arrangement—and its microstructure—for example, grain size, anisotropy, residual stresses, defect characteristics, and adherence between components.

The foregoing suggests that details of the mechanical response of the material system such as wave propagation, localized plastic deformation and fracture, crack propagation, and others play an important role in determining armor performance because they affect the ability to erode projectiles, diffuse or divert the load, distribute damage away from the impact location, dissipate energy at sufficiently fast rates, and delay failure. A key unanswered question in armor applications is this: Given constraints on the weight (and/or, perhaps, cost) of candidate high-performance protection materials, what is the optimal, possibly hierarchical, structural layout that maximizes performance for a given threat? It is expected that even an approximate answer to this question will greatly benefit threat defeat and/or weight reduction. There is a universe of possibilities among which the answer will be found. A science-based approach with the ability to quantitatively describe the details of the physical event constitutes a sine qua non to achieve this goal.

This is precisely what M&S does well: It can assess the role of operative, possibly competing, mechanisms that influence macroscopic behavior. M&S is also an invaluable tool for helping to interpret material testing experiments. Experiments play two fundamental roles in M&S. On the one hand, they provide the input data on material properties and behavior for the simulations. On the other hand, lab-scale and field tests with adequate instrumentation provide quantitative data that can be compared with simulation results to validate the models. A validated computational framework can then be used to explore the design parameter space via simulation of material properties/behavior, structural topology, and geometry and dimensions to obtain solutions with improved performance and, conceivably, solutions of the inverse problem of finding the optimal solution for the given problem constraints.

As seen in this chapter, the promise of M&S has been only partially achieved thus far. In brief, current M&S technology is able to describe basic aspects of the interaction of a threat—for example, a kinetic energy penetrator—and a target armor material, including momentum transfer, dissipation of the kinetic energy of the insult by plastic deformation, friction, and, to some extent, material damage. The predictive capability of M&S has been used for improving the basic understanding of penetration mechanics beyond what experiments and simple analytical models can provide, and in some cases for guiding armor designs. However, a number of key phenomena as well as mathematical and numerical aspects of M&S are beyond the ability of existing technology and need to be addressed for M&S to achieve its potential.

Application of M&S to Protection Materials

The standard approach in M&S has five elements:

  • Computational framework. The computer software that encodes the fundamental mathematical formulations and algorithms for solving the initial boundary value problem governing the dynamics of the physical event.
  • Constitutive models. These are integrated into the computational framework and describe the material response in mathematical form at each material point in the problem domain. As such, they are responsible for capturing the relevant mechanisms of material deformation and failure.
  • Model calibration. Owing to the fundamentally phenomenological character of the constitutive models in use, the specific response associated with different materials is encoded in material parameters, which must be calibrated to experiments. In most cases the calibration is applicable for only a limited range of the material response—for example, strain rate—and different calibrations are required, depending on the problem.
  • Model verification and validation (V&V). This is the
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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process by which the fidelity of the computational framework is established. One of the most important phases of the V&V process is to conduct simulations of specially designed experiments and to assess the ability of the computational framework to quantitatively reproduce specific features of the experiments by comparing simulation and test results.

  • Production runs—large-scale simulations of problems of interest. This corresponds to the stage when the validated M&S framework is used for simulating an application of interest in protection materials. The outcome consists of spatially and temporally resolved numerical values of the continuum fields describing the physical problem. These results are postprocessed and analyzed to draw conclusions about the role of the various threat defeat mechanisms and about the suitability of the protection design.

Despite the advances made based on this paradigm, significant modifications and enhancements will be required to fully reap the potential benefits of M&S in protection materials. Two key components missing in this picture are (1) multiscale, multiphyscis material models and algorithms incorporating information about the subscale or microstructural response, especially for improving the description of material damage and failure; and (2) the quantification of uncertainty for the overall problem analysis, including simulations and experiments.

Computational Framework

Decades of research and development have given us mathematical formulations, computational algorithms, and computer software which, to varying degrees, depending on the method and the problem, possess many of the desired attributes sought in a computational framework for numerically solving the fundamental continuum equations governing the response of protection materials. These responses include versatility, robustness, efficiency, and scalability. The history and state of the art of the so-called hydrocodes developed by the DoE and the DoD up to the early 1990s are discussed in detail in Benson’s review.53 Some of those legacy hydrocodes are still the workhorse tools used in armor applications. That history may be summarized as follows.

The vast majority of the codes in use for the analysis of protective materials employ explicit second-order accuracy for time integration and first-order spatial accuracy. The success of low-order explicit methods can be explained by their simplicity, robustness, and scalability. However, low-order methods pose a key limitation for the proper description of some features of material response where important opportunities for improvements in protection performance may be found—for example, multiscale structured materials, including composites, fabrics, phononic band-gap topological materials, and highly nonlinear granular chains. New classes of high-order accuracy implicit or semi-implicit algorithms have emerged from academic research that could be incorporated in existing or new codes to gain new levels of physical detail in protection material simulations.

The finite-element method has been the traditional Lagrangian approach. Its main advantage is that the description of material state and history, as well as the evolution of material boundaries and interfaces, is a natural outcome of the simulation. Its main disadvantage is the distortion of the mesh elements induced by large deformations, which invalidates or breaks the numerical method. A variety of remedies for this problem have been proposed, including adaptive remeshing and element “erosion,” each with its own limitations. Particle-based Lagrangian discretizations avoid this problem as the neighborhood of interacting particles is allowed to evolve freely. However, this introduces discontinuous jumps in the continuum notion of the gradient fields (strains, for example) associated with the particles, which result in convergence problems. Lagrangian meshless methods54 have emerged as a way to combine the advantages of particle methods and finite elements. The recent peridynamic formulation of the continuum problem55,56 is also a promising Lagrangian approach that results in a nonlocal particle method with a rigorous mathematical framework and a natural introduction of a characteristic length, as required for modeling material damage.

The main advantage of Eulerian formulations, by contrast, is that the computational grid does not distort and thus allows for unconstrained deformations. These formulations originally found their main application in fluid dynamics. The ability to describe a solid material’s “strength” was subsequently added to these formulations, but not without significant difficulty. Since the governing equations involve the material-time derivative of the stress tensor, the constitutive models need to be formulated in rate form in terms of frame-indifferent stress-rate measures. In addition, the material state and history, including the elastic response, need to be convected with the flow, which introduces an additional source of complexity and errors. This approach includes the tracking of free boundaries and material interfaces, all of which require special treatment, in contrast to the Lagrangian approach. Owing to the low order of the advection algorithms used, the associated dispersion errors grow over time and the

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53Benson, D.J. 1992. Computational methods in Lagrangian and Eulerian hydrocodes. Computer Methods in Applied Mechanics and Engineering 99(2-3): 235-394.

54Belytschko, T., and J.S. Chen. 2007. Meshfree and Particle Methods. New York, N.Y.:John Wiley and Sons.

55Foster, J.T., S.A. Silling, and W.W. Chen. 2010. Viscoplasticity using peridynamics. International Journal for Numerical Methods in Engineering 81(10): 1242-1258.

56Silling, S.A., O. Weckner, E. Askari, and F. Bobaru. 2010. Crack nucleation in a peridynamic solid. International Journal of Fracture 162(1-2): 219-227.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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convergence is poor. Another disadvantage of Eulerian codes is that the fixed grid must cover the entire region of interest.

The arbitrary Lagrangian-Eulerian formulation,57 a combination of both approaches, attempts to exploit the advantages of each approach by allowing high distortions to be represented in a Lagrangian framework. Combinations of finite-element and meshless-particle methods have been developed, as have combinations of finite-element and Eulerian methods. The rest of this section summarizes the history and evolution of the codes developed and utilized for armor applications.

