Proposal for Multiscale Modeling of Tungsten Heavy Alloy (WHA) for Kinetic Energy Perpetrators

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Introduction

Modern militaries of global superpowers rely on the capability of kinetic energy penetrators (KEP) to defeat armored targets at long range in ground-to-ground combat operations. KEP are dense projectiles that impact at high velocity, utilizing kinetic energy to penetrate thick armor. In a fundamental sense, limits to achievable projectile velocities lead to utilization of projectile material of higher density to maximize penetration from kinetic energy. KEP are also known as “long-rod penetrators,” and new prototype models often undergo many iterations of design and experimental testing in order to optimize projectile geometries such as length, diameter, and nose shape. Figure 1 shows a KEP shortly after being fired from a muzzle.

Figure 1. KEP discarding sabot in early flight. Source: [1].

Complex plasticity and damage/fracture mechanisms can be analyzed using the multiscale model approach outlined by Horstemeyer[2] and then evaluated using metamodeling-based optimization (MBO) processes[3]. The use of design of experiments (DOE) can further reduce the amount of high-fidelity simulations required during the optimization process[2]. The combination of the Integrated Computational Material Engineering (ICME) multiscale modeling techniques with the MBO and DOE methods will allow for faster, lower-cost design and development of new, state of the art KEP that are able to defeat increasingly sophisticated armor systems.

Historically, depleted uranium alloys (DUA) have been used for many of the highest performance KEP; however, environmental and occupational hazards of the material have driven focus toward alternative materials[4]. Tungsten heavy alloys (WHA) have been used as an alternative to DUA KEP, but require higher impact velocity to achieve the same penetration depth for equivalent mass and geometry as DUA KEP[4]. Fabrication of WHA consists of mixing tungsten powders within a small amount of lower-melting metals with solubility for tungsten[5]. Sintering of the low melting additives forms a liquid that rapidly hardens into a fully dense, two-phase structure in a relatively short amount of time[5]. Of the many WHA produced, W-Ni-Fe based alloys have become the industry standard[5]. A 90W-7Ni-3Fe (% weight contents) WHA material was selected for validation of the multiscale modeling and optimization methods.

Material Considerations

An accurate modeling of the WHA KEP will require thorough understanding and quantification of damage progression throughout penetration of the target material. The WHA macrostructure exists of rounded W particles cemented in the Ni-Fe matrix (Figure 2). Rabin et al.[6] discovered that failure modes for 90W-7Ni-3Fe WHA consisted of a fracture surface area of 29% tungsten cleavage, 52% matrix rupture, 16% tungsten-tungsten boundary separation, and 3% tungsten-matrix separation. Focusing on void nucleation, growth, and coalescence within the Ni-Fe matrix and on the cleavage/fracture of W particles will provide the refined multiscale model required for successful optimization of the KEP.

Figure 2. 90W-7Ni-3Fe microstructure indicating the tungsten particles (W), the Ni-Fe matrix (M), the tungsten-tungsten grain boundaries (W-W), and the tungsten-matrix boundaries (W-M). Edited from[5].

Another important material consideration to study is compressibility. Advances in weaponry, such as the electromagnetic rail gun, will provide capabilities to launch KEP at even higher velocities[7]. Song et al.[7] found that at KEP velocities of 2 km/s < V < 10 km/s, KEP strength affects penetration efficiency at lower velocities and KEP material compressibility affects efficiency at higher impact velocity. Both compressible[8] and approximate compressible[9] models need to be considered in regard to advancements.

One area in which WHA KEP are highly inferior to DUA is shear sensitivity. DUA has high shear sensitivity which allows for a “self-sharpening” phenomena to occur during travel through target material[10]. Lower scale analysis may provide insight into ways to increase WHA shear sensitivity and reduce “blunting” of the KEP that is typical at lower impact velocities.

The end goal is to obtain an ISV, or material model, capable of capturing mechanical history and predicting mechanical properties of WHA during impact and penetration of a given target material. The ISV will be able to represent a given volume element of the complex material without needing to capture all local phenomena at lower length scales. The breakdown of the applicable length scales and the required bridging information are illustrated in Figure 3.

