This article reviews the anti-penetration principles and strengthening mechanisms of metal materials, ranging from macroscopic failure modes to microscopic structural characteristics, and further summarizes the micro-macro correlation in the anti-penetration process. Finally, it outlines the constitutive models and numerical simulation studies utilized in the field of impact and penetration. From the macro perspective, nine frequent penetration failure modes of metal materials are summarized, with a focus on the analysis of the cratering, compression shear, penetration, and plugging stages of the penetration process. The reasons for the formation of adiabatic shear bands (ASBs) in metal materials with different crystal structures are elaborated, and the formation mechanism of the equiaxed grains in the ASB is explored. Both the strength and the toughness of metal materials are related to the materials’ crystal structures and microstructures. The toughness is mainly influenced by the deformation mechanism, while the strength is explained by the strengthening mechanism. Therefore, the mechanical properties of metal materials depend on their microstructures, which are subject to the manufacturing process and material composition. Regarding numerical simulation, the advantages and disadvantages of different constitutive models and simulation methods are summarized based on the application characteristics of metal materials in high-speed penetration practice. In summary, this article provides a systematic overview of the macroscopic and microscopic characteristics of metal materials, along with their mechanisms and correlation during the anti-penetration and impact-resistance processes, thereby making an important contribution to the scientific understanding of anti-penetration performance and its optimization in metal materials.
Due to the rapid development of industrialization, the military’s key research focus on impact and penetration has attracted increasing attention from civil industries such as the nuclear, auto, and aerospace industries, making anti-penetration materials and their function mechanisms a research priority in these industries as well [1], [2], [3], [4]. Metal materials are the first engineering materials to be applied in the area of anti-penetration due to their high strength, high ductility, and excellent energy absorption properties. Examples include the AlCoCrFeNi2.1 eutectic high-entropy alloy (HEA) [5], the CoCrFeMnNi HEA [6], and the 316L stainless steel to Inconel 625 functionally graded material [7] with high strength and high ductility. Since the 1960s, numerous researchers have been dedicated to the study of the anti-penetration mechanism of metal targets, conducting in-depth and comprehensive analyses of the deformation process and mechanical mechanism of metal targets under projectile penetration [4], [8], [9], [10], [11], [12], [13].
The common goal of these researchers has been to improve the anti-penetration performance of metal materials. In published studies, a qualitative consensus has been reached regarding the correlation between the anti-penetration performance of metallic materials and relevant parameters such as the mechanical properties (strength, toughness, hardness, etc.) of the target material and its structure. In other words, enhancing the strength, toughness, and other mechanical properties of the target material—or the combination and arrangement structure of the target materials—can result in better anti-penetration performance of metal materials [14], [15], [16], [17], [18]. The anti-penetration performance, also known as the ballistic performance, typically improves with the strength of the metal target, due to the resistance of the strength toward the plastic flow. However, beyond the critical point, an increase in strength normally accompanies a decrease in toughness, resulting in a reduction in ballistic performance. Therefore, studies on enhancing the penetration resistance of metal materials focus on two areas. The first area involves endowing metal materials with high strength, high hardness, and significant anti-penetration performance by regulating their microstructures through heat treatment [19]. For example, during the heat treatment of titanium (Ti) alloys, as the solid solution temperature increases or the cooling speed accelerates after the solid solution procedure, the alloy undergoes a phase transition, resulting in an increase in strength and a decrease in plasticity [20]. The second area involves enlarging the plastic deformation of metal materials under impact and penetration by improving their toughness, thereby converting penetration kinetic energy into plastic work. For example, a recrystallization sample of Cr26Mn20Fe20Co20Ni14, an HEA with low stacking fault energy (SFE), exhibited excellent ductility in the temperature range of 4.2-293.0 K; moreover, when the temperature decreased from 293 to 77 K, the ductility increased by 30%-95% [21]. The excellent properties of this alloy at low temperature are attributable to its low SFE (9.9 mJ∙m−2), which promotes the formation of numerous crystal twins and induces more phase transitions, thereby achieving efficient defect (i.e., dislocation, twin boundary, and phase interface) storage. Furthermore, both strength and ductility can be simultaneously increased. The tensile ductility of the HfNbTiVAl10 alloy, which is prepared via the negative mixing enthalpy effect, is significantly enhanced at room temperature [22]. AlCoCrFeNi2.1, which has a dual-phase structure, has high strength and high ductility due to the stress distribution effect of its soft disordered face-centered cubic (FCC) and hard ordered B2 body-centered cubic (BCC) phases structures [5]. Similar strategies have been reported in (W1.5Ni2.25Fe)95Ta5 [16]. In addition, the optimal combined configuration for specific metal materials to resist impact and penetration can be explored by altering the material thickness, the connection mode between layers, and the arrangement order [23], [24], [25], [26], [27].
Under high-speed impact and high-strain-rate loading conditions, the internal temperature of the material rises sharply, leading to thermal softening in local areas. When this thermal softening exceeds the strain and strain rate hardening, most metallic materials will form adiabatic shear bands (ASBs) locally. Subsequently, these bands can trigger the nucleation and propagation of cracks, ultimately leading to material failure, which manifests as a macroscopic failure mode [27]. The width of an ASB increases with an increase in the impact velocity [28], [29]. The evolution order of the ASB and cracks in a metal material are as follows: First, dense dislocation appears in the local areas of shear and recrystallization occurs, giving rise to the formation of an ASB; afterward, crack nucleation, growth, and propagation occur due to the deformation of the ASB; finally, the merging and propagation of cracks lead to the failure of the metal material.
The deformation process and penetration mechanism of metal materials under a projectile impact have been widely analyzed in order to understand the essence of improving the anti-penetration of metal materials and thereby guide the improvement of the impact resistance of metal materials. The results indicate that the ballistic performance of a material is closely related to its mechanical properties (strength, toughness, etc.), and a material’s mechanical properties are determined by its microstructure characteristics [30]. However, no systematic review of the correlation mechanism between different macroscopic failure modes and materials’ microstructure has been published thus far.
Therefore, this article discusses the impact and penetration resistance behavior of metal materials; systematically elaborates on the anti-penetration performance of metal materials, ranging from macroscopic failure modes, penetration mechanisms, and ballistic limits to microscopic morphology characteristics and formation mechanisms; and summarizes the dominant correlation mechanism between the micro and macro levels in the anti-penetration process. In addition, it systematically reviews the theoretical calculations of constitutive models and numerical simulations relevant to the field of impact and penetration. Finally, existing problems and future development directions of anti-penetration research on metals are summarized.