The HEMP58 code was developed in the early 1960s by Wilkins, at the Lawrence Livermore Laboratories.59 This was a two-dimensional Lagrangian code based on an explicit finite-difference formulation that could handle large strains, elastic-plastic flow, wave propagation, and sliding interfaces. It was a significant new computational capability at that time. The TOODY code was a similar finite-difference code developed at Sandia National Laboratories.60 In the late 1960s, Wilkins and others used the HEMP code for the design and analysis of light armor, which included ceramic, metallic, and composite components. The first of five progress reports was entitled An Approach to the Study of Light Armor.61 This highly influential work underpinned much of the subsequent numerical work.

During the same time frame implicit finite-element methods were introduced. However, finite-element methods for analyzing fast dynamic response only became practical when explicit methods for integrating time were introduced. Three different codes emerged in the 1970s implementing this approach: EPIC,62 HONDO,63 and WHAMS.64 A determinant advantage of finite-element over finite-difference methods is their natural ability to represent complex geometries.

Numerous Eulerian codes that incorporated the effect of material strength (CTH, HULL, JOY, MESA) soon emerged as contenders to finite-element codes.65 Of the several Eulerian codes available today, the CTH code66 has been widely distributed by Sandia Laboratories and is the most commonly used code for impact and penetration computations for protection structures and materials.

Because of some of the limitations associated with Eulerian codes, Lagrangian approaches for severe distortions continued to be developed. In 1987, two three-dimensional erosion algorithms were published67,68 that allowed highly distorted elements to be discarded (eroded) and the interfaces to be automatically updated as the solution progressed. Most of the current Lagrangian finite-element codes used for impact and penetration (EPIC, DYNA, LSDYNA, PRONTO, and PRESTO) now have some form of an erosion option. Although this approach introduces some inaccuracies, it allows problems with very severe distortions to be simulated in a Lagrangian framework.

One well-known limitation of element erosion is that it gives the wrong energy-release rate when a crack propagates at an angle to the mesh.69 The reason for this failure of consistency and convergence is that, in conventional erosion implementations, the crack is forced to zig-zag through the mesh, with the result that the fracture energy is overestimated by a geometrical factor. However, it has been recently shown that a local averaging of the energy in the computation of the energy-release rate eliminates the mesh bias and results in convergent approximations.70

Of the particle methods, the smoothed particle hydrodynamics approach, which included material strength, was introduced in Libersky and Petschek.71 After much initial enthusiasm it was soon discovered that the smoothed-particle hydrodynamics algorithm (and other similar particle algorithms that carried all of the variables at the nodes) had some

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57Hirt, C.W., A.A. Amsden, and J.L. Cook. 1974. An arbitrary Lagrangian-Eulerian computing method for all flow speeds. Journal of Computational Physics 14(3): 227-253.

58In this report, this and other such codes are referred to by the abbreviated forms familiar to the community associated with the topics discussed.

59Wilkins, M.L. 1964. Calculation of elastic-plastic flow. Pp. 211-263 in Methods in Computational Physics, Volume 3: Fundamental Methods in Hydrodynamics. New York, N.Y.: Academic Press.

60Bertholf, L.D., and S.E. Benzley. 1968. TOODY II: A Computer Program for Two-Dimensional Wave Propagation, Technical Report SC-RR-68-41. Albuquerque, N.M.: Sandia Laboratories.

61Wilkins, M.L., C.A. Honodel, and D. Sawle. 1967. Approach to the Study of Light Armor, Technical Report UCRL-50284. Livermore, Calif.: Lawrence Radiation Laboratory.

62Johnson G.R. 1976. Analysis of elastic-plastic impact involving severe distortions. Journal of Applied Mechanics 43 Ser E(3): 439-444.

63Key, S.W., Z.E. Beisinger, and R.D. Krieg. 1978. HONDO II—A Finite Element Computer Program for the Large Deformation Dynamic Response of Axisymmetric Solids, Technical Report SAND78-0422. Albuquerque, N.M.: Sandia Laboratories.

64Beltyschko, T., and R. Mullen. 1978. WHAMS: A program for transient analysis of structures and continua. Pp. 151-212 in Structural Mechanics Software Series, Volume 2. N. Perrone and W. Pilkey, eds. Charlottesville, Va.: University Press of Virginia.

65Immele, J.D., C.E. Anderson, R.J. Asaro, S.G. Cochran, L.W. Davison, J.C. Foster, G. Johnson, G. Randers-Perhson, and J. Short. 1989. Report of the Review Committee on Code Development and Material Modeling, LA-UR-89-3416. Arlington, Va.: Defense Advanced Research Projects Agency.

66McGlaun, J.M., S.L. Thompson, and M.G. Elrick. 1990. CTH: A three-dimensional shockwave physics code. International Journal of Impact Engineering 10(1-4): 351-360.

67Johnson, G.R., and R.A. Stryk. 1987. Eroding interface and improved tetrahedral element algorithms for high-velocity impact computations in three dimensions. International Journal of Impact Engineering 5(1-4): 411-421.

68Belytschko, T., and J.I. Lin. 1987. A three-dimensional impact-penetration algorithm with erosion. International Journal of Impact Engineering 5(1-4): 111-127.

69Negri, M. 2007. Convergence analysis for a smeared crack approach in brittle fracture. Interfaces and Free Boundaries 9(3): 307-330.

70Schmidt, B., F. Fraternali, and M. Ortiz. 2009. Eigenfracture: An eigendeformation approach to variational fracture. Multiscale Modeling and Simulation 7(3): 1237-1266.

71Libersky, L.D., and A.G. Petschek. 1991. Smooth particle hydrodynamics with strength of materials. Pp. 248-257 in Advances in the Free-Lagrange Method, Lecture Notes in Physics Volume 395. H.E. Trease, M.J. Fritts, and W.P. Crowley, eds. Berlin, Germany:Springer-Verlag.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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FIGURE 4-15 Optimal transportation mesh-free simulation of a steel plate perforated by a steel projectile striking at various angles. Top: evolution of the perforation process. Bottom: perforated configurations for several incidence angles.

limitations in terms of instabilities, accuracy, and efficiency. For the past 20 years there has been a strong emphasis on the development of a wide range of meshless-particle algorithms for a wide range of applications. A promising new direction combines elements of optimal transportation theory with meshfree (max-ent) interpolation of the fields, material-point sampling of material states, and provably convergent erosion schemes to account for fracture (see Figure 4-15). The optimal transportation mesh-free method is an example of this approach. Compared to other particle methods, optimal transportation exhibits strong and provable convergence properties and eliminates tension instabilities that afflict traditional particle methods.

An approach based on the conversion of elements into particles has shown to effectively deal with the problem of element distortion.72 As Johnson notes, with this approach the entire initial geometry is represented by elements, and then, as the elements on surfaces or interfaces become highly distorted, they are converted into meshless particles. All of the element variables are transferred to the particle, and the particle is attached to the face of an adjacent element (if one exists). With this approach, most of the problem is represented by accurate and efficient elements, with only the highly distorted regions represented by particles. Very severe distortions can be represented in a Lagrangian framework.

An alternative approach to alleviate deformation-induced mesh distortion in Lagrangian finite-element algorithms is to adaptively and continuously regenerate the mesh during the simulation. An additional advantage of adaptive remeshing methods is the ability to optimally refine the mesh for maximum accuracy. This idea was applied successfully to penetration mechanics problems in axisymmetric conditions. Recent advances in computational geometry and mesh optimization have enabled the extension of this idea to three dimensions. Figure 4-16 shows its application to simulating the oblique impact of a spherical-nosed steel penetrator on an aluminum target.

