**1. Introduction**

When perforating or penetrating the intended target, reactive materials (RMs) will chemically react due to the shock wave passing through them, thereby increasing the damaging effects from the combination of the kinetic energy (KE) and chemical energy (CE) of a reactive projectile [1–3]. RMs are a class of shock-induced energetic materials, including thermites, intermetallics, metal-polymer mixtures, metastable intermolecular composites (MICs), and so on. With the benefit of fine mechanical and chemical performance, polytetrafluoroethylene based RMs have been extensively researched recently. In order to investigate their lethality, ground tests have been conducted, and several physicsbased models were established [4–8]. However, RMs are generally formulated to release appreciable CE under intense dynamic loads (such as high-velocity impact or detonation), so the activation time is extremely short, making the measurement of many physical quantities very difficult. Consequently, an appropriate analytical tool for RMs is required to predict target damage beyond that measured under experimental conditions [3]. Popular dynamic calculation codes, such as ANSYS-Autodyn or Ls-dyna, were employed to predict the response of energetic materials. In these codes, the simulation results are dependent on an appropriate material model, which includes the equation of state (EOS), strength model, failure model, erosion model, and so on. Researchers have paid close attention to the material model of RMs.

**Citation:** Xiao, J.; Wang, Y.; Zhou, D.; He, C.; Li, X. Research on the Impact-Induced Deflagration Behavior by Aluminum/Teflon Projectile. *Crystals* **2022**, *12*, 471. https://doi.org/10.3390/ cryst12040471

Academic Editors: James L. Smialek, Yong He, Wenhui Tang, Shuhai Zhang, Yuanfeng Zheng and Chuanting Wang

Received: 9 February 2022 Accepted: 26 March 2022 Published: 28 March 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

For the unreacted reactant of RMs, the shock EOS model was used to research the critical velocity of the reactive materials projectile (RMP) to initiate the covered explosive [9,10], and Instron compression tests and high-rate split Hopkinson bar experiments were carried out to determine the parameters of the Johnson–Cook strength model, which can be used to effectively simulate the deformation and penetration behavior of reactive materials [11,12]. For reaction product, the Jones–Wilkins–Lee (JWL) EOS was used to characterize the expansion behavior after the chemical reaction of RMs [13]. In fact, compared to the KE damage caused by traditional inert metal materials, it is mainly the CE that causes the remarkably high-efficiency damage during the impact events of RMs. The ignition time, reaction rate, reaction efficiency, and so on, play an important part in the energy release of CE. In particular, the initiation criterion, which is characterized by the values of the impact pressure *P* and its duration *τ* or by the values of an impacting projectile's velocity *V* and diameter *d* (*P*2*τ* or *V*2*d* criteria), significantly influences the damage event of RMs. The forest fire model was provided and developed to match pressure–time data obtained from gauges embedded in the energetic materials in a broader set of experiments [14]. Recently, the Naval Surface Warfare Center has estimated the impact velocity and pressure initiation threshold of reactive materials with different particle size with a gas gun experiment [15,16]. They found that the initiation reaction occurs earlier in reactive materials with smaller particle size; this is mainly induced by the shear band formed in the impact event, and empirical formulas (*t<sup>a</sup>*(*<sup>σ</sup>*−*σTS*)*<sup>b</sup>* = *c*)) were proposed to characterize the ignition behavior of Al/PTFE reactive materials.

The above literature reviews show that the EOS and ignition model for RMs have been improved. However, an integrated, analytical method to reproduce the high-efficiency damage caused by RMs has not been presented, to the best of our knowledge. In past decades, relevant simulations often divided the damage event into two relatively independent phases. For example, the damaging effects on concrete targets produced by reactive material liner shaped charges were researched by dividing the physical process into an inert impact-penetration stage and an internal deflagration stage for RMs. The shock model was used to simulate the inert penetration behavior of RMs, and either the JWL or powder burn model was used to simulate the internal deflagration behavior of RMs [17–20]. Although the Lee–Tarver model embedded in Autodyn or Ls-dyna can characterize the detonation performance of high explosives, no interface is provided to adjust the initiation criterion that is crucial to simulate the damage event for RMs.

The purpose of this effort is to combine the divided stages into one by developing the EOS subroutine based on Autodyn code; then, quantitative research of real-time reaction can be conducted by using the tunable ignition criteria. A simulation method is proposed to investigate the impact-induced deflagration behavior of polytetrafluoroethylene based RMP. This work is of grea<sup>t</sup> value in the design of RMPs and understanding their damage mechanisms more clearly.