2. Macroscopic failure description
2.1. Macroscopic failure mode
Metal materials have always had important applications for resisting high-strain-rate loading such as explosion impact and high-speed penetration in armored structures and crucial constructions. Under impact loading, metal materials predominantly absorb energy through plastic deformation and crack formation and propagation, thereby achieving an anti-penetration function. A material’s failure is the result of multiple mechanisms.
Different metals and alloy materials exhibit nine main failure modes: radial fractures perpendicular to the impact direction, fractures under the effect of initial stress waves, spallation, plugging, bulging, ductile reaming, back and frontal petal-shaped fractures of the targets, and brittle fragmentation (Fig. 1) [9], [27], [31], [32], [33], [34], [35], [36], [37].
The failure modes of metal target plates subjected to a high-speed impact are related to the toughness and thickness of the plates. A target plate with a thickness less than the projectile diameter is a thin target plate; otherwise, it is classified as thick. For a more intuitive display, the abovementioned failure modes are categorized according to the material properties and penetration state, as shown in Table 1.
Usually, brittle and thick metal target plates are prone to initial stress wave fractures (Fig. 1(b)), radial fractures (Fig. 1(a)), and fragmentation (Fig. 1(i)) [38], [39]; tough and thick targets are susceptible to ductile reaming (Fig. 1(f)), bulging (Fig. 1(e)), and spallation (Fig. 1(c)); brittle and thin targets are prone to plugging (Fig. 1(d)); and tough and thin targets are susceptible to petal fractures (Figs. 1(g) and (h)). It is generally acknowledged that fragmentation and petal fractures—particularly back petal fractures—absorb more energy. However, tests reveal more than one penetration failure mode. Usually, multiple failure modes interact with each other, and brittle and ductile failure modes often take place simultaneously. Table 2 [13], [14], [23], [24], [25], [26], [27], [30], [31], [33], [34], [35], [36], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66], [67], [68] summarizes the failure modes in penetration tests on common metal targets.
2.2. Penetration mechanism
A typical complete blunt-projectile ductile reaming penetration is a three-stage process, including the cratering, compression shear, and penetration-and-plug stages [69], [70]. Each stage has different deformation modes and energy absorption mechanisms. Fig. 2 shows a schematic and numerical simulation diagram of the deformation and stress characteristics of each stage.
(1) Cratering stage: As shown in Fig. 2(a), when the projectile hits the target plate at a high speed, the high-contact velocity between the projectile and the target generates a collision stress of up to tens of gigapascals, far exceeding the dynamic strength of the target. As a result, the target suffers local deformation, and crushing damage occurs in the impact area. The projectile deforms under the effect of a strong reverse pressure. Subsequently, the projectile nose thickens due to the squeeze, enlarging the contact area between the projectile and the target plate. Next, the strong friction between the projectile and target and the target deformation consume the high-speed penetration kinetic energy of the projectile and convert it into internal energy. Owing to the high penetration speed and short duration, the heat from the collision cannot quickly dissipate, so the impact area of the target is heated locally. Under the effect of pressure, the molten metal splashes out in the direction with the least resistance, inducing luminescence and heating, indicated by the splashed sparks shown in Fig. 2(a).
(2) Compression shear stage: As shown in Fig. 2(b), when the projectile penetrates further into the target, the velocity of the projectile and the target changes drastically, producing a strong inertial force. Under the effect of the inertial force and the pressure, the velocity of the projectile steadily decreases. Simultaneously, the velocity of the compressed part of the target gradually increases. Due to the smaller velocity of the target’s adjacent parts, a velocity gradient is produced, inducing a shear force. However, the shear force only contributes to the plastic deformation of the target. When the accelerated part of the target extends to the back of the target, a bulge appears, indicating the end of this stage.
(3) Penetration-and-plug stage: As shown in Fig. 2(c), as the projectile proceeds to penetrate the part of the target that accelerated in the previous stage (see the plane diagram), a strong shear force is generated inside the target, as shown in the numerical simulation, where significant stress is generated at the shear point. This process is intricate, as the shear limit point and the location where plugging shearing occurs are dependent on multiple factors, such as the properties of the penetrated metallic target materials, the shape of the projectile, and the projectile’s velocity [38], [71], [72]. Different metallic target materials exhibit varying strengths, hardness, and ductility, which can affect the magnitude of the shear force and the location of plugging. An increase in target thickness may lead to an increase in shear force and a change in plug location, while an increase in impact speed could result in a greater impact force, increasing the shear force and the likelihood of plugging. The shape and size of the projectile can also affect the shear force and the location of plugging. For example, the performance of pointed and blunt projectiles may differ. In practical terms, these factors may interact with one another, making the shear forces and plugging locations more complex. At this time, most of the plastic work is instantly converted into heat and cannot dissipate into the surrounding area in time. Moreover, the strain rate hardening effect, the strain strengthening effect, and the thermal softening effect caused by adiabatic heating simultaneously exist in certain areas of the penetrated part, making these the weakest areas. When the shear strain reaches the critical strain, the thermal softening effect begins to dominate, and the metal target suffers from structural failure, resulting in adiabatic shear and ultimately leading to shear plugging failure.
When the damage extends to the entire target, the residual projectile, accelerated target parts, and partial metal fragments are ejected from the cavity at the remaining velocity, and the penetration is completed, as shown in Fig. 2(d).
2.3. Ballistic limits
Studies on projectile penetration into metal targets have been rapidly increasing in number; the relevant studies on penetration in recent years are summarized in Table 2. Most of these studies focus on the exploration of anti-penetration performance, trying to identify composite modes with excellent anti-penetration performance by changing the combined structural configuration of the metal targets (i.e., layer number, thickness, shape) [56], [68], [73]. However, compared with the composite modes of metal targets, the mechanical properties of the metal materials being used are the key factors that directly determine the targets’ anti-penetration performance. Therefore, the relationship between the mechanical properties and penetration resistance of metal materials has always been of great concern [14], [34], [35], [47], [58], [59], [62], [65], [67], [74]. Research suggests that dynamic strength and quasi-static strength have a decisive influence on the anti-penetration performance of alloy materials, whereas the impact absorbing energy, dynamic plasticity, and quasi-static plasticity have a non-decisive impact [58]. Temperature also has a significant impact on the anti-penetration performance of metal targets. For example, the ballistic limit velocity of the GH4169 alloy target is approximately linearly related to its temperature [55].
Analysis of the anti-penetration performance of metallic materials is relatively more complicated. At present, there is no absolute single index that reflects the anti-penetration performance of metal materials. There are three primary reasons for this lack.