One of the issues with adaptive remeshing approaches is the error introduced in the transfer of field variables from the old to the new mesh, which tends to produce artificial diffusion. This problem can be somewhat alleviated by adapting the mesh locally instead of completely regenerating it. Another important issue is scalability in parallel calculations. It is well established in computational geometry that algorithms involving general topological changes in the data structures are very hard to implement in parallel and are usually inherently nonscalable because they require the propagation (communication) of unstructured and evolving data among processors. As a result, parallel calculations are efficient only up to a few tens of processors at best.

Another significant concern is that different codes produce different answers for the same problem, a telling indication of the lack of convergence in the solution. This is illustrated in Figure 4-17, where five different computa-

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72Johnson, G.R., and R.A. Stryk. 2003. Conversion of 3D distorted elements into meshless particles during dynamic deformation. International Journal of Impact Engineering 28(9): 947-966.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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FIGURE 4-16 Example of a Lagrangian finite-element simulation that uses adaptive re-meshing and refinement to eliminate element distortion and to optimize the mesh.

tional approaches are used for the same problem (a tungsten projectile impacting a steel target at an impact velocity of 1,615 m/s), and all five approaches used exactly the same material models. The five approaches use (1) a finite-volume (Eulerian) algorithm, (2) an erosion algorithm that discards highly distorted elements, (3) a generalized particle algorithm where the entire problem is represented by particles, (4) a conversion algorithm that converts distorted elements into particles, and (5) a hybrid algorithm where the pressures are computed with particles and strength is computed with elements. On the one hand it is encouraging that several different approaches can provide good general agreement with the experimental results. On the other hand, there are noticeable differences in the size of the fragments and the response of the tungsten projectile.

image

FIGURE 4-17 A comparison of results from five computational approaches for a tungsten projectile impacting a steel target at 1,615 m/s. SOURCE: Beissel, S.R., C.A. Gerlach, T.J. Holmquist, and J.D. Walker. In press. Comparison of numerical methods in the simulation of hypervelocity impact. Proceedings of 11th Hypervelocity Impact Symposium, Freiburg, Germany 2010.

Finding 4-2. Although much progress has been made in developing computational frameworks for the analysis of protection materials, all of the algorithms have strengths and weaknesses.

Additional Challenges in Computational Framework Another important issue for future threats that may subject protective materials to conditions well in the nonlinear shock physics regime has to do with the numerical treatment of shock-type discontinuities. It has been widely established that special computational methods are needed to address the jump discontinuities associated with shocks that arise in materials under extreme compressive loadings.73 A standard approach in hydrodynamic calculations using the existing low-order methods is introducing a viscous term into the equations to smooth out the shock. Although this method has proven to be a robust and simple approach for capturing shock, it introduces errors and problems. “Shockless heating” and “wall heating” occur in strong shocks, leading to errors in the energy, both behind and in front of the shock. Concomitant with errors in the energy are errors in the density and the shock speed. Emerging high-order implicit or semi-implicit methods developed by the fluid mechanics community for compressible turbulence, in which both the compressibility shock and viscous effects are important, have significant potential for solid materials as well.

A critical missing component in the protective material simulation tools in use today is the ability to represent material damage and failure explicitly. The conventional approach is to make use of so-called continuum damage models (see the section “Constitutive Models” below). Such models have been effective for describing damage in an average, or “smeared,” sense but are unsuitable for capturing (1) the discrete nature of material fracture and (2) crack nucleation and propagation, according to the laws of fracture mechanics. A promising class of approaches for doing so is based on the “discrete crack” model of fracture.74 In this approach,

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73Benson, D.J. 1992. Computational methods in Lagrangian and Eulerian hydrocodes. Computer Methods in Applied Mechanics and Engineering 99(2-3): 235-394.

74Radovitzky, R., A. Seagraves, M. Tupek, and L. Noels. 2011. A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method. Computer Methods in Applied Mechanics and Engineering 200 (1-4): 326-344.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×

crack initiation and propagation are modeled explicitly by the introduction of surfaces of discontinuity within the material. At these surfaces of discontinuity, fracture processes can be described by cohesive zone models (CZMs) of fracture75,76 via a phenomenological traction-separation law. The key advantage of CZMs is their ability to encode in the calculation well-established laws of fracture mechanics governing the nucleation, propagation, branching, and coalescence of cracks.

The “cohesive element” method77,78 is the most popular implementation of this concept. In this method, crack openings are represented as displacement jumps at the interelement boundaries using “interface” or “cohesive” finite elements. Camacho and Ortiz79 presented the first formulation of this method for impact problems involving extensive fracture and fragmentation. They demonstrated that the extrinsic CZM was successful at capturing conical crack patterns in ceramic plate impact as long as finely resolved meshes were employed in the calculations. Cohesive elements provide a notable alternative to erosion and are one of the key innovations brought to ballistic calculations in the 1990s. This development finally enabled the robust and reliable tracking of sharp cracks and complex fracture and fragmentation properties. Cohesive-element calculations have proven highly predictive and have been extensively validated in a number of areas of application by, for example, Bjerke and Lambros80 and Chalivendra et al.81

A full three-dimensional description of crack patterns in ceramic plate impact has recently been enabled by a new extension of CZM based on a discontinuous Galerkin reformulation of the continuum problem.82 The main advantages of this method are its inherent scalability (demonstrated up to 4,096 cores on DoD platforms and problems involving 3 billion degrees of freedom) and its accuracy in describing wave propagation. Figure 4-18 shows the ability of the method to capture conical as well as radial and lateral cracks in ceramic plate impact.

One of the issues commonly attributed to CZM based on interface elements is that the set of available paths for crack propagation is constrained by the mesh, which is a form of mesh dependency. A variety of methods have been put forth to enable arbitrary crack paths in simulations for the purpose of reducing mesh dependency. Essentially, these approaches allow surfaces of discontinuity to propagate through the interior of volumetric elements (see, for example, the extended finite-element method,83,84 the embedded localization line method,85,86,87 and the cohesive segments method).88 In this family of methods, however, highly refined meshes are still necessary to resolve the size of the fracture process zone in brittle materials. Another issue is the possibility of describing crack branching, especially in three dimensions. So far, these types of methods have only been implemented for single-processor computations. Their scalability is marred by the same problem of propagating topological changes across processors alluded to in the discussion of parallel adaptive remeshing. Efforts are currently under way to include methods of the extended finite-element type in existing codes: LS-DYNA89 and Abaqus.90

Finding 4-3. A critical missing component of protective material simulation tools in use today is the ability to represent material damage and failure explicitly.

Constitutive Models

In addition to having numerical algorithms it is essential to have computational models to accurately represent the response of the materials. Numerous computational material models have been developed during the past 20 years, but

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75Dugdale, D.S. 1960. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 8(2): 100-104.

76Barenblatt, G.I. 1962. The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 7(C): 55-129.

77Ortiz, M., and S. Suresh. 1993. Statistical properties of residual stresses and intergranular fracture in ceramic materials. Journal of Applied Mechanics, Transactions ASME 60(1): 77-84.

78Xu, X.P., and A. Needleman. 1994. Numerical simulation of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 42(9): 1397-1434.

79Camacho, G.T., and M. Ortiz. 1996. Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures 33(20-22): 2899-2938.

