**1. Introduction**

The dynamic behavior of materials is a field at the confluence of several scientific disciplines. The processes that occur when materials are subjected to rapid loads can differ significantly from those under static or quasi-static situations. The understanding of the dynamic behavior of materials involves the mechanics of high-strain-rate deformation (elastic, plastic, shock, and detonation waves) and the dynamic responses of materials (constitutive models, shear instabilities, microstructural evolutions, dynamic fractures, and chemical reactions).

This Special Issue on the "Dynamic Behavior of Materials" collected recent research findings on the dynamic behavior of various materials. A collection of fifteen peerreviewed research articles were included in this Special Issue. The main topics covered include processing technology, state-of-the-art characterization, testing, theoretic modeling, and simulation.

#### **2. Microstructural Evolution of Materials under Dynamic Deformation**

Yan et al. [1] investigated the microstructural evolution of a near-αtitanium Ti-6Al-1Mo-2Zr-0.55Fe-0.1B alloy after dynamic deformation. The results indicated that the strength of the alloy increased significantly under dynamic loading. An abundance of deformation twins released the dislocation pile-up and coordinated the plastic deformation of the alloy during dynamic loading. The Johnson–Cook (J–C) constitutive equation of the alloy was obtained. Yang et al. [2] performed uniaxial tensile loading tests on coarse-grained and fine-grained D6A steel, finding that grain refinement effectively improved the strength of fine-grained steel, attributing this to the high density of grain boundaries and cementite particles hindering the movement of dislocations. The parameters of the J–C constitutive model were calibrated. Zhao et al. [3] investigated the microstructure and properties of hotrolled NM500/Q345 clad plates after heat treatment. They found that the microstructure of the NM500/Q345 clad plate before austenitization was mainly pearlite and ferrite, and both were transformed into lath martensite after austenitization. Ding et al. [4] studied the dynamic response of several metallic materials under explosive loading; the microscopic features of the metals were examined and analyzed with the fracture model.

#### **3. Equations of State and Constitutive Equation of Materials**

The complicated composition of unsaturated clay, e.g., solid mineral particles, water, and air, makes it difficult to obtain its precise equation of state (EOS) over a wide pressure range. Ran et al. [5] discussed the high-pressure EOS of unsaturated clay at the mesoscale; a high-pressure EOS of the unsaturated clay up to 30 GPa was developed, and it was in good agreemen<sup>t</sup> with the experimental data. Xiao et al. [6] considered the phase change during the impact as initiating a chemical reaction process, introducing three different EOSs to describe the material parameters from a solid reactant state to a solid–gas mixing

**Citation:** Wang, C.; Zheng, Y.; Zhang, S.; Tang, W.; He, Y. Editorial for the Special Issue "Dynamic Behavior of Materials". *Crystals* **2023**, *13*, 44. https://doi.org/10.3390/ cryst13010044

Received: 20 December 2022 Accepted: 22 December 2022 Published: 27 December 2022

**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/).

state and a gas state. The Johnson–Cook constitutive equation was modified by the adiabatic temperature rise term, and a nonlinear fit was performed to construct a dynamic constitutive relationship at room temperature, which could describe the rheological behavior of the Ti-6Al-1Mo-2Zr-0.55Fe-0.1B alloy under high-strain-rate conditions at room temperature [1]. Similar constitutive equation work was performed on D6A steel, and a corresponding equation was obtained [2].

#### **4. Material and Structure under High-Velocity Impact**

Du et al. [7] designed tungsten-fiber-reinforced Zr-based bulk metallic glass rods with gradient structures and conducted penetration experiments of the rods against rolled armor steel. The penetration failure mode of the rods, including bending, the backflow of tungsten fibers, and shear failure, was observed. It was suggested that the bending space and ultimate bending diameter of tungsten fibers should be considered in order to achieve a higher penetration ability of the fiber-reinforced rods. Jiang et al. [8] designed projectile-resistant composite armor consisting of curved ceramic, a steel frame, and a metal back plate. The anti-penetration performance of the armor against 12.7 mm armor-piercing incendiary (API) projectiles was tested. The penetration process was divided into four main stages: the asymmetric erosion of the projectile, ceramic cone squeezing movement, back plate failure, and projectile exit.