(1) The thickness variation of metallic target plates dictates different evaluation methods for their anti-penetration performance. Changes in the thickness of the plate trigger various unique destruction patterns during the penetration process. For example, when dealing with medium-thick or semi-infinite plates, penetration depth is typically used as an assessment metric for anti-penetration performance. The smaller the penetration depth, the better the anti-penetration performance of the material. However, for thin metal plates that can be completely penetrated by the projectile, penetration depth no longer serves as an appropriate quantifier. In this scenario, residual velocity is often employed to evaluate the anti-penetration capability, where a slower residual velocity signifies stronger resistance to penetration.
(2) The structural type of the metallic target plate dictates different assessment schemes for evaluating its anti-penetration performance. For example, in some specially structured metallic target plates such as honeycomb, layered, or stair-like structures, the projectile deviates during penetration rather than proceeding in a straight line, rendering penetration depth an ineffective quantifier of the plate’s anti-penetration capability. In these cases, factors such as the damage area created by penetration, the morphology of the crater, or the energy absorption rate are used to assess anti-penetration ability. Here, the smaller the penetration damage area, the stronger the resistance to penetration of the material.
(3) Depending on the actual application requirements, different metrics are used to evaluate the anti-penetration performance of the material. In scenarios where the metallic target plate is not fully penetrated, even though the plate can absorb all of the kinetic energy of the projectile to prevent penetration, it may generate intense shockwaves or fragments behind the target, potentially causing damage to any protected objects behind the plate. Hence, in such cases, factors such as the pressure of the shockwave, the quantity of fragments, and the velocity of the fragments become key indicators of anti-penetration performance. The smaller the pressure of the shockwave, the fewer the number of fragments, and the slower the speed of the fragments, the better the anti-penetration performance of the material.
Overall, since there is no comprehensive metric available as yet that can fully reflect the anti-penetration performance of metallic materials, performance should be evaluated based on the specific circumstances of the study.
The studies listed in Table 2 can be divided into two categories according to the thickness of the metal target plate under investigation: studies on thin plate perforation and studies on thick plate or semi-infinite plate penetration. For thick or semi-infinite thick plates, penetration depth, crater morphology, and energy absorption rate are the main focuses. The morphological parameters of the craters, such as depth and diameter, play a crucial role in the validation of numerical simulations. For thin plates, the ballistic limit velocity and failure mode of metal plates are the research priority. The ballistic limit velocity is an essential indicator for quantitatively characterizing the elastic resistance of the tested material; it is defined as the incident velocity of a bullet penetrating the tested sample with a 50% probability. The ballistic limit speed is typically regarded as the reference value for the safety assessment of protective materials or is utilized to determine the “reference” ballistic resistance of materials in ballistics; it is defined as the average value between the maximum impact velocity without perforation and the minimum impact velocity with complete perforation of the target [75].
A frequently used calculation method for ballistic limit velocity is a model proposed by Recht and Ipson [76] based on energy and momentum conservation:
where vi and vr are the initial impact velocity and residual velocity, respectively; vbl is the ballistic limit velocity; and a and p are the model constants. A series of initial impact and residual velocities are obtained through ballistic impact tests. Afterward, the obtained data points are fitted to obtain the values of a and p, making it possible to calculate the ballistic limit velocity.
Another widely used calculation is based on the energy method, which assumes that the kinetic energy of the penetrating projectile is fully converted into the energy required to damage the target. Taylor [77] built a suitable model for the ductile reaming failure mode, Thomson [78] built a model for disc-shaped damage, and Sun and Liu [79] analyzed the energy consumption of the mixed damage modes of ductile reaming and disc-shaped damage produced in the target and proposed the formula shown in Eq. (2):
We/mpwhere We is the energy required to damage the metal target; mp is the projectile mass; Rh is the bullet hole radius of the projectile penetrating the target plate; σ0 is the maximum stress of the crushing target plate; ht is the thickness of the target plate; and Rp is the radius of the projectile.
The ballistic limit velocity of the metal target can be calculated with different methods, where the method to be used depends on the experimental design and measured data. However, regardless of the method, the results still need to be further verified by comparison with experiments or other means.
3. Microscopic failure description
3.1. Microscopic failure mechanism
As early as 1944, Zener and Hollomon [80] observed a clear white ASB, also known as a white etching band, in a test on the high-speed perforation of steel, indicating a phase transition within the ASB [81]. White ASBs have been observed in steel [82], [83], [84], Ti and its alloys [85], [86], [87], tantalum (Ta) and its alloys [88], [89], aluminum (Al) alloys [90], and magnesium (Mg) alloys [91], and have been studied extensively. Me-Bar and Shechtman [92] were the first to observe the microstructure inside the ASB of a Ti-6Al-4V alloy using transmission electron microscopy (TEM). Later, a multitude of researchers began extensive research on the evolution of the complex microstructure inside the ASB [93], [94], [95], [96], [97], [98]. By using TEM to characterize the microstructure within the ASB, exceedingly fine grain structures can be observed [92], [99], [100], [101], [102], [103]; these are known as recrystallized grains and typically reach the nano-size. Under a high-speed impact, the size of the equiaxed grains ranges from 10 to 500 nm in the ASB of metal materials. A key contributing factor to the generation of the recrystallized grains is that the heat generated during the plastic deformation and high-speed shear reaches the β conversion point [104]. Owing to the short duration, the heat cannot fully dissipate and therefore causes recrystallization. The grain rotation mechanism [103] also plays a crucial role in the recrystallization process, promoting the generation of new equiaxed grains [102].
The typical microscopic morphology of an ASB at different scales is shown in Fig. 3 [89], [96], [97], [105], [106]. Fig. 3(a) shows the millimeter-scale morphology of the ASB; Figs. 3(b) and (c) show the micron-scale morphology; Figs. 3(d)-(g) show the nanoscale morphology; and Figs. 3(h)-(j) show a high-magnification electron diffraction view of the ASB. Under a high-speed impact, clear white bright bands appear on the macroscopic surface of a Ti-5553 alloy, accompanied by cracks [97], as shown in Fig. 3(a). Figs. 3(b) and (c) show ASBs in the microstructure of a Ti-5553 alloy and a Ti-3Al-5Mo-4.5V alloy. There is a visible and clear boundary between the ASB and the normal organizational structure. In the partially enlarged view of the structure within the ASB, as shown in Figs. 3(d) and (e), exceedingly small nanograins can be observed, indicating recrystallization in the ASB. Figs. 3(f) and (g) show that the recrystallized grains may be equiaxed grains, and similar phenomena are observed in a cobalt-nickel alloy [96]. Figs. 3(h)-(j) respectively correspond to the high-magnification electron diffraction patterns outside, at the edge of, and inside the ASB of a ZK60 magnesium alloy [105]. It can be seen through comparison that the microstructure outside the ASB has not changed significantly, and its diffraction pattern is an orderly arranged single-crystal structure; in contrast, a circular polycrystal structure can be seen in the ASB, indicating the formation of recrystallized grains with significant orientation differences within the band. The edge of the ASB exhibits a transition between the above two phenomena.
