Dimensionless Parameters for Optimization of Textile ...

Dimensionless Parameters for Optimization of Textile-Based Body Armor Systems Philip M. Cunniff U.S. Army Soldier and Biological Chemical Command Soldier Systems Center, Natick Natick, MA 01760-5019

A set of dimensionless parameters for the optimization of textile-based body armor systems is described, which provide critical guidance to fiber developers, body armor system material integrators, and body armor system designers for the continuous product improvement of personnel armor items. The dimensionless parameters allow for directed optimization of textile fibers based on an objective assessment of the trade-off in ballistic performance associated with altering a fiber’s mechanical properties. In addition to the utility of these dimensionless groups in the directed optimization of textile fibers, the framework for analysis that these tools allow will contribute to defining enhanced performance armor materials using existing fibers. Using these tools, developers may express the potential of a fiber to perform as an armor material using a single non-dimensional number.

INTRODUCTION Empirical work to relate ballistic impact performance to projectile and target characteristics has yielded dimensionally awkward relationships between perforation velocity and target and projectile quantities [1-4]. Mechanical properties of the armor systems have been routinely ignored in these approaches. Apart from the aesthetics of developing dimensionally equivalent relationships between perforation velocity, projectile properties, and armor system characteristics, such relationships are useful in optimizing armor system construction and provide direction in the alteration of material properties. Improvements in armor materials’ mechanical properties due to variations in processing conditions are constrained by the limitations of the existing material processing envelopes, but considerable flexibility still exists to produce improved materials. Analysis tools are required to further elucidate a path to the development of optimal materials for use in textile based body armor systems.

DIMENSIONAL ANALYSIS Dimensional analysis is used as a tool to help eliminate extraneous information in a relation between quantities [5]. Dimensional analysis may be applied to problems where it is known that only a single relationship exists between a number of physical quantities and that all of the pertinent quantities have been identified. In the dimensional analysis presented here, it is assumed that fiber specific toughness and fiber strain wave velocity are the only essential mechanical properties of the system, and that presented area and mass are the only essential characteristics of the projectile. We assume the fiber is linearly elastic and use the product of ultimate strength and elongation at break to determine the fiber toughness; fiber strain wave velocity is taken to be the square root of the specific tensile modulus. The objective of the analysis is to relate these system and projectile characteristics to the principal design parameters of an armor system, namely V50 velocity (the velocity where impacting projectiles are expected to defeat a system 50% of the time) and system areal density (weight per unit area). The physical quantities for this system are: σε Φ  ----- 2ρ where: σ

E --ρ

,

,

A ------p mp

,

V 50

,

A d = 0 

(1)

- Fiber ultimate axial tensile strength

ε ρ

- Fiber ultimate tensile strain - Fiber density

E

- Fiber modulus (fibers are assumed to be linearly elastic)

A p - Projectile presented area m p - Projectile mass V 50 - V50 ballistic limit Ad

- System areal density

The dimensional ratios for this system are: Ad A   V 50 - , -------------p = 0 Φ  -------------------mp   ( U *) 1 ⁄ 3

(2)

E * σε- --- the product of fiber specific toughness and strain wave where: U = ----2ρ ρ velocity Examination of Equation 2 indicates the dimensionless parameters relate ballistic impact performance to fiber mechanical properties independent of impacting projectile mass, presented area or armor system areal density (weight per unit area). The first parameter, a dimensionless V50 velocity, is defined as the V50 velocity normalized by the cube root of the product of specific work to break the

fiber and the acoustic wave speed in the fiber. The second dimensionless parameter relates to the armor system configuration and penetrator and is defined as the product of the system areal density (Ad) and projectile presented area (Ap) divided by the projectile mass (mp). Hence, results of the dimensional analysis indicate that a single curve may be used to relate the V50 performance of any armor system material to any penetrator, independent of the system areal density.

