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.



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