In addition to the nano-crystalline structure, more complex structures can be observed around and within the ASB. For example, Fig. 3(d) shows a twin structure inside the ASB of M54 steel. A deformed twin structure and hexagonal close packed (HCP) regions were observed in the FCC structure of a CrMnFeCoNi HEA under quasi-static compression [107], [108].
Different materials can produce unique structures, which largely depend on the adiabatic temperature produced by penetration and the microstructural composition of the material. The generation of adiabatic temperature is derived from thermomechanical coupling, in which the deformation of metallic materials under high strain rates converts mechanical energy into internal energy, which is then dissipated. Within an extremely short time frame and on a minuscule spatial scale, this process can be considered adiabatic [109], leading to an increase in the internal temperature of the material. Although heat release can occur uniformly throughout the solid, in special cases of severe local strain, it can cause local temperature rise [110]. The temperature rise in an ASB is an important parameter index of the evolution of the microstructure and phase transition mechanisms [111]. The following equation has been widely used to estimate the temperature rise during high strain rate deformation [112].
where ΔT is the adiabatic temperature rise; Tad is the adiabatic temperature; T0 is the initial temperature; ρ is the density; Cv is the specific heat capacity; β is the ratio of heat dissipation to mechanical work during deformation; WP is the plastic work; εy and εf are the yield and final strain, respectively; and σ is the shear stress.
Regarding the microstructural composition of materials, Ti1023-5 is taken as an example [113]. In the adiabatic shear area near the ASB, two different orientations of twinning structures were found to be distinct through high-resolution transmission electron microscopy (HRTEM) analysis. Fig. 4 shows a TEM image of the Ti1023-5 ASB center [113]. Fig. 4(a) presents a low-power TEM bright field image of the entire sample in the central region, in which the grains in the ASB center are significantly refined. In the selected region of Fig. 4(a), the needle-like structure with white contrast parallel distribution inside the black contrast grain is a twin sheet, as shown in Fig. 4(b). Electron diffraction analysis of the white circular region in Fig. 4(b), as shown in Fig. 4(c), confirms the structure of the twin. The pink rectangular region in Fig. 4(b) is subjected to HRTEM, and the results are shown in Fig. 4(d). The rectangular region 1 in Fig. 4(d) is determined by fast Fourier transform (FFT), as shown in Fig. 4(e). The rectangular region 2 in Fig. 4(d) is shown by FFT (Fig. 4(f)) and contains both a matrix and twins. This phenomenon is confirmed in Fig. 4(h). Fig. 4(g) shows the FFT results of the rectangular region 3 in Fig. 4(d), where α-martensite spots and α-matrix spots are observed.
The appearance of twins in or near the ASB center is mainly due to the high sensitivity of mechanical twins to the strain rate. Some specific areas generate a local stress concentration, thereby triggering the formation of twins. This formation of twins is beneficial to effectively adapting plastic deformation under dynamic conditions [114]. During dynamic loading, the formation of nanotwins might further divide the ASB nanograins into smaller fragments and create more boundaries to increase the obstacle to dislocation movement. This effect, which enhances strain hardening and offsets thermal softening, enables the material to achieve a relatively stable state under dynamic loads. Similar phenomena have also been observed in published studies [115].
To further enhance the penetration resistance of metallic materials, it is essential to minimize the formation of ASBs. The generation of complex structures in or near ASB areas may cause stress concentration and aggravate the damage of the ASB. Therefore, the performance of these materials can be optimized in two dimensions: The thermal conductivity of the material can be increased, ensuring the uniformity and high thermal diffusivity of the material in order to reduce its adiabatic temperature; and innovative techniques can be applied to enhance the work hardening rates of metallic materials or alloys can be fabricated with an excellent strength-toughness combination, to limit the occurrence of ASBs [5], [16], [22].
In addition to the typical structures above, metals with different crystal structures differ in terms of their microstructure characteristics and the evolution of micro ASB structures [116]. These differences directly affect the mechanical response of the materials.
3.1.1. ASB characteristics of conventional FCC crystal structure metals
Extensive research focusing on aluminum and aluminum alloys, copper and copper alloys, and nickel-based alloys with FCC crystal structures [30], [52], [117], [118], [119] has concluded that the recrystallized grains in FCC metals form via dislocation recombination, and their evolution mode is primarily determined by the SFE. As the SFE diminishes, the dislocation cross slip trend decreases, and the dislocation stacking trend increases [120], [121]. During the plastic deformation process of metals with a higher SFE [122], dislocation slip is the primary deformation mechanism; therefore, the microstructure of the slip layer can be observed in their ASBs, as shown in Figs. 5(a)-(c) [93], [122]. As shown in Figs. 5(d)-(f) [122], [123], [124], numerous nanoparticles formed by recrystallization are distributed in the slip bands [123], and their sizes are uneven [123], [125]. Figs. 5(e) and (f) [122], [124] provide high-magnification electron diffraction views of the equiaxed grains, showing that the grain orientation is randomly distributed but primarily forms high-angle grain boundaries (GBs) [124]. High-density dislocations in some grains [123] indicate that severe shear deformation occurred during the process.
3.1.2. ASB characteristics in conventional BCC crystal structure metals
Owing to the high strain rate sensitivity of BCC metals, their yield stress is strain rate dependent [116]. Therefore, the mechanism of producing ASBs in BCC metals is distinctly different from that in metals with an FCC crystal structure. BCC crystal structure metals principally exhibit damage softening, with thermal softening only playing a secondary role, whereas FCC crystal structure metals principally exhibit thermal softening [126]. The formation of an ASB in a BCC metal is often accompanied by a phase transition. For example, when a hat test was performed on a β Ti-5Al-5Mo-5V-1Cr-1Fe alloy under high strain rates, both the α-martensitic phase and α-phase grain were observable in the ASB, indicating the occurrence of a phase transition from β-Ti to the α-orthogonal phase [127]. Similarly, stress was generated by inducing a phase transition from BCC to HCP when a β Ti-5Al-5V-5Mo-3Cr-0.5Fe alloy was dynamically loaded [128].
3.1.3. ASB characteristics in conventional HCP crystal structure metals
Compared with FCC and BCC metals and their alloys, titanium, magnesium, and their alloys with an HCP crystal structure are more prone to ASBs in the plastic deformation under high strain rates, due to their lower slip system and poor plastic deformation capacity at room temperature [105], [129]. Meyers et al. [73] used a split Hopkinson pressure bar to test an α-Ti hat sample for its dynamic compressive properties. The results demonstrated that, when the strain reached 0.83, adiabatic shear localization occurred, with a shear band width varying within 3-20 μm. The shear bandwidth increased with an increase in the plastic strain.
