The range of materials in use today for protection appli- cations 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 projec- tiles 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 promis- ing 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 defor- mation and failure over a wide range of strain rates, temperatures, and multiaxial stresses.
• Computational methods capable of capturing defor- mation and fracture under intense dynamic loads.
• Experimentation to supply basic material inputs to the constitutive models implemented in the computa- tional 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- There are two important challenges to be considered in
improving protection systems. The first is to develop mate- rials 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 proper- ties. 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 pre- scribed 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 mod- eling 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 mul- tiscale, 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.
36 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS
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 experi- mental and computational methods.
THREE EXAMPLES OF CURRENT CAPABILITIES FOR MODELING AND TESTING
Three examples illustrate current capabilities for simu- lating 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 com- mittee’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 simula- tions of these tests.
The constitutive relation used to characterize plastic deformation of AA7075 in the simulations of Børvik et al.2
1Børvik, T., O.S. Hopperstad, and K.O. Pedersen. 2010. Quasi-brittle fracture during structural impact of AA7075-T651 aluminum plates. Inter- national Journal of Impact Engineering 37(5): 537-551.
2Ibid.
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 ef- fect 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 de- formation relation is supplemented by a material fracture criterion that usually employs a critical value of the equiva- lent 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 diffi- cult 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 pen- etration owing to distortion of the meshes is evident in Figure 4-4. The blunt-nosed projectile produces shear local- ization 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
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 Bal- listics, The Hague, The Netherlands. Available online at http://www.lajss.
org/HistoricalArticles/A%20constitutive%20model%20and%20data%20 for%20metals.pdf. Last accessed April 5, 2011.
4Børvik, T., O.S. Hopperstad, and K.O. Pedersen. 2010. Quasi-brittle fracture during structural impact of AA7075-T651 aluminum plates. Inter- national Journal of Impact Engineering 37(5): 537-551.
5See http://www.lstc.com.
INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS 37
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.
Initial velocit
Figure 4-3.eps
y [m/s]
0 50 100 150 200 250 300 350
Residual velocity [m/s]
Experimental data
Best fit (a = 0.89 and p = 2.15)
Blunt projectiles vbl = 183.8 m/s
150 200 250 300 350 400
150 200 250 300 350 400
Initial velocity [m/s]
0 50 100 150 200 250 300 350
Residual velocity [m/s]
Experimental data
Best fit (a = 0.87 and p = 2.54)
Ogival projectiles vbl = 208.7 m/s
a b
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.
150 200 250 300 350 400
Initial velocity [m/s]
Figure 4-3.eps
0 50 100 150 200 250 300 350
Residual velocity [m/s] Residual velocity [m/s]
Numerical result (3D - fine mesh) Numerical result (3D - coarse mesh) Numerical result (2D - coarse mesh) Fit (a = 0.87 and p = 2.32)
vblc (3D) = 185 m/s
Blunt projectiles vblf (3D) = 181 m/s
vblc (2D) = 180 m/s
150 200 250 300 350 400
Initial velocity [m/s]
0 50 100 150 200 250 300
350 Numerical result (3D - fine mesh) Numerical result (3D - coarse mesh) Fit (a = 1 and p = 2)
vblf = 268 m/s
Ogival projectiles vblc = 271 m/s
a b
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 Engineer- ing 37(5): 537-551.
38 OPPORTUNITIES IN PROTECTION MATERIALS SCIENCE AND TECHNOLOGY FOR FUTURE ARMY APPLICATIONS
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 ma- terial 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 inde- pendently 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. Consequent- ly, 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 500 μ in the three-dimensional case. Either element size calibration or a constitutive length parameter will continue to be an essential, non-straightforward requirement in pen- etration simulations.
The simulation of penetration represented by the results in Figure 4-3 must be pushed further to demonstrate the ro- bustness of the predictive capability. Would the agreement between simulation and experiment continue to hold if plate thickness was doubled or if the target was two air-separated plates? Would the agreement hold up for projectiles impact- ing the plate at an oblique angle? More sophisticated con- stitutive models that incorporate the evolution of damage prior to failure and a material length based on mechanisms of deformation and failure hold promise for simulations that are more closely tied to fundamental material mechanisms and properties and freed from element size calibration.
While the potential of such added sophistication has been 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 inves- tigate 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,7 known 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
6Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide subjected to high-velocity impact. International Journal of Impact Engineer- ing 35(8): 742-752.
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 Pro- gram, 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 Engineer- ing 35(8): 742-752.
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.
INTEGRATED COMPUTATIONAL AND EXPERIMENTAL METHODS 39
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 bi- layer build up gradually as the point of the projectile flattens, enabling the ceramic to remain intact for longer and to serve as better armor against the threat of the pointed projectile.
The JHB constitutive law is summarized in Figure 4-5, 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 ε*. 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 in- creases. The plots for intact ceramic (Figure 4-5) interpolate this behavior between the extremes of tensile stress and very
10Wilkins, M.L. 1967. Second Progress Report of the Light Armor Pro- gram, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence Livermore National Laboratory.
high pressure. The plots also indicate that the strengths will be slightly different at high and low strain rates.
It is obvious that when the ceramic cracks and frac- tures, 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 termi- nates 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
11Holmquist, T.J., and G.R. Johnson. 2008. Response of boron carbide subjected to high-velocity impact. International Journal of Impact Engineer- ing 35(8): 742-752.
12Wilkins, M.L. 1967. Second Progress Report of the Light Armor Pro- gram, Technical Report No. UCRL 50284. Livermore, Calif.: Lawrence Livermore National Laboratory.
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
ε*. 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 permis- sion from Johnson, G.R., T.J. Beissel, and S.R. Beissel, Journal of Applied Physics, 94, 1639, (2003). Copyright 2003, American Institute of Physics.