MATERIAL MECHANICAL PROPERTIES Material mechanical properties were obtained from published quasi-static mechanical properties for yarns for each material with the exception of nylon, where fully dynamic mechanical properties were used. Table 1: Fiber Mechanical Properties Fiber

1 ---

Strength

Failure Strain

Modulus

Density

(σ) (GPa)

(ε) (%)

(E) (GPa)

(ρ) (kg/ m3)

(m/s)

PBO [6]

5.20

3.10

169

1560

813

Spectra® 1000 [6]

2.57

3.50

120

970

801

600 denier Kevlar® KM2 [8]

3.40

3.55

82.6

1440

682

850 denier Kevlar® KM2 [9]

3.34

3.80

73.7

1440

681

840 denier Kevlar® 129 [10]

3.24

3.25

99.1

1440

672

1500 denier Kevlar® 29 [11]

2.90

3.38

74.4

1440

625

200 denier Kevlar® 29 [12]

2.97

2.95

91.1

1440

624

1000 denier Kevlar® 29 [13]

2.87

3.25

78.8

1440

621

1140 denier Kevlar® 49 [14]

3.04

1.20

120

1440

612

carbon fiber [15]

3.80

1.76

227

1800

593

3500*

4.7†

74

2550

559

0.91

N/A‡

9.57

1135

482

E-Glass [16] nylon [17]

σε E 3  ----- -- 2ρ ρ 

*. Virgin fiber tensile strength at room temperature †. A linear stress-strain relationships is assumed. ‡. Smith [10] gives breaking energy of nylon yarns subjected to impact loading. This value is used for U in this work.

EXPERIMENTAL Archival data for the V50 ballistic limit of several hundred different V50 tests was used in this work. System areal densities ranged from 0.27 g/cm2 (8.9 oz/ft2) to 2.5 g/cm2 (81 oz/ft2). Projectiles had a length-to-diameter ratio of approximately one; they were either steel or tungsten with mass of 2-, 4-, 16- 64-or 128-grain (0.12, 0.26, 1.0, 4.1, or 8.2-g). Material types included Kevlar 29®, Kevlar 129®, Kevlar 49®, Kevlar KM2®, heady tow carbon fiber, E-glass, poly(p-phenylene benzobisoxazole) (PBO obtained from Dow Chemical Co.), nylon 6,6, and Spectra 1000® fabrics. Composite materials investigated were Kevlar® 29/poly(vinyl-butyral)/phenolic, Kevlar® KM2/poly(vinyl-butyral)/ phenolic, Spectra 900 fabric/vinylester, SPECTRA shield®/Kraton®, E-glass/ polyester, carbon fiber / epoxy, and nylon/poly(vinyl-butyral)/phenolic. In each case (with the exception of E-glass and carbon fiber composites) the resin content was approximately 15-18% by weight; the resin content of the glass and carbon composites was approximately 30%. Processing conditions, and details of sample preparation and testing will be left to a more lengthy discussion of this work. RESULTS 1⁄3

The fiber property of interest is ( U * ) . Tabulated values are provided in Table 1; the dimensionless relationship is plotted in Figures 1 and 2. In Figure 1, the V50 performance of seven different fabric armor systems are plotted on the as a function of the dimensional parameters. Also plotted in each Figure is a smooth curve which corresponds to a regression analysis of the Kevlar 29 V50 data; the same smooth curve is plotted in each Figure to facilitate comparison. Similarly, the plots of Figure 2 represent the dimensionless V50 performance of seven different composite armor systems; the smooth curve plotted in these plots corresponds to a regression analysis of the Kevlar 29 PVB/phenolic composite V50 data. The V50 velocity of an armor system is a function of obliquity. In several cases in the plots of Figures 1 and 2, V50 data at obliquities other than 0-degrees has been included. In sec ( θ ) – 1 all cases, the V50 velocity has been scaled by the parameter X 8 , where X 8 is a regression constant for the armor system. As illustrated in Figures 1 and 2, broad agreement was shown among the differing armor systems and projectiles, with the notable exceptions of ultrahigh molecular weight polyethylene, carbon fiber/epoxy and E-glass/polyester. Note that 1⁄3 the ( U * ) value used to plot Spectra data was 652, whereas the tabulated value 1⁄3 determined from the dimensional analysis is 801; similarly reduced ( U * ) values were used for glass and carbon composite systems. Spectra systems significantly under-performed expectations, presumably due to fiber softening during the impact event. In the case of Spectra, the failure to correlate well with the U* theory is taken to be an indication that impact performance of high melting point fibers may exceed the performance of equivalent low-melting point fibers. Some of the scatter in the data of the dimensionless plot is due to variations in the textile structure, some of it is due to the statistical nature of failure of materials. The dimensionless parameters do not allow for analyze these more subtle