80Bjerke, T.W., and J. Lambros. 2003. Theoretical development and experimental validation of a thermally dissipative cohesive zone model for dynamic fracture of amorphous polymers. Journal of the Mechanics and Physics of Solids 51(6): 1147-1170.

81Chalivendra, V.B., S. Hong, I. Arias, J. Knap, A. Rosakis, and M. Ortiz. 2009. Experimental validation of large-scale simulations of dynamic fracture along weak planes. International Journal of Impact Engineering 36(7): 888-898.

82Radovitzky, R., A. Seagraves, M. Tupek, and L. Noels. 2011. A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method. Computer Methods in Applied Mechanics and Engineering 200 (1-4): 326-344.

83Belytschko, T., and T. Black. 1999. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 45(5):601-620.

84Moës, N., J. Dolbow, and T. Belytschko. 1999. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 46(1): 131-150.

85Dvorkin E.N., A.M. Cuitiño, and G. Goia. 1990. Finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions. International Journal for Numerical Methods in Engineering 30(3): 541-564.

86Simo, J.C., J. Oliver, and F. Armero. 1993. An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. Computational Mechanics 12(5): 277-296.

87Armero, F., and C. Linder. 2009. Numerical simulation of dynamic fracture using finite elements with embedded discontinuities. International Journal of Fracture 160(2): 119-141.

88Remmers, J.J.C., R. de Borst, and A. Needleman. 2003. A cohesive segments method for the simulation of crack growth. Computational Mechanics 31(1-2 SPEC): 69-77.

89See http://www.lstc.com.

90See http://www.simulia.com.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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FIGURE 4-18 Prediction of conical, radial, and lateral crack patterns in ceramic plate impact by the recent cohesive zone/discontinuous Galerkin method.

only a few have taken root in the application to protection materials. These models have ranged from those for simple dynamic flow stress and dynamic failure strain to very complex models that include microstructural details. Currently, some models for materials are advanced enough to provide helpful and meaningful results, such as those illustrated in the first section of this chapter, but details of failure are not sufficiently robust to allow the predictive design of material systems to protect against specific threats.

For projectile-target interaction computations, the materials are usually modeled using phenomenological models that compute strength and failure as a function of strain, strain rate, temperature, and pressure. For metals the most commonly used strength models are the Johnson-Cook model,91 the Zerilli-Armstrong models,92 the SteinbergGuinan-Lund models,93 the Bodner-Partom models,94 and

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91Johnson, G.R., and W.H. Cook. 1983. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. Available online at http://www.lajss.org/HistoricalArticles/A%20constitutive%20model%20and%20data%20for%20metals.pdf. Last accessed April 7, 2011.

92Zerilli, F.J., and R.W. Armstrong. 1987. Dislocation-mechanics-based constitutive relations for material dynamics calculations. Journal of Applied Physics 61(5): 1816-1825.

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 51(3): 1498-1504.

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.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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the Mechanical Threshold Stress model.95 The Johnson-Cook model is a phenomenological model, and the others are more physically based. Generally these models require a characterization of a specific material, and it is not possible to predict the strength from a microstructural description of the material. There are fewer failure models available, with the Johnson-Cook failure model96 being the most widely used. Although this is primarily a phenomenological model, it includes some physically based features of the ductile fracture mechanism.97 More mechanistic constitutive models of damage and fracture based on ductile void growth,98 such as the Gurson model,99 have been proposed. However, they are still to be incorporated and widely adopted in production codes for ballistic analyses. Recent contributions have proposed improvements to the characterization of failure in the Johnson-Cook model100 and the Gurson model.101

For ceramics there are fewer models available. A unique feature of ceramics, compared to other materials (such as metals), is that they have such high compressive strengths that they cannot be tested with typical laboratory stress-strain tests.102 Instead, their material properties must be inferred from plate impact tests and/or penetration tests. This characteristic has made it difficult to directly obtain failure data under high (compressive) pressures and to obtain the (shear) strength of failed ceramic under high pressures. The JHB phenomenological model103 used in the illustrative example in the beginning of the chapter has an intact strength, a failed strength, a failure component based on plastic strain and pressure, and bulking. Recently Deshpande and Evans proposed a mechanism-based model to compute damage and failure in ceramics based on microstructural parameters such as fracture toughness, crack growth rates, flaw size, and densities.104 This new work sets an important direction for the development of constitutive models of material failure for other protection materials.

Issues with Models of Material Damage and Failure Material damage and failure in existing M&S codes is described at the constitutive model via so-called continuum damage models. In these approaches, damage is considered a state variable of the material, whose history evolves according to prescribed phenomenological laws. Either the elastic or plastic response of the material is “softened” as material damage progresses in an irreversible manner. These laws describe the effect of the operative driving forces and mechanisms such as stress intensity and triaxiality, which depend on the material type (brittle or ductile) and characteristics such as defect size and porosity. Damage models require additional parameters that must be calibrated to experiments or that sometimes have physical meaning, such as initial porosity, defect size and distribution, toughness, and so forth.

Damage is characterized by a reduction in the material’s load-carrying capacity after reaching damage threshold conditions. This is always accompanied by a localization of the deformation in narrow regions, which is a precursor to failure. There is a fundamental mathematical problem with continuum damage models and any other model describing weakening material response—for example, the models of de Borst and Sluys105and Sluys et al.106 In the region where softening occurs, the governing equations of the dynamic problem change their mathematical character in a fundamental way, from hyperbolic to elliptic. For elliptic equations, waves cannot propagate as their speeds become imaginary, and the softening region collapses to a vanishing width. This, in turn, implies that no energy is dissipated by the softening material, which is far from the real material response. What happens in reality is that there is always a physical process that limits the localization process and introduces a characteristic length scale in the problem, which is not considered in the classical continuum equations.

In the presence of softening, the numerical solution of the conventional continuum problem provides an erroneous resolution of the physical phenomenon. The element or grid size effectively sets the length scale necessary to regularize the problem as it imposes a lower bound for the localization zone width. However, this is just an illusion, because the solution does not converge as the mesh is refined. In the limit

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95Follansbee, P.S., and U.F. Kocks. 1988. A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable. Acta Metallurgica 36(1): 81-93.

96Johnson, G.R., and W.H. Cook. 1985. Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Engineering Fracture Mechanics 21(1): 31-48.

97Hancock, J.W., and A.C. Mackenzie. 1976. On the mechanism of ductile failure in high-strength steels subjected to multi-axial stress states. Journal of the Mechanics and Physics of Solids 24(2-3): 147-160.

98McClintock, F.A. 1968. A criterion for ductile fracture by the growth of holes. Journal of Applied Mechanics 35(2): 363-371.

99Gurson, A.L. 1977. Continuum theory of ductile rupture by void nucleation and growth: Part I, yield criteria and flow rules for porous ductile media. Journal of Engineering Materials and Technology, Transactions of the ASME 99 Ser H(1): 2-15.

100Bao, Y., and T. Wierzbicki. 2004. On fracture locus in the equivalent strain and stress triaxiality space. International Journal of Mechanical Sciences 46(1): 81-98.

101Nahshon, K., and J.W. Hutchinson. 2008. Modification of the Gurson Model for shear failure. European Journal of Mechanics-A/Solids 27(1): 1-17.

102Johnson, G.R. 2011. Numerical algorithms and material models for high-velocity impact computations. International Journal of Impact Engineering 38(6): 456-472.

103Johnson, G.R., T.J. Holmquist, and S.R. Beissel. 2003. Response of aluminum nitride (including phase change) to large strains, high strain rates, and high pressures. Journal of Applied Physics 94(3): 1639-1646.