Near an ASB formed by typical HCP crystals, conspicuously elongated grains can be observed along the shear direction [89], [97], [130], and the stress-strain curve exhibits plastic flow [131]. In the boundary between the interior and periphery of the ASB, known as the ASB transition zone, subgrain transformation or deformation twinning is observable [86], [132]; in the center of the ASB, subgrain fragmentation or a rotation dynamic recrystallization mechanism induced by twinning occurs, forming a nanoscale equiaxed grain structure with relatively low dislocation density [89], [97]. Moreover, the changes in the ASB are not usually accompanied by phase transitions [129]. Fig. 6 shows the microstructure of an ASB in a fine-grained Ti-3Al-5Mo-4.5V alloy with an HCP crystal structure [89]. Fig. 6(a) shows an ASB width of approximately 13 μm. Figs. 6(b)-(d) provide enlarged views of the periphery, transition zone, and interior of the ASB, respectively, exhibiting clear structural changes from the edge to the center of the ASB. Due to significant shear deformation, a fiber structure appears in the transition zone (Fig. 6(c)) and interior (Fig. 6(d)) of the ASB; in particular, the structure in the ASB is elongated and refined along the shear direction. Fig. 6(f) shows an elongated unit structure formed in the ASB with a width of approximately 0.2-0.5 μm that splits into several subgrains with different orientations in the perpendicular shear direction, with low internal dislocation density and typical recrystallization characteristics.
3.1.4. ASB characteristics in HEA metals
HEAs are remarkably different from traditional alloys. Due to their superior mechanical properties, especially their excellent strain hardening capability and significant resistance to shear localization [52], [133], HEAs have great application potential in the field of ballistic protection. The distribution of elements in an HEA is often non-uniform, which may lead to different structural phases. For example, BCC and FCC structures may coexist in some HEAs, while an HCP structure might be observed in others [134], [135]. The composition of an HEA is usually complex, requiring thermodynamic calculations and phase diagram analysis to determine the optimal structure of elements [136], [137], [138]; for example, the Gibbs free energy is calculated to determine the stability of structures, where the lower the Gibbs free energy, the more stable the structure. By plotting a graph of alloy composition versus temperature, the possible phases formed at different temperatures can be identified. Due to the complex elemental composition and variable structures of HEAs, there are significant differences in both the formation mechanisms and the micro-morphologies.
Multiple strengthening mechanisms including solution strengthening (Figs. 7(a) and (b)) [48], [139], dislocation strengthening (Figs. 7(c) and (d)) [140], [141], twin strengthening (Figs. 7(e) and (f)) [142], [143], and phase transition strengthening (Figs. 7(g) and (h)) [134] contribute to the excellent work hardening rate of HEAs [144], [145], [146]. Current research on the dynamic behavior of HEAs under high-speed impact and high strain rates includes HEAs with FCC structures [144], [147], [148], BCC structures [107], [146], and FCC/BCC dual phase structures [5]. However, it should be noted that, although some research exists on non-FCC HEAs, the application of BCC HEAs is limited due to their low work hardening rate and easy ASB formation [149].
3.2. Dynamic recrystallization
Ultrafine nanograins generated by dynamic recrystallization are typically observable in ASBs. The discovery of the dynamic recrystallization process dates back to the 1980s [86]. According to Derby’s classification, the process is divided into two types: migration dynamic recrystallization and rotation dynamic recrystallization [150]. To explore the recrystallization mechanism occurring in ASBs, Hu and Rath [151], [152] derived a model formula for the GB migration rate through theoretical calculations, as follows:
where v is the migration rate of the GB, MGB is the constant referring to the migration rate of the GB, RGB is the GB radius, γGB is the GB energy, and m is the GB migration index. According to calculations, the migration speed is estimated to be 22 nm∙s−1 at 900 K and higher at 1000 and 1100 K, reaching 141 and 652 nm∙s−1, respectively.
According to calculations by Meyers et al. [103] and Hines and Vecchio [153], the cooling time after adiabatic shear action is approximately 10-3 s. Therefore, Eq. (6) can be used to calculate the distance that the crystal boundary migration has moved during this period. The results showed that the distance was much smaller than the size of the nanograins in the ASB (20-200 nm). The researchers then indicated that the migration recrystallization mechanism alone is insufficient to produce nanograins in the ASB.
Li et al. [154] reported a model for grain nucleation growth based on the change and diffusion mechanisms of the GB energy, calculating the grain growth rate during the shear localization in the narrowband as follows:
where D is the diameter of the recrystallized grains, t is the time, DB0 is the GB diffusion coefficient, k1 is a constants, kB is the Boltzmann constant, $\dot{\gamma}$ is the instantaneous strain rate, DBv is the GB vacancy diffusion coefficient, η is the boundary energy density, τi is the applied shear stress, E is the elastic modulus, Ω is the atomic volume, δ is the grain interface thickness, Ta is the absolute temperature, αμb is the energy per unit length of dislocation (where α is a constant between 0.5 and 1.0) [155], and ρm is the moving dislocation density.
Eq. (7) shows that the diameter D of the recrystallized grains increases linearly with time t and shifts to exponential growth in a few microseconds. However, owing to the short duration of this stage, the size of the grains is limited, suggesting that, practically speaking, grain growth does not occur during dynamic loading; that is, the dynamic phenomenon accompanying the impact penetration is not attributed to grain growth.
Fig. 8 shows the rotation dynamic recrystallization model. In 1994, Andrade et al. [100] proposed an evolution model for the formation of nano equiaxed grains and extended their study using dislocation dynamics [103]. The process model is shown in Figs. 8(a)-(e) [156]. Through the rearrangement of the dislocations of the elongated elliptical subgrains (Fig. 8(b)) formed by randomly disordered high-density dislocations (Fig. 8(a)), the subgrains gradually gained various orientations (Fig. 8(c)). Afterward, the elongated subgrains (Fig. 8(d)) broke down through the rotation of every stage and eventually formed equiaxed grains (Fig. 8(e)).
Fig. 8(a) shows the random distribution of the dislocations; the corresponding TEM is shown in Fig. 8(f) [141], exhibiting the randomness and intensiveness of the dislocations. The randomly distributed dislocation strain energy is calculated as follows:
$E_{1}=\rho_{\mathrm{dis}}\left(\frac{A G \boldsymbol{b}^{2}}{4 \pi}\right) \ln \left(\frac{a_{\mathrm{w}}}{2 \boldsymbol{b} \rho_{\mathrm{dis}}^{1 / 2}}\right)$
where ρdis is the dislocation density, A is the constant decided by the dislocation property, G is the shear modulus, b is the Burgers vector, and aw is the parameter related to the dislocation core energy.