performance differences; such differences are more appropriately studied using more sophisticated analytical and numerical tools [16,17]. However, the approach taken here does provide an elegant framework to analyze performance trade-offs associated with system design modifications. Plotting experimental data (for example resulting from a weave type study) on a plot similar to Figure 1 allows a materials systems integrator access to a much more powerful comparative tool than had previously been available. For example, the performance of Kevlar KM2 and Spectra composites consistently exceeds expectations. The Kevlar composites were prepared using a novel adhesion modifier developed by duPont which is thought to degrade adhesion. The additional increase in performance (after the increase expected due to enhanced mechanical properties is accounted for) of Kevlar KM2 composites is thought to be due to this adhesion modification. Unfortunately, neither Kevlar 29 composites with the adhesion modifier nor Kevlar KM2 composites without the adhesion modifier have been tested. The elegance of the dimensionless formulation is a reflection of the assumptions embodied in the model. It is assumed that lateral compressive forces on the fibers of a body armor system do not contribute to appreciable energy absorption or to premature failure of the system. Since lateral compressive stresses are quite localized, the former assumption appears to be reasonable, the latter assumption is expected to lead to discrepancies for some materials. Examination of scanning electron micrographs of the region immediately under the impact point in a poly(pphenylene terephthalamide) (e.g., Kevlar KM2) fabric armor system indicates considerable localized yielding of the fibers; similarly deformed fibers are observed in poly(p-phenylene benzobisoxazole) (e.g. Zylon) fibers and ultra high molecular weight polyethylene (e.g. Spectra) fiber armor systems. Evidence that lateral yielding does not contribute to premature axial tensile failure, as suggested by the dimensional analysis presented here, is reinforced by experiments on Kevlar fibers. Comparison of virgin Kevlar fiber and Kevlar 29 fiber following local compression and yield of the fiber indicates excellent agreement. In these tests, fibers where compressed in a region of approximately 20 fiber diameters (~2 mm); compression was sufficient to cause plastic deformation which increased fiber diameters by at least 100%. The stress-strain response of the yielded fiber is almost indistinguishable from the virgin fiber response. The ability of Kevlar- type fiber to support a large axial tensile load in the presence of a (large) lateral compressive load is consistent with the microfibrillar structure of the fiber. In the context of the present work, these microfibrils are understood to be the load-bearing members of the fiber. To the extent that they are not fractured under the lateral loads, the axial tensile stress for the fibers is essentially decoupled from the lateral stresses. Clearly, neglecting the contribution of lateral compressive stress to the premature failure in axial tension is expected to lead to errors for brittle materials, such as carbon or glass fibers, where it is more appropriate to include an analysis of a combined stress theory of failure. This failure of the dimensional analysis approach discussed here to predict this performance is apparent in Figures 1 and 2. The objective of this work was to attempt to elucidate an optimal path to increase armor system performance through changes in fiber properties, but not necessarily to

FIGURE 1. Fabric armor systems. The (U*)1/3 value for Spectra is a fictive number; i.e. not the number calculated in TABLE 1