104Deshpande, V.S., and A.G. Evans. 2008. Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model. Journal of the Mechanics and Physics of Solids 56(10): 3077-3100.

105de Borst, R., and L.J. Sluys. 1991. Localisation in a Cosserat continuum under static and dynamic loading conditions. Computer Methods in Applied Mechanics and Engineering 90(1-3): 805-827.

106Sluys, L.J., R. de Borst, and H.-B. Muhlhaus. 1993. Wave propagation, localization and dispersion in a gradient-dependent medium. International Journal of Solids and Structures 30(9):1153-1171.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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when the mesh size goes to zero, the dissipated energy in the localization zone is zero. This numerical manifestation of the ill-posedness of the mathematical problem is what is usually referred to as “damage-induced mesh dependency.” A common approach to circumvent this problem in existing codes is to calibrate the material model parameters for a given mesh size. In other words, not only the model parameters but also the mesh size are tied to a specific application. The illustrative example in the introduction to this chapter for the projectile penetrating the aluminum plate was approached in this manner. This is clearly a significant limitation.

A proper mathematical treatment of softening material response necessarily involves the modification of the classical governing equations in a way that the physically relevant length scale is introduced. A number of generalizations of the classical formulation have been proposed to this end. They involve either the introduction of higher-order derivatives in the constitutive model (gradient models, as, for example, Aifantis107 and Fleck and Hutchinson108) or the spatial averaging of strains (nonlocal models such as Bazant et al.109). Both generalizations reflect the fact that micromechanical processes in the localization zone have an inherently nonlocal character. In the particular case of gradient-type softening or damage models, it can be shown that an internal length scale exists and that the resulting set of governing equations is well posed, having wave speeds that remain real in the softening regime. The immediate computational consequence of this reformulation is that softening-induced mesh dependence is eliminated.

These models have not permeated production computational frameworks, primarily for two reasons: (1) new (high-order) algorithms and computer codes are required because the existing algorithmic frameworks cannot accommodate the higher-order derivatives and their field continuity requirements and (2) additional constitutive parameters have emerged that in many cases do not have a clear physical meaning or a discerning experiment that can be used to calibrate them. Multiscale modeling might be one way to address this issue.

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 macroscopic constitutive descriptions to account for details of the material’s microstructure or for the associated micromechanical responses that affect global behavior. The ability to consistently incorporate the effect of micromechanical features on material response would enable rational microstructure design.

There is therefore a critical need to develop descriptions of material behavior directly rooted in the first principles of micromechanics, a long-standing aspiration of solid mechanics. This requires new mathematical frameworks; multiscale, multiphysics constitutive models; and numerical algorithms. Multiscale modeling is a rational and systematic way to construct hierarchical models for the behavior of complex material with the least amount of empiricism and uncertainty. In this approach, the pertinent unit processes at every length scale in the hierarchy of material behavior are identified. The processes at any scale are the average of the unit processes taking place at the length scale just below. The modeling effort for systems in which these relations are well defined simply involves analyzing each unit mechanism in turn and computing the averages, which eventually results in a full description of the material’s macroscopic behavior. This inductive process ceases at the atomic scale, at which point the fundamental theories describing atomic bonds take over.

For instance, as part of the Caltech advanced simulation and computing program, a full multiscale model of material response was developed for tantalum.110 The multiscale hierarchy that underlies metal plasticity is shown schematically in Figure 4-19. The foundational theory on which the hierarchy rests is quantum mechanics and, in particular, the electronic structure of metals. Quantum mechanics encapsulates the fundamental laws that govern the behavior of materials at the angstrom scale. In their density-functional-theory approximation, quantum mechanical calculations can characterize the structure and properties of crystal lattices and isolated crystal defects, especially when coarse-graining techniques are employed.111 Fundamental properties of dislocations such as kink structure and mobility can be evaluated using molecular dynamics and empirical potentials.112 These properties can be used to formulate theories of linear-elastic dislocation dynamics. Dislocation dynamics models—for example, the models of van der Giessen and Needleman113

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107Aifantis, E.C.. 1984. On the microstructural origin of certain inelastic models. Journal of Engineering Materials and Technology, Transactions of the ASME 106(4):326-330.

108Fleck, N.A., and J.W. Hutchinson. 1993. A phenomenological theory for strain gradient effects in plasticity. Journal of the Mechanics and Physics of Solids 41(12): 1825-1857.

109Bazant, Z.P., T.B. Belytschko, and T.-P. Chang. 1984. Continuum theory for strain-softening. Journal of Engineering Mechanics 110(12): 1666-1692.

110Cuitiño, A.M., L. Stainier, G. Wang, A. Strachan, T. Cain, W.A. Goddard 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 orbital-free density-functional theory: A route to multi-million atom non-periodic DFT calculation. Journal of the Mechanics and Physics of Solids 55(4): 697-718.

112Cuitiño, A.M., L. Stainier, G. Wang, A. Strachan, T. Cain, W.A. Goddard III, and M. Ortiz. 2001. A multiscale approach for modeling crystalline solids. Journal of Computer-Aided Materials Design 8(2-3): 127-149.

113Van Der Giessen, E., and A. Needleman. 1995. Discrete dislocation plasticity:A simple planar model. Modelling and Simulation in Materials Science and Engineering 3(5): 689-735.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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FIGURE 4-19 Multiscale hierarchy for metal plasticity. The arrows indicate upscaling directions across length scales.

and Arsenlis et al.114—have the potential for characterizing the work-hardening characteristics of metals. However, to date, such models are restricted to small deformations and impossibly high dislocation densities and deformation rates. The deformation of individual grains is often strongly heterogeneous and entails the formation of lamellar dislocation structures. Variational formulations of plasticity based on incremental energy minimization have proven effective at predicting such structures and characterizing the effective behavior of the material, including well-established scaling relations such as those of Hall-Petch and Taylor.115 Finally, the direct simulation of polycrystalline behavior, in which the polycrystalline structure is resolved by the mesh, is within the reach of present petascale computing power.116,117 Large-scale simulations and a detailed experimental validation process showed that this multiscale approach not only reproduced the observed effective response of polycrystalline metals but also captured local details of the deformation and grain interactions.

It is, however, easier to expound the multiscale paradigm than to carry it out. Today, the unit mechanisms can be analyzed and the effective behavior characterized based either on numerical schemes or on a motley assortment of analytical tools, such as mean-field theories, statistical mechanics, transition-state theory, or homogenization. The great breadth of the field and its current state of development mean that multiscale modeling generally cannot be easily formalized as a self-contained, unified theory and therefore remains as much art as a science. As a result, there is a tendency to base multiscale modeling on purely numerical schemes such as molecular dynamics, kinetic Monte Carlo, quasicontinuum, and direct numerical simulation of polycrystals. One common multiscale paradigm is “information-passing”—that is, computing material constants that are then used to inform upscale models. An important limitation of this type of multiscale analysis is that it does not provide insight into, nor does it supply, the functional form of the models governing material behavior at the various scales of interest. A competing paradigm consists of running several schemes, each operating on a different length scale and feeding average information to the upper scales, as part of the same calculation, which is referred to as “concurrent multiscale computing.” However, this paradigm is self-limiting owing to the inordinate volume of computing that it generates, and

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114Arsenlis, A., W. Cai, M. Tang, M. Rhee, T. Oppelstrup, G. Hommes, T.G. Pierce, and V.V. Bulatov. 2007. Enabling strain hardening simulations with dislocation dynamics. Modelling and Simulation in Materials Science and Engineering 15(6): 553-595.

