Effects Of Lamination And Spacing On Finite Thickness Plate Perforation

Abstract

In determining ballistic limits and residual projectile characteristics for very thick targets (situations where the ratio of target thickness T to projectile diameter D exceeds 10), resort must frequently be made to constructing the target from a number of layers whose thickness is less than that of the monoblock target. This holds true for determining penetration depths in semiinfinite plates as well. This paper presents results of numerical simulations comparing projectile residual characteristics, primarily residual mass, for monoblock and equivalent thickness layered targets for a number of situations involving T/D 10. It is found that for thick plates, results obtained from layered target perforation compare favorably with those from monoblock targets provided that the layering is not excessive and care is taken to insure that the individual layers have the same material properties as the monoblock target. For thin targets, the correlation ranges from poor to non-existent. Introduction Impact and impulsive loading onto layered media targets consisting of different materials is a problem of long standing. It occurs naturally when dealing with impact effects into geological media, where different strata have different material properties. It can occur in the design of protective structures where materials of different density, strength and cross-sectional area are employed to reduce the intensity of the impact stress. This aspect of the impact problem is well understood and is covered in modern textbooks and reference books dealing with transient phenomena. Another aspect of layering involves the impact of projectiles onto targets consisting of multiple layers of plates of the same density] In impact testing, this often occurs when very thick targets need to be constructed yet the target material in question is not manufactured in the required thickness. Take, for example, the requirement to construct an effective semi-infinite target, one where the rear of the plate does not influence the penetration process. It is Transactions on the Built Environment vol 22, © 1996 WIT Press, www.witpress.com, ISSN 1743-3509 104 Structures Under Shock And Impact desired to build such a target of rolled, homogeneous armor (RHA) steel. The maximum thickness of RHA commercially available is 20.32 cm. At this thickness, uniformity of material properties is a problem, as is cost. Hence, targets for deep penetration studies are often constructed by using a number of plates of smaller thickness, stacking them until the desired thickness is reached. This target stack is then contained in some fashion (e.g. trapped, welded at the periphery) and the test conducted. In the course of testing the restraints are broken and the front and rear plates are observed to move considerable distances, even for tests involving target plates weighing several terns. Each layer acts as a momentum trap and the outermost layers dissipate the residual energy through rigid body motion. Several questions must now be answered before the test results may be accepted as valid: (a) does the penetration event occur on the same time scale as the rigid body motion of the target plates? In other words, is a layered target an effective simulant of a monoblock target? (b) what is the effect of layering as the number of plates required to simulate the monoblock thickness increases? (c) if target plates do separate before completion of the penetration/perforation process, what is the effect on the penetration depth (or, if a perforation, on the projectile residual mass and velocity) These questions must be answered for three classes of targets: (a) thin targets (T/D 10) Thin and Intermediate Thickness Targets For thin and intermediate thickness targets the answers may be readily inferred from the existing literature. In their study of containment structures, Zaid, ElKalay and Travis (1973) point out that for very thin plates (thicknesses < 2 mm), lamination greatly reduces the resistance of the target plate to ballistic impact. Netherwood (1979), conducting in situ pressure measurements of impacted plates found the laminated target to be much weaker than a solid one of the same thickness so that the mechanism of penetration of a laminated target was different than that for a solid target. Nixdorff (1984) examined analytically the effect on lamination on the ballistic limit for up to five layers and found considerable differences as the number of layers increased. Similar conclusions were reached by Segletes and Zukas (1989) in a numerical analysis Transactions on the Built Environment vol 22, © 1996 WIT Press, www.witpress.com, ISSN 1743-3509 Structures Under Shock And Impact 105 of laminated plates. Other studies could be cited but these suffice to show that for thin targets, lamination can alter the response mechanism under impact loading and fail to correlate with the behavior of a solid target, especially if the number of layers is large. The problem for intermediate thickness targets can be seen from the results of the following calculations. The ZeuS code [Segletes and Zukas (1987), Janzon et al (1992), Zukas (1993)], a two-dimensional explicit finite element code for fast, transient analysis on personal computers, was used to calculate the impact of a 64.5 gram S-7 tool steel projectile with length-todiameter (L/D) ratio of 5 into a single RHA plate with a thickness of 3.18 cm. The projectile had a diameter of 1.3 cm and a striking velocity of 1164 m/s. Experimental data was taken from the report by Lambert (1978). The experimentally determined values of projectile residual mass and residual velocity were 22.9 grams and 223 m/s, respectively. ZeuS calculations indicated a residual mass of 25.5 grams and a residual velocity of 233 m/s. These were deemed acceptably close. Next, a series of calculations was undertaken where the solid target above was assumed to consist of 2, 4 and 6 layers, each with properties identical to those of the solid target. Penetration of the four-layer target at various times is shown in Figure 1. The variation of projectile normalized residual mass ( mjm^ and normalized residual velocity (V,IV^ V striking velocity) can be seen in Figures 2 and 3. With the 4-layer laminated target, the difference between Lambert's data for the solid target and the computed residual masses is 43% while for the residual velocity it is 143%. The differences continue to increase with increasing lamination. Even though the plates making up the laminated target have the same density and material properties as the solid target, the differences noted above could be anticipated. The plates in the laminated target are not restrained and are allowed to slip freely over each other. As they separate after the passage of the projectile, a free surface is created. The inability of a free interface to support rarefaction waves changes the stress wave propagation characteristics of multiplate penetration events at early times. As these stress differences are integrated in time, the difference between the simulations becomes more visible, with the multiplate case demonstrating more bending than the equivalent solid plate case (Figure 4). This can also be inferred from plate theory which gives for the bending stiffness of the plate E7 /12(1 -v*), where E is the elastic modulus, T the plate thickness and v Poisson's ratio. Since bending stiffness follows plate thickness to the third power, simply cutting a monoblock plate in half reduces its bending stiffness by a factor of 8. Transactions on the Built Environment vol 22, © 1996 WIT Press, www.witpress.com, ISSN 1743-3509