FIGURE 2. Composite armor systems. The (U*)1/3 values for Spectra, glass and carbon composites are fictive numbers; i.e. not the numbers calculated in TABLE 1.

predict the performance of every fiber. It is sufficient to note that isotropic fibers (such as glass fibers, which are expected to fail in a manner well characterized by, say, a distortion energy theory of failure) or other fibers that are brittle in lateral compression are expected to be inferior to fibers with similar mechanical properties that are fibrilar, or otherwise yield under lateral compression without disrupting the load-bearing elements of the fiber. SUMMARY

For traditional textile armor, two dimensionless groups define the potential of a fiber as a candidate armor material and are considered the most appropriate firstlevel screening tool available to assess performance of new fibers. Armor system performance is constrained by the ultimate mechanical properties of the fiber but is not completely defined by these properties. Armor system performance is “tethered” to the curve, but textile or composite engineering allows one to manipulate performance. The dimensionless groups developed in this work provide a framework to evaluate performance improvements that may result from system-level modifications, such as those that may result from application of textile engineering. REFERENCES 1. Project THOR - The Resistance of Various Non-Metallic Materials to Perforation by Steel Fragments. Ballistics Research Laboratory Technical Report No.51, (AD336461), 1963. 2. Johnson, W.P., Collins L.I., and Kindred F.A., A Mathematical Model for Predicting the Residual Velocities of Fragments After Perforating Helmets and Body Armor, Ballistic Research Lab, BRL Tech Note 1705 (AD 394512), 1969. 4. Cunniff, P.M., Text. Res. 66, 45-60, 1996. 5. Taylor, E.S., Dimensional Analysis for Engineers, Claredon Press, Oxford, 1974. 6. Developmental Product Specification for 600 denier Kevlar KM2 Yarn, Type 964H. DuPont Quality Assurance; Spruance Plant, Richmond, VA. Date Effective: 20 May 1998. 7. Developmental Product Specification for 850 denier Kevlar KM2 Yarn, Type 964H. DuPont Quality Assurance; Spruance Plant, Richmond, VA. Date Effective: 18 Aug. 1998. 8. Developmental Product Specification for 840 denier Kevlar 129 Yarn, Type 964C. DuPont Quality Assurance; Spruance Plant, Richmond, VA. Date Effective: 1 Mar. 1997. 9. Developmental Product Specification for 1500denier Kevlar 29 Yarn, Type 964. DuPont Quality Assurance; Spruance Plant, Richmond, VA. Date Effective: 1 Mar. 1997. 10.Developmental Product Specification for 200 denier Kevlar 29 Yarn, Type 964. DuPont Quality Assurance; Spruance Plant, Richmond, VA. Date Effective: 1 Mar. 1997. 11.Developmental Product Specification for 1000 denier Kevlar 292 Yarn, Type 964. DuPont Quality Assurance; Spruance Plant, Richmond, VA. Date Effective: 1 Mar. 1997. 12.Developmental Product Specification for 1140 denier Kevlar 49 Yarn, Type 965. DuPont Quality Assurance; Spruance Plant, Richmond, VA. Date Effective: 1 Mar. 1997. 13.Smith, J. C., Shouse, P.J., Blandford, J.M., and Towne K.M., Tex. Res. J., 31 (8), 721, 1961 14.Cape Composites Product Description for Carbon Fiber 15.Gupta P.K., Glass Fibers for Composite Materials. in Fiber Reinforcements for Composite Materials, A.R. Bunsell Editor, Elsevier, New York 1988 16.Cunniff, P. M., Numerical Simulation of Ballistic Impact of Textiles, Personal Armour Systems Symposium, Colchester, Essex, 1994. 17.Ting, J., Roylance, D., Chi, C.H., Chitrangrad, B., Numerical Modeling of Fabric Panel Response to Ballistic Impact, 25th International SAMPE Tech. Conf., 26-28 Oct, 1993.