Figure 3. Multiscale modeling breakdown indicating bridging information passed between length scales and to the ISV. [1][2][10]

Downscaling Requirements

To start the ICME process outlined by Horstemeyer[2], downscaling is required from the full-structure scale model to lower length scales to determine what pertinent information is necessary to create an accurate ISV. The ISV will require material properties (Bridge 6), plasticity (Bridges 7-8), and damage/fracture information (Bridges 9-11) from lower length scales. The macroscale consists of a polycrystalline material volume with many W particles constrained in the Ni-Fe matrix. The crystal plasticity model of the W particles will be required from the mesoscale in order to study the W cleavage failure mode. Dislocation information from nanoscale and microscale models will be required to accurately model the failure of the Ni-Fe matrix. Damage nucleation, growth, and coalescence parameters from the mesoscale and microscale models will also be required for the Ni-Fe matrix. Material properties such as elastic moduli will be obtained from the electronic scale.

Upscaling Requirements

Upscaling prescribes the methods to facilitate material properties and structure parameters into higher length scale models. An emphasis on quantifying uncertainty bands for studied phenomena will be made throughout the upscaling process. At the lowest scale, density field theory (DFT) will be used to obtain elastic constants of W, Ni, and Fe for the macroscale ISV. Lattice constants, heat of formation and elastic moduli are used for atomistic model calibration, while surface energies, generalized stack fault curves, and vacancy formation energies will be used for validation (Bridge 1)[2].

At the nanoscale, the modified embedded atom method (MEAM) will be used to analyze different temperature and strain rate effects for the BCC W and Fe, and the embedded atom method (EAM) will be used for the FCC Ni. These models will also provide the dislocation mobility and twinning effects on plasticity and fracture upscaling to dislocation dynamics at the next length-scale (Bridge 2)[2].

Dislocation dynamics (DD) based models incorporate the dislocation mobility from the nanoscale MEAM and EAM models as well as elastic properties from the atomic scale. DD simulations will provide the stress-strain relationships along with work hardening rates that will upscale to crystal plasticity models at the mesoscale (Bridge 3). Properties of the W particles and Ni-Fe matrix will be obtained and upscaled separately.

DD parameters are incorporated into crystal plasticity models to study damage nucleation, growth, and coalescence that is both transgranular and intergranular. At the single-grain mesoscale, the W particles and Ni-Fe matrix will be modeled separately to analyze transgranular fracture (Bridge 4). Intergranular crack nucleation, growth, and coalescence along W-W and W-M boundaries will be analyzed together at the polycrystalline mesoscale level (Bridge 5). The particle, particle-void, and void-crack interactions will be upscaled to the macroscale plasticity and damage/fracture models.

References

  1. 1.0 1.1 “APFSDS,” MilitaryImages.Net [Online]. Available: https://www.militaryimages.net/media/apfsds.33143/. [Accessed: 11-Feb-2019].
  2. 2.0 2.1 2.2 2.3 2.4 2.5 Horstemeyer, M. F., 2012, Integrated Computational Materials Engineering (ICME) for Metals, John Wiley & Sons, Inc.
  3. Wang, H., Li, E., Li, G. Y., and Zhong, Z. H., 2008, “Development of Metamodeling Based Optimization System for High Nonlinear Engineering Problems,” Advances in Engineering Software, 39(8), pp. 629–645.
  4. 4.0 4.1 Magness, L., Schuster, B., Weil, C., and Lavender, C., 2014, Demonstration of Tungsten Nanocomposite Alternatives to Depleted Uranium in Anti-Armor Penetrators, T14-311, Army Research Laboratory, Aberdeen, MD.
  5. 5.0 5.1 5.2 5.3 Bose, A., Sadangi, R., and German, R. M., 2012, “A Review on Alloying in Tungsten Heavy Alloys,” Supplemental Proceedings, Tms, ed., John Wiley & Sons, Inc., Hoboken, NJ, USA, pp. 453–465.
  6. Rabin, B. H., 1989, “Characteristics of Liquid Phase Sintered Tungsten Heavy Alloys,” The International Journal of Powder Metallurgy, 25(1), p. 8.
  7. 7.0 7.1 Song, W., Chen, X., and Chen, P., 2018, “The Effects of Compressibility and Strength on Penetration of Long Rod and Jet,” Defense Technology, 14(2), pp. 99–108.
  8. Flis, W. J., 2013, “A Jet Penetration Model Incorporating Effects of Compressibility and Target Strength,” Procedia Engineering, 58, pp. 204–213.
  9. Song, W., Chen, X., and Chen, P., 2018, “A Simplified Approximate Model of Compressible Hypervelocity Penetration,” Acta Mechanica Sinica, 34(5), pp. 910–924.
  10. 10.0 10.1 Li, J., Chen, X., and Huang, F., 2018, “Ballistic Performance of Tungsten Particle / Metallic Glass Matrix Composite Long Rod,” Defense Technology.
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