115Ortiz, M., and E.A. Repetto. 1999. Nonconvex energy minimization and dislocation structures in ductile single crystals. Journal of the Mechanics and Physics of Solids 47(2): 397-462.

116Zhao, Z., R. Radovitzky, and A. Cuitino. 2004. A study of surface roughening in fcc metals using direct numerical simulation. Acta Materialia 52(20): 5791-5804.

117Zhao, Z., M. Ramesh, D. Raabe, A.M. Cuitiño, and R. Radovitzky. 2008. Investigation of three-dimensional aspects of grain-scale plastic surface deformation of an aluminum oligocrystal. International Journal of Plasticity 24 (12): 2278-2297.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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to the difficulty in interpreting and learning from the vast amounts of numerical data that it generates. Thus, whereas much of multiscale computing is driven by the rapid pace of development of computational platforms, the goal of “full physics”—that is, of employing solely fundamental theories in calculations and brute computational force—remains elusive at present.

An appealing alternative to computational multiscale schemes is to derive models of effective behavior across length scales analytically. In recent years, powerful techniques for characterizing such effective, or macroscopic, behavior, including relaxation and gamma convergence, have been developed in the context of the “modern calculus of variations” by, among others, Müller.118 What these methods do is to exhaustively evaluate all the possible subscale behaviors, or microstructures, that may develop in the material in response to macroscopic deformation and to determine the optimal, or “softest,” material response enabled by those microstructures. Examples of a material with microstructures that can be treated in this manner include martensite, sub-grain dislocation structures, dislocation walls and networks, ferroelectric domains, shear bands, spall planes, and others. By using the relaxed, or macrocoscopic, material model in calculations, the microstructural length scale is effectively pushed down to the subgrid level and need not be accounted for in the calculations explicitly, at enormous computational savings.119 Remarkably, the calculations still capture the exact macroscopic behavior exactly, since the effect of all possible microstructures has in effect been precomputed in the course of determining the relaxed model. Finally, the upscaling of the material behavior happens without a loss of information, since the optimal microstructures can always be reconstructed from the macroscopic solution. This ability to reconstruct microstructures from the macroscopic response may be critical in applications where the extreme values of the microscopic deformation and temperature fields, and not just their average values, are of consequence.

Unfortunately, explicit relaxations are known for only a handful of material models, although the list of such models continues to grow. Despite this paucity of explicit results, relaxation and related methods illustrate the important role that analytical methods can play in the field of multiscale analysis. Indeed, when used in simulations, each material model that is added to the list of explicitly known relaxations, or homogenizations, saves vast volumes of computation and, perhaps more importantly, makes feasible calculations that would otherwise be intractable using sheer brute force. Clearly, for this important effort to be effective, stronger coordination and collaboration between experimentalists and modelers must be encouraged. In summary, mathematical analysis could give simulations a great competitive advantage and should be an important part of a balanced approach to multiscale modeling. Efforts are under way at the Army Research Laboratory to apply this paradigm to protection materials.

Model Verification and Validation

Verification and validation are defined in the DoE plan for the Strategic Computing& Simulation Validation & Verification Program as follows:

  • Verification. The process of determining that a computer simulation correctly represents the conceptual model and its solution.
  • Validation. The process of determining the degree to which a computer simulation is an accurate representation of the real world.

The DoE Accelerated Strategic Computing Initiative has defined V&V requirements for the computer codes used as part of the national nuclear Stockpile Stewardship Program. One of the requirements is to develop a well-defined plan for V&V for each code. The idea is that a successfully executed V&V plan will certify the suitability of a computer code for a particular application. This paradigm is now commonplace for large-scale simulation efforts at DOE Defense Programs laboratories.

Although the idea has taken hold that some form of V&V is required in protection material simulation codes and some efforts have been made, a rigorous formalism and framework such as those established at DOE would greatly benefit the DoD research community (see Figure 4-20).

The next step beyond V&V is UQ to determine the uncertainties that affect not only simulations but experiments as well. It is widely accepted that experimental results are accompanied by systematic and random errors. UQ attempts to quantify these errors in a meaningful way. Each computation involves both numerical and physical parameters that have ranges, and distributions, of values. UQ techniques quantify the effect on the simulation outcomes of these parameter variations. Such sensitivity information is directly relevant to design.

Production Runs—Large-Scale Simulations of Problems of Interest

Simulations of protective material performance are commonly conducted on multiprocessor parallel computers available in DoD as part of the High Performance Computing Modernization Program. The DoD platforms belong to the so-called teraflop generation (1012 flops, where a flop is the number of floating point operations per second) (www.top500.org)

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118Müller, S. 1999. Variational models for microstructure and phase transitions. Pp. 85-210 in Calculus of Variations and Geometric Evolution Problems, Springer Lecture Notes in Math 1713. F. Bethuel, G. Huisken, S. Mueller, K. Steffen, S. Hildebrandt, and M. Struwe, eds. Berlin, Germany: Springer-Verlag.

119Conti, S., P. Hauret, and M. Ortiz. 2007. Concurrent multiscale computing of deformation microstructure by relaxation and local enrichment with application to single-crystal plasticity. Multiscale Modeling and Simulation 6(7): 135-157.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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FIGURE 4-20 V&V process. SOURCE: Reprinted from ASME V&V 10-2006, by permission of the American Society of Mechanical Engineers. All rights reserved.

and have on the order of 104 cores (processing units). Existing hydrocodes are reasonably scalable in the range of hundreds to a few thousand processors. But production armor simulations seldom need more than a few hundred processors. A typical large simulation involves a few million degrees of freedom and requires tens of gigaflops. Although this resolution makes it possible to conduct the simulations in three dimensions, in most cases much higher resolution is necessary to obtain results that converge.

Record-breaking platforms have recently achieved the petaflop (1015 flops) scale and involve between 105 and 3 × 105 cores. After conducting a study of the key technology challenges for exascale computing, the Defense Advanced Research Projects Agency (DARPA), announced the Omnipresent High Performance Computing Program (OHPC), aimed at building computers that exceed current petascale computers to achieve the mind-boggling speed of one quintillion (1,000,000,000,000,000,000) calculations per second (1 exaflop).120 Such computers are needed, according to DARPA, to “meet the relentlessly increasing demands for greater performance, higher energy efficiency, ease of programmability, system dependability and security.”121They 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.

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120Kogge, P., K. Bergman, S. Borkar, D. Campbell, W. Carlson, W. Dally, M. Denneau, P. Franzon, W. Harrod, K. Hill, J. Hiller, S. Karp, S. Keckler, D. Klein, R. Lucas, M. Richards, A. Scarpelli, S. Scott, A. Snavely, T. Sterling, R.S. Williams, and K. Yelick. 2008. ExaScale Computing Study: Technology Challenges in Achieving Exascale Systems, September 28. Available online at http://www.er.doe.gov/ascr/Research/CS/DARPA%20exascale%20-%20hardware%20%282008%29.pdf. Last accessed April 7, 2011. On June 20, 2010, DARPA announced the Omnipresent High Performance Computing Program (OHPC). See https://www.fbo.gov/index?s=opportunity&mode=form&id=3ba522c52b23884843a6639c8cbd1154&tab=core&_cview=0.

121Dillow, C. 2010. DARPA Wants to Usher in the Age of Exaflop Computing. Available at http://www.popsci.com/technology/article/2010-06/darpa-wants-usher-age-exaflop-computing. Accessed May 2, 2011.

122National Research Council. 2008. Evaluation of Quantification of Margins and Uncertainties Methodology for Assessing and Certifying the Reliability of the Nuclear Stockpile. Washington, D.C.: The National Academies Press.

123Eardley, D., H. Abarbanel, J. Katz, J. Cornwall, S. Koonin, P. Dimotakis, D. Long, S. Drell, D. Meiron, F. Dyson, R. Schwitters, R. Garwin, J. Sullivan, R. Grober, C. Stubbs, D. Hammer, P. Weinberger, R. Jeanloz, and J. Kammerdiener. 2005. Quantification of Margins and Uncertainties (QMU), JSR-04-330, March. Available online at http://www.stanford.edu/group/uq/docs/jason_qmu_margins.pdf. Last accessed April 7, 2011.

124Helton, J.C. 2009. Conceptual and Computational Basis for the Quantification of Margins and Uncertainty, SAND2009-3055, June. Available online at http://www.scribd.com/doc/27238941/Conceptual-andComputational-Basis-for-the-Quantification-of-Margins-and-Uncertainty. Last accessed April 7, 2011.

125Pilch, M., T.G. Trucano, and J.C. Helton. 2006. Ideas Underlying Quantification of Margins and Uncertainties (QMU): A White Paper, SAND2006-5001, September. Available online at http://www.stanford.edu/group/uq/docs/qmu_ideas.pdf. Last accessed April 7, 2011.

126Sharp, D.H., and M.M. Wood-Schultz. 2003. QMU and nuclear weapons certification:What’s under the hood. Los Alamos Science 28: 47-53.

127Lucas, L., H. Owhadi, and M. Ortiz. 2008. Rigorous verification, validation, uncertainty quantification and certification through concentration-of-measure inequalities. Computer Methods in Applied Mechanics and Engineering 197(51-52): 4591-4609.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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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.

QMU is also thought of as a tool for making high-consequence decisions about the design, certification, and deployment of high-value assets whose failure to perform safely and reliably could cause severe economic losses or loss of life. QMU radically alters the picture of predictive science and extreme-scale computing in many ways:by insisting on rigorously quantified uncertainties in the predictions as a measure of the confidence that decision makers can place in such predictions; by injecting probability and statistics into the calculations; by insisting on a global view of the response of the system over its entire operating range, thus breaking away from the “hero calculation” mode; and by the very tight coupling between simulations and validation or integral experiments that is required in order to establish confidence in the physics models.

In the context of protection materials, QMU, as enabled by extreme-scale computing, holds the promise of physics-based qualification of armor and protection systems. In this approach, computational models would be used to compute the variability of the response of a protection system given the randomness of inputs to the model and, potentially, the stochasticity of the response. In general, providing a measure of the maximum variability of the protection system over its operating range as computed by the model would require solving global optimization problems over input parameter space. This variability in turn provides a measure for the uncertainty in the response of the protection system—that is, a measure of how well the response of the system can be pinned down under operating conditions given the randomness of the system. Such global optimization calculations are inordinately intensive, hence the need for extreme-scale computing. However, the model uncertainty is only one part of the uncertainty budget: The level of confidence that can be placed in the physics and in the computations themselves, and the level of confidence that can be placed in the experimental data, need to be rigorously evaluated. The evaluation of both these terms in the uncertainty budget requires experimental data, either data-on-demand or archival (legacy) data.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
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Finding 4-4. The formulation of rigorous quantification of margins and uncertainties (QMU) protocols leading to the high-confidence certification of complex systems poses a challenge. However, the benefits of the application of QMU to the design and qualification of protective systems are potentially enormous.

NEW PROTECTION MATERIALS AND MATERIAL SYSTEMS: OPPORTUNITIES AND CHALLENGES

Polymeric materials such as some polycarbonates and Kevlar have demonstrated capabilities for certain protection applications, including transparent face shields and body armor. Polyethylene-based fiber materials such as Dyneema and Spectra have some properties, such as very high specific strength, that make them very effective in ballistic and blast applications when they are employed either as a single material or in combination with ceramics and metals in the form of a composite armor system. Preliminary ballistic tests have indicated their promise, especially for some of the higher strength versions of these fibers that are not yet available commercially. Nor are the constitutive laws and property inputs available that are needed to characterize these fibers in the range of strains and strain rates relevant to ballistic or blast simulations. Even the constitutive laws and material properties needed to characterize an established fiber such as Kevlar for these purposes are not fully in place. Thus far, these materials have been assessed largely based on projectile testing alone—make a target and shoot it. Efforts to employ constitutive models of fibers and yarns in simulations of protection systems have been published in recent years, including an assessment of lightweight fragment barriers for commercial aircraft128,129 and a multiscale model of impacts on textile fabrics.130

Improving the properties of specific materials used in protection systems is one route to improved ballistic performance but may not open up opportunity for significant advances for some of the most widely employed protection materials given their maturity (some polymers are clear exceptions). By contrast, there is almost certainly scope for major advancement in the design of protection material systems made up of combinations of metals, ceramics, and polymers. Given the potential of polymer/ceramic/metal composite material protection systems and given the huge number of material and architectural combinations that should be considered, there is strong motivation to select among the multitude of combinations using simulation rather than testing alone, since the latter is time consuming, expensive, and not necessarily insightful. It was noted earlier in this chapter that, to perform effectively, a block of ceramic 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 materials for ceramic protection systems.

Finding 4-5. Accurate simulation of the performance of armor protection systems under various ballistic threats and multiple hits necessitates advances in numerical methods, as outlined in the section “Modeling and Simulation Tools,” as well as a better understanding of mechanisms of deformation and fracture coupled with better constitutive descriptions.

Computational Materials Methods

The focus in this chapter has been on characterizing materials with respect to their performance as protection materials using observation and the experimental and computational methods of mechanics. These methods can be used to evaluate new materials, and they are essential for establishing material properties that would enhance protection performance; however, they cannot be used to design new materials nor are they able to predict fundamental material parameters such as modulus, hardness, or toughness. These more fundamental objectives are in the realm of computational materials science. Computational materials methods have been covered in a variety of reports, among them Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security, published by the NRC in 2008,131and a report by DOE.132 In view of these widely available documents, the techniques of computational materials science, other than those already outlined above, will be described only briefly in the current report. Integrated Computational Materials Engineering is drawn on heavily for what is provided in the next few paragraphs, in many cases verbatim. That report also recommends a computationally enabled way forward for improving the development and insertion cycle for new materials across the entire spectrum of materials science and engineering and is therefore an important forerunner 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 Computational Materials Engineering.

In addition to methods designed to simulate structural

______________

128Shockey, D.A., D.C. Erlich, and J.W. Simons. 1999. Lightweight fragment barriers for commercial aircraft, paper presented to the 18th International Symposium on Ballistics, San Antonio, Tex. Available online at 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 constitutive model for the mechanical behavior of woven fabrics. International Journal of Solids and Structures 42(13): 3867-3896.

130Nilakantan, G., M. Keefe, T.A. Bogetti, and J.W. Gillespie, Jr. 2010. Multiscale modeling of the impact of textile fabrics based on hybrid element analysis. International Journal of Impact Engineering 37(10): 1056-1071.

131National Research Council. 2008. Integrated Computational Materials Engineering:A Transformational Discipline for Improved Competitiveness and National Security. Washington, D.C.: The National Academies Press.