The dislocation will evolve into a subcrystalline structure as it rearranges, as shown in Fig. 8(b), and its energy will change. The total energy is
$E_{2}=\rho_{\mathrm{dis}}\left(\frac{A G \boldsymbol{b}^{2}}{4 \pi}\right) \ln \left[\frac{\mathrm{e} a_{\mathrm{w}}}{2 \pi \boldsymbol{b}}\left(\frac{S}{V}\right) \frac{1}{\rho_{\mathrm{dis}}}\right]$
where S is the subgrain surface area, and V is the subgrain volume, expressed as follows:
where W is the short axis of the elliptical subgrain, and r is its aspect ratio.
Presuming that Eqs. (8), (9) are equal, that is, E1=E2, the critical dislocation density ρdis* can be obtained, as can the relationship between ρdis* and the critical short axis length W and critical orientation angle θ*:
where k is a constant related to material properties.
Eqs. (13), (14) show that the higher the dislocation density, the smaller the W. When r → ∞, f(r)/r = π/2, and the energy difference between Figs. 8(a) and (b) reaches its maximum.
Through Eq. (13), it can be inferred that the size of the quasi-elliptical cell unit is primarily influenced by the dislocation density. The relationship between the dislocation density and the short axis length, 2W, of the cell unit can be seen in Fig. 9 [103]. This conclusion is consistent with the results observed through TEM experiments [103]. In those observations, the typical cell unit size was found to vary between 100 and 300 nm, and the moment of dislocation cell formation occurred approximately when the strain reached 1.8. At that moment, the temperature rise was about 400 K and the corresponding dislocation density was 1010 cm−2, which is consistent with the results in Fig. 9.
Figs. 8(b) and (c) illustrate the formation of subgrains, as shown in the micrograph in Fig. 8(g); during the plastic deformation, the dislocation density increases with the increase in the deformation amount, as does the GB mismatch (Fig. 8(h)). As the mismatch continuously increases, the long elliptical grains can no longer adapt to a large deformation; therefore, their dislocation undergoes forced dynamic rotation, as shown in Fig. 8(d). They then decompose into small grains (Fig. 8(e)), whose microstructure is shown in Fig. 8(i). Meyers et al. [157] named this theory the GB rotation. To prove the correctness of this mechanism, it is necessary to confirm that the GB rotation can be completed within the short period of the shear localization and at the temperature the shear localization undergoes.
The time required for the GB rotation to form equiaxed grains is typically obtained as follows [158]:
where L1 is half the initial grain length, δGB is the thickness of GB, θGB is the GB rotation angle, and DGB is the GB diffusion coefficient. The calculation results show that it takes a short time of 0.5 ms for the 200 nm grains in stainless steel to rotate from rectangular to an equiaxed shape [89]. Thus, both experiments and theories demonstrate that, during shear localization, GB rotation can lead to the formation of an equiaxed nanocrystalline structure. The coexistence of the elongated and rectangular subgrains observed in the ASB of stainless steel is crucial proof of the rotation dynamic recrystallization mechanism forming equiaxed grains.
4. Connection between the microscale and macroscale
The core indicators for measuring the anti-penetration performance of metals are the ballistic limit velocity, penetration depth, and the metals’ macroscopic failure modes, which are closely related to the mechanical properties of the metals (i.e., strength and toughness). Due to the comprehensive effect of the mechanical properties, there are varying degrees of failure modes. A metal’s mechanical properties are determined by its microstructures, such as the micro lattice structure, grain size, and dislocation density. Owing to microstructure deformation, an ASB forms at the micro-level during high-speed penetration.
The typical failure process of a metal under a high-speed impact is shown in Fig. 10(a). The failure begins with the appearance of macroscopic cracks, and an ASB is induced by the generation and propagation path of the cracks. The formation of the ASB is due to the greater thermal softening effect of the metal over its hardening and strengthening effect. As a result of the significant dynamic recrystallization near the ASB, which is caused by the temperature increase during plastic deformation, ultrafine grains form near or within the ASB, as shown in Figs. 10(b) and (c). In the ballistic impact process, the dislocation density within the dynamic recrystallization grains significantly increases, promoting the formation and aggregation of interspaces and eventually leading to crack nucleation and growth [159]. An ASB in an equiaxed microstructure typically exhibits regular interval propagation, as shown in a Ti-6Al-4V alloy in Figs. 10(d)-(f) [60], while an ASB in a layered microstructure typically displays reticulation propagation, as shown in the HEA material Al-Co-Cr-Fe-Ni in Figs. 10(g)-(i) [13].
During the penetration resistance process in a metal material, complex plastic deformation occurs between the macroscopic failure mode and the microscopic ASB, which is closely related to the dynamic strength of the material. Therefore, to explain the connection between the macroscopic and microscopic failure modes, a clear understanding of the deformation and strengthening mechanisms is necessary.
4.1. Deformation mechanism
4.1.1. Dislocation slip and twins
Dislocation motion (Figs. 11(a) and (b)) [160] and twins (Fig. 11(c)) [161] are the most common deformation modes in metals. FCC and BCC alloys have more slip systems that can be triggered during plastic deformation; therefore, their deformation mechanism is usually dominated by the dislocation motion. In comparison, alloys with an HCP structure usually undergo plastic deformation in a twinning manner, due to the limited number of slip surfaces that can be triggered. Consequently, the microstructures of most metals permit dislocations as well as frequent nucleation and proliferation of deformation twins, leading to a superior combination of ductility and strength [162], [163], [164]. Figs. 11(a) and (b) clearly exhibit the dislocation slip process of γ-TiAl. Over time, the dislocation line shifts significantly.
Deformation twins are generated and propagated to accommodate large plastic strains; they contribute to the maintenance of good ductility [114]. This is mainly because deformation twinning can change the crystal structure, grain orientation, and increase dislocations, thereby affecting the mechanical properties of the material [30], [165], [166]. When a material is subjected to external forces, stress and strain are produced within the grains. If these stresses and strains exceed the bearing capacity of the grains, grain fracture and material failure can ensue. However, if deformation twins form within the grains, they can change the grain orientation and crystal structure [167], [168], [169], reducing the stress concentration and GB cracking, making the internal stress distribution within the grains more uniform, decreasing areas of stress concentration, and thereby reducing the brittleness of the material. Furthermore, the formation of deformation twins can increase the dislocation density within the grains because the growth of twins creates additional boundaries, enhancing the material’s ability to store dislocations [170] and making it easier for dislocations within the grains to move, and thereby promoting plastic deformation in the material.