Besides the various physical changes, dynamic loading may also trigger a series of chemical reactions of the materials. Xiao et al. [6] proposed a simulation method for the impact-induced deflagration behavior of reactive materials by introducing tunable ignition threshold conditions. The ignition, reaction ratio, pressure, and temperature distribution of an Al/Teflon projectile impacting multilayer targets were analyzed. The increasing trend in the reaction ratio was consistent with the change in radiated flash in the experiments. Li et al. [9] designed a reactive projectile with an Al/PTFE composite as the inner core and a steel shell as the outer case. They studied the penetration and chemical reaction behavior of such a projectile impacting a multilayer target. The influential factors, including impact velocity, target thickness, and projectile structure, on the damage effect were discussed.

#### **5. Explosive–Material Interaction**

Dynamic loading on materials could be generated by an explosion; the interaction between explosion products and materials is very quick, and the strain rate could be extremely high. Lu et al. [10] investigated the formation process of reactive-material-shaped charges under an explosion. A two-dimensional finite element model of a shaped charge and a reactive material liner was established; the jet formation process, particle dispersion, and jet particle distribution were analyzed. The results showed that the PTFE matrix accelerated faster than the Al particles under shock loading. The relative displacement results in a density gradient along the axis of the jet, and PTFE becomes the main component of the jet. The initial granule distribution in the liner had a grea<sup>t</sup> influence on the particle distribution in the formed jet. Similarly, Guo et al. [11] studied the jet formation process of reactive Al/PTFE liners via X-ray photography. It was observed that the reactive Al/PTFE composite reacted during jet formation, which can be divided into a local reaction stage and an overall reaction stage. Secondary collision occurred in the inner layer of the liner during the jet formation, where the chemical reaction initiated. Moreover, the Al particle size led to a large difference in the jet formation process, showing that the jet formed from liners with larger Al particles was more condensed due to a slower chemical reaction. For tungsten-based materials, the flow behavior of the material under a high strain rate had a significant influence on the final jet formation [4]. Achieving a reasonable coupling effect between the explosive and liner material is a challenge, aiming to achieve a jet/EFP without obvious cracking fracture.

#### **6. Theoretic Modeling and Simulation**

Due to the difficulty of experimentally observing dynamic processes, especially those under high strain rates, theoretic modeling and simulation have become very important in explaining and visually displaying dynamic processes that are difficult to observe. In order to study the dynamic response associated with the impact of a kinetic projectile on the internal structure of an artificial satellite, a simulation model of the projectile damaging the multilayer plates was established in ABAQUS by Yue et al. [12]. The influences of initial velocities and incident angles on the damage characteristics were discussed. According to the dynamic characteristics of the adhesion–desorption process between gecko-like polyurethane setae and the contact surface, the microcontact principle of an elastic sphere and plane was established. On this basis, combined with the cantilever beam model, microscale adhesive contact models in the cases of a single and an array of setae were obtained. The contact process was numerically simulated and verified by the adhesion– desorption test. The results showed that the simulation model could reflect the real contact procedure of setae [13]. Shi et al. analyzed [14] the deployment process of an unmanned aerial vehicle's parachute recovery. A dynamics model of the parachute deployment phase was established. The effect of the parachute weight and launch temperature on the dynamic characteristics of the deployment was discussed. Zhu et al. [15] established a threedimensional numerical model to describe the melt flow field and inclusions movement in the cold hearth for the Ti-0.3Mo-0.8Ni alloy during electron beam cold hearth melting. The solidification and discrete phase models in ANSYS were used to quantitatively analyze the movement of inclusions in the cold hearth. Autodyn was employed to simulate the penetration and reaction processes of reactive projectiles impacting targets, where a modified EOS was embedded via secondary development [6,9]. An adaptive coupling algorithm based on the finite element method and smooth particle hydrodynamics in LS-DYNA was adopted to study the anti-penetration performance of the composite armor structure against the API projectile [8]. LS-DYNA and Autodyn were employed to simulate the jet/EFP formation process of various materials under explosions [4,14,15].

This Special Issue includes a small number of discrete case studies on the "Dynamic Behavior of Materials". We hope that this Special Issue will be interesting for the academic community, and also hope that it will shed light on future research activities in this field.

**Funding:** This research received no external funding.

**Acknowledgments:** The contributions of all authors are gratefully acknowledged.

**Conflicts of Interest:** The authors declare no conflict of interest.