132Department of Energy. 2005. Opportunities for Discovery: Theory and Computation in Basic Energy Sciences. Available online at http://www.sc.doe.gov/bes/reports/files/OD_rpt.pdf. Last accessed April 7, 2011.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×

materials behavior at the macroscopic level, as described above, the computational materials scientist has a host of techniques for simulation for a variety of purposes. The wide variety of tools available reflects the fact that materials response and behavior involve a multitude of physical and chemical phenomena whose accurate treatment in models requires the spanning of many orders of magnitude in length and time. Further, computational simulation is used to tackle a wide variety of materials attributes and phenomena, including thermodynamic, kinetic, and structural properties, to bring advances in areas such as materials processing, microstructural evolution, structure-property relationships, materials stability and corrosion, and stiffness and strength. Moreover,

…the length scales in materials response range from nanometers of atoms to the centimeters and meters of manufactured products. Similarly, time scales range from the picoseconds of atomic vibrations to the decades over which a component will be in service. Fundamentally, properties arise from the electronic distributions and bonding at the atomic scale of nanometers, but defects that exist on multiple length scales, from nanometers to centimeters, may in fact dominate properties. It should not be surprising that no single modeling approach can describe this multitude of phenomena or the breadth of scales involved. While many computational materials methods have been developed, each is focused on a specific set of issues and appropriate for a 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 bonding, magnetic moments, and transport properties of atoms in different configurations. As the simulation cells get larger and the times scales longer, empirical interatomic potentials are used to approximate these interactions. Optimization and temporal evolution of electronic structure and atomistic methods are achieved using conjugate gradients, molecular dynamics, and Monte Carlo techniques. At still larger scales, the information content of the simulation unit decreases until it becomes more efficient to describe the material in terms of the defect that dominates at that length scale. These units might be defects in the lattice (for example, dislocations), the internal interfaces (for example, grain boundaries), or some other internal structure, and the simulations use these defects as the fundamental simulation unit in the calculation.133

Table 3-1 (Table 4-1 in the current report) from the above-mentioned NRC report Integrated Computational Materials Engineering134 lists a variety of computational materials methods, some of them standard and already adopted in materials development and industry activities, and others strictly research tools. As noted in the source study from which it was taken,

…the table is not intended to be complete but rather to exemplify the methods available for modeling materials characteristics. This table indicates typical inputs and outputs of the software and examples of widely used or recognized codes. Electronic structure methods employ different approximate solutions to the quantum mechanics of atoms and electrons to explore the effects of bonding, chemistry, local structure, and dynamics on the mechanisms that affect material properties. Typically, tens to hundreds of atoms are included in such a calculation and the timescales are on the order of nanoseconds. In atomistic simulations, arrangements 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 millions of atoms. Length scales and timescales are in the nanometer and nanosecond regime, and longer length scales and timescales are possible in the case of molecular system coarse graining from “all-atom” to “united atom” models (that is, interacting clusters of atoms). Dislocation dynamics methods are used to study the evolution of dislocations (curvilinear defects in the lattice) during plastic deformation. The total number of dislocations is typically less than a million, and strain rates are large compared to those measured in standard laboratory tests. Thermodynamic methods range from first-principle predictions of phase diagrams to complex database integration methods using existing tabulated data to produce phase diagrams and kinetics data.135

Microstructural evolution methods predict material stability and evolution at the microscopic level based on free-energy functions, elastic parameters, and kinetic databases.

Micromechanical and mesoscale property models include solid mechanics and FEA methods that use experimentally derived models of materials behavior to explore microstructural influences on properties. The models may incorporate details of the microstructure (resolving scales at the relevant level). Results may be at full system scale. Mesoscale structure models include models for solidification and solid state deformation using combinations of the previous methods to predict favorable processing conditions for specific microstructural characteristics. Methods for code and systems integration offer ways to connect many types of models and simulations and to apply systems engineering strategies. Statistical tools are often used to gain new understanding through correlations in large data sets. Other important ICME tools include databases, quantifiable knowledge rules, error propagation models, and cost and performance models.136

Finding 4-6. Computational methods have considerable potential for aiding the architectural design of composite protection packages, but they require robust constitutive

______________

133National Research Council. 2008. Integrated Computational Materials Engineering:A Transformational Discipline for Improved Competitiveness and National Security. Washington, D.C.: The National Academies Press. P. 69.

134National Research Council. 2008. Integrated Computational Materials Engineering:A Transformational Discipline for Improved Competitiveness and National Security. Washington, D.C.: The National Academies Press.

135Ibid., p. 71.

136Ibid.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×

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

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×

Overall Recommendations

Recommendation 4-1. The Department of Defense should pursue an initiative for protection materials by design by exploiting the capabilities of advanced computational and experimental methods. The initiative will (1) enable improved understanding of fundamental material deformation and fracture mechanisms governing protection materials performance and (2) provide guidance for changes in material processing.

Recommendation 4-2. The protection materials by design initiative should also use advanced computational and experimental methods to simulate the ballistic and blast performance of candidate material protection systems.

Recommendation 4-3. The protection materials by design initiative should include a concerted effort to develop the next generation of Department of Defense advanced protection codes that incorporate experimentally validated, high-fidelity scientific models, as well as the necessary high-performance computing infrastructure. Progress in this direction will require the development of high spatial and temporal resolution (with 10-μ resolution in space and microsecond resolution in time) capabilities for in situ visualization of deformation and failure mechanisms during the impact event.

Recommendation 4-4. As part of the initiative, a program should be established with primary focus on code validation and verification; multiscale, multiphysics material models; integrated simulation/experimental protocols; prediction with quantified uncertainties; and simulation-based qualification to help advance predictive science for protection materials and material systems.

Recommendation 4-5. The initiative should identify a series of unclassified protection material challenge problems comprising simulation and experimental validation whose solution would convincingly demonstrate the effectiveness of protection materials by design. One such canonical problem might be the characterization of the high-strain-rate response of brittle armor materials such as ceramics and glasses under combinations of high pressure and shear representative of ballistic penetration, followed by a demonstration of the effectiveness of the new characterization in simulating the performance of a particular ceramic armor package.

Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 35
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 36
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 37
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 38
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 39
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 40
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 41
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 42
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 43
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 44
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 45
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 46
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 47
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 48
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 49
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 50
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 51
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 52
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 53
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 54
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 55
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 56
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 57
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 58
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 59
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 60
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 61
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 62
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 63
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
Page 64
Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
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Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
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Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
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Suggested Citation:"4 Integrated Computational and Experimental Methods for the Design of Protection Materials and Protection Systems: Current Status and Future Opportunities." National Research Council. 2011. Opportunities in Protection Materials Science and Technology for Future Army Applications. Washington, DC: The National Academies Press. doi: 10.17226/13157.
×
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Armor plays a significant role in the protection of warriors. During the course of history, the introduction of new materials and improvements in the materials already used to construct armor has led to better protection and a reduction in the weight of the armor. But even with such advances in materials, the weight of the armor required to manage threats of ever-increasing destructive capability presents a huge challenge.

Opportunities in Protection Materials Science and Technology for Future Army Applications explores the current theoretical and experimental understanding of the key issues surrounding protection materials, identifies the major challenges and technical gaps for developing the future generation of lightweight protection materials, and recommends a path forward for their development. It examines multiscale shockwave energy transfer mechanisms and experimental approaches for their characterization over short timescales, as well as multiscale modeling techniques to predict mechanisms for dissipating energy. The report also considers exemplary threats and design philosophy for the three key applications of armor systems: (1) personnel protection, including body armor and helmets, (2) vehicle armor, and (3) transparent armor.

Opportunities in Protection Materials Science and Technology for Future Army Applications recommends that the Department of Defense (DoD) establish a defense initiative for protection materials by design (PMD), with associated funding lines for basic and applied research. The PMD initiative should include a combination of computational, experimental, and materials testing, characterization, and processing research conducted by government, industry, and academia.

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