Alloys of metals with high SFE are conducive to the formation of deformed microbands, whereas metals with low SFE are prone to dislocation decomposition. The latter is conducive to the generation of deformed microbands and a reduction in the driving force for microband formation [171], which improves the material’s work hardening rate and plasticity [117]. Therefore, there is competition between microbands and twins in low-SFE materials under high strain rates.
The geometric structures of shock waves can also determine the microscopic deformation mechanism [172]. When an impact crater is caused by spherical shock waves, metals with high SFE are prone to forming microbands, whereas metals with low SFE typically form a mixture of twinning and microbands or only microbands [173].
4.1.2. Phase transition
Phase transitions result in fundamental changes in a metal material’s structure, which may substantially affect the metal’s mechanical properties. During the plastic deformation of a metal material, the phase transition induced by deformation can hinder the motion of dislocations, thereby improving the work hardening rate and ductility of the material [134].
In general, phase transitions occur in metals with low SFE [134], [174]. For example, in a Fe80−xMnxCo10Cr10 alloy composed of FCC and HCP two-phase structures (Figs. 12(a)-(c)) [134], the early stages of deformation mainly occurred in the FCC phase matrix, and the transition from FCC to HCP occurred simultaneously. In the later stages of deformation, additional mechanical twinning, dislocation slip, and HCP phase stacking faults became the main deformation mechanisms [134].
At the atomic level, when a metallic material is subjected to a high impact pressure, the distances between the internal atoms may change, and the lattice structure may become distorted or deformed. This situation is shown in the classic example of a phase transition in gold nanowires from FCC to body-centered tetragonal (BCT) structure in Figs. 12(d)-(j) [175], which has been demonstrated by the embedded atom method [176], [177] and density functional theory calculations [178]. In this example, the model extends along the axial direction of the two crystals on the {001} plane. During this process, crystals with the FCC structure can spontaneously transform into either a BCC or BCT structure by relaxation along another direction, thus undergoing a phase transition.
The Bain model can be used to explain the cause of this phase transition [152]. In the model, this process is completed either through the relaxation of interlayer spacings or dislocation migration on adjacent planes [179]. Wang et al. [180] observed this phase transition in nickel nanowires under bending conditions. As the bending strain increased, the angle between the two planes changed from 70.5° to 90.0°, and the structure changed from FCC to BCT, as shown in Figs. 12(k)-(o) [180].
4.2. Strengthening mechanism
4.2.1. Deformation strengthening
The phenomenon of increased strength in metals after plastic deformation is called deformation strengthening. After plastic deformation, the internal dislocation density of the metal grains increases; after further plastic deformation, the dislocation motion is hindered, due to the large amount of dislocation entanglement caused by the dislocation slip.
As shown in Fig. 13(a), dislocation tangles (DTs) and dislocation cells (DCs) are introduced in the plastic deformation of an Fe40Mn20Cr20Ni20 HEA [30]. With an increase in the strain rate, the dislocation density increases, the DT phenomenon becomes more pronounced, the DC size decreases, and the average DC diameter is inversely proportional to the general dislocation density [181]. During a high-speed impact, dislocation slip produces deformed microbands, as shown in Fig. 13(b). Moon et al. [182] noted that microband crossing minimized the effective free path of dislocation motion (referred to as the microband-induced plasticity (MBIP) effect), which typically led to continuous strain hardening and a good balance between strength and ductility [161], [183]. Microbands generally appear in the impact penetration of high-SFE metal materials, such as Al and Ni [173]. At the impact crater of an Fe40Mn20Cr20Ni20 HEA after a high-speed impact, a dislocation plane array—that is, a high-density dislocation wall—was found, as shown in Fig. 13(c) [30]. Nanoscale twins can provide a strong strengthening effect [184], [185], potentially breaking the balance between metal strength and ductility [186].
4.2.2. GB strengthening
GB strengthening, also known as fine grain strengthening, is a method of increasing the number of GBs and enhancing a metal material’s resistance to plastic deformation in order to improve the strength of the material by refining the grains. In metal materials composed of polycrystals, GBs can powerfully hinder the dislocation motion, leading to the GB strengthening effect. In general, the relationship between the GB strengthening effect and grain size follows the classical Hall-Petch criterion [187], where the strengthening effect increases with a decrease in grain size. In metal materials with large grain sizes, perfect dislocation motion dominates plastic deformation. When the grain size decreases to a critical value, imperfect dislocations begin to control the plastic deformation. As the grain size continues to decrease, the process transforms into GB-induced plastic deformation, which can be further divided into GB slip (Figs. 14(a) and (b)) [188], grain rotation (Figs. 14(c) and (d)) [189], and GB migration (Figs. 14(e)-(g)) [190], in terms of the motion mechanism.
The plastic deformation of a metal material with excellent ductility often induces a GB slip mechanism. Figs. 14(a) and (b) show the process of a GB slip in fine-grain Al, where the slip can be clearly observed. By means of identification and visual simulation of the uneven displacement atom region in the sample, Schiøtz et al. [191], [192] and Yip [193] simulated the low-temperature plastic deformation process of nano copper, demonstrating the presence of GB slip and grain rotation during the process.
In the grain rotation mechanism, high-angle GBs are first converted into low-angle GBs, which then disappear, leaving behind higher-density dislocations [194]. This process plays a crucial role in metal deformation and has been observed in many metal materials [189], [195]. As shown in Figs. 14(c) and (d), during dynamic torsional loading in a Ni-Fe alloy, a 6° rotation movement occurs at the junction of the alloy interface. It is noteworthy that the grain rotation process is often accompanied by grain growth [195].
Figs. 14(e)-(g) show GB migration in a gold alloy, where a disconnection preexists on the GB of the alloy. Next, shear stress at a 5° angle to the GB plane is applied to grain G2, as shown by the yellow arrow. The directions of GB migration and motion disconnection are indicated by red and blue arrows, respectively. During the loading process, continuous GB migration is observed; after 4.3 s, the total distance of GB migration is 5d113, where d113 represents the lattice spacing of the (113) planes. Many models have been developed to explain the GB migration process. Among them, Mott [196] presented a model in which a group of atoms on one side of the grain jumped to the other side, while Gleiter [197] presented a kink model for GB migration. The shear coupling model presented by Cahn et al. [198] is considered the key deformation model for GB migration at low temperatures, as demonstrated by many molecular dynamics and quasi-continuous studies on bicrystal and nano copper metals [199]. Caillard et al. [200] presented a new model suggesting that GB migration only involves very short GB atomic rearrangements. While all these models can explain GB migration, the specific application conditions and new models require further exploration.
4.2.3. Solution strengthening
Solid solution strengthening (Figs. 15(a) and (b)) [201] is a method of improving the strength of alloy materials by introducing other elements (metal or non-metal) into the matrix material to form a solid solution, which causes lattice distortion in the matrix and effectively hinders dislocation slip. In a multi-element system, all atoms of different sizes interact with each other to cause elastic deformation of the lattices, leading to the formation of local elastic stress fields; this hinders the dislocation motion and thus increases the strength [140]. For example, the high hardness and strength of the HfZrTiTa0.53 HEA are mainly attributed to severe lattice distortion caused by solid solution strengthening [140]. Adding gallium (Ga) to Mg alloys can achieve better solid solution strengthening effects [201]. The Ga atoms in a Mg-Ga alloy treated with a solid solution exist in two ways, as shown in Fig. 15(c) [201]. Eight Mg atoms surrounding a Ga atom form a dodecahedron composed of upper and lower hexahedrons, or two Ga solute atoms occupy the vertices of the upper and lower hexahedrons and combine with seven Mg elements in the middle to form a dodecahedron cluster. As shown in the strengthening model action diagram in Fig. 15(d) [201], Ga with its small atomic radius causes lattice distortion upon dissolution in an α-Mg matrix, and interaction occurs between dislocations and the atomic configuration or lattice distortion, increasing the resistance and improving the strength.
The solid solution formed by the replacement of the lattice positions is called a substitution solid solution. The alloy phase that is formed by adding a small amount of other metals to a pure metal that still retains its solvent type upon the solute atoms melting into the solvent lattices is called a solid solution. The most common types of solid solutions, such as manganese (Mn) steel, aluminum alloys, and titanium alloys, are strengthened by replacing the original solvent atoms with solute atoms. For example, in manganese steel, iron (Fe) atoms are the solvent, and Mn atoms are the solute. Because of the different radii and electronegativities of the iron and manganese atoms, physical and chemical changes (e.g., significant lattice distortion) occur locally in the crystal. Such changes in local positions hinder the dislocation slip, thereby strengthening the metal.
The solute atoms can also dissolve into the interstices of the solvent atoms, in what is called an interstitial solid solution. For example, when carbon (C) or nitrogen (N) atoms dissolve in Fe, they occupy the octahedral or tetrahedral interstices in the Fe crystal cells. The atoms in the interstices generate powerful stress fields in the original crystal structure, which interact with the stress fields of the dislocations, pinning or dragging them and thus exerting a strengthening effect. Moreover, research suggests that small non-metal elements such as C, B, N, and O can effectively enhance the lattice distortion of alloys, leading to a stronger solid solution strengthening effect [202], [203], [204].
4.2.4. Second-phase strengthening
Second-phase strengthening improves the mechanical properties of metal materials by introducing second-phase particles into the materials to hinder dislocation motion. Although the addition of second-phase particles can improve the material strength, it may reduce the plasticity because the interface of the second-phase particles and the matrix is prone to local stress concentration, which causes microcracking and material failure. Second-phase strengthening can be categorized into dispersion strengthening and precipitation strengthening.
Precipitation strengthening is a strengthening process driven by the segregation of the solute atoms of the metals in a supersaturated solid solution and/or the dispersion of dissolved particles in the matrix [205], [206]. The second-phase particles precipitated from the parent phase are dispersed in the matrix, hindering the dislocation motion and thus strengthening the metal. Therefore, the two phases usually have an orientation relationship and a coherency relationship—that is, the interface bonding is good and has a high strengthening effect. Precipitation strengthening can be achieved by two mechanisms: the shear mechanism and the Orowan bypass mechanism. The mechanism to be triggered depends on various factors, including the size of the precipitate phase, its coherency relationship with the matrix, the antiphase boundary energy, and the strength (or hardness) of the precipitate. Typically, if the precipitate is small in size and coherent with the matrix, the shear mechanism is activated; if it is large and not coherent with the matrix [206], [207], the Orowan mechanism takes precedence.
Fig. 16 [207] shows the precipitation strengthening of an Al0.2Co1.5CrFeNi1.5Ti0.3 HEA. A large amount of uniformly distributed precipitates with different sizes can be observed in Fig. 16(a), which is the L12 ordered phase, as shown by their diffraction spots. Fig. 16(b) is a high-resolution view of the matrix and the L12 phase, with the crystal zone axis in the [111] direction. The Orowan dislocation ring can be observed in Fig. 16(c), where the dislocations bend around the spherical precipitates. Due to the existence of intragranular nanoprecipitates, the dislocations within the grains of the Al0.2Co1.5CrFeNi1.5Ti0.3 HEA are pinned, which enhances the material’s strain hardening and ductility [207].
4.2.5. Contribution of strengthening mechanisms
The strengthening of metallic materials essentially results from the interaction of various types of strengthening and deformation mechanisms. Thus, there is a relationship between the macroscopic manifestation of strength and the microscopic forces. For example, the relationship between the flow stress shown in the tensile test and the microscopic force can be expressed by a specific formula [16], [208]:
where σflow is the flow stress, σf is the micro friction, σb is the back stress estimated by a loading-unloading-reloading tensile test, and σd is the dislocation strengthening force.
$\sigma_{\mathrm{d}}=M \alpha_{\mathrm{d}} G \boldsymbol{b} \sqrt{\rho_{\mathrm{dis}}}$
where M is the Taylor factor, αd is the empirical constant, G is the shear modulus, b is the Burgers vector, and ρdis is the dislocation density, which is calculated by X-ray diffraction (XRD) detection [209], [210].
where βw is the full width at half maximum, θ is the Prague angle, and λ is the wavelength of the XRD source.
4.3. Influence of microscopic characteristics of materials on failure modes
Under a high-speed impact, the vast majority of metal materials are subject to plastic deformation. When the deformation reaches a critical point, an ASB occurs; then, cracks begin to expand within the ASB, resulting in failure, which manifests as various failure modes at the macro level. Table 3 [13], [14], [30], [44], [45], [46], [48], [52], [60], [117], [118], [119], [134], [140], [161], [183], [206], [212], [213], [214], [215], [216], [217], [218] provides a summary of the processing technology, structure, deformation mechanism, and strengthening mechanism of metal materials.
As shown in Table 3, the high strength of a grain structure with the microscopic characteristics of a single-phase structure and uniform distribution is dominated by the dislocation slip and deformation strengthening of high-density dislocation, which is the most common strengthening mechanism [41], [44], [52], [146], [161]. Metal materials to which precipitates have been added are prone to precipitation strengthening. The strengthening mechanism in precipitation-strengthened HEAs is mainly controlled by the shear mechanism [206], [216]. The high strength of HEA materials such as AlCoCrFeNi2.1, FeCoNiCr, and HfNbTaTiZr is mainly attributed to second-phase (B2 or σ phase) strengthening [215], [217], [218]. Dispersion strengthening mainly explains the strengthening mechanism of the Ni1.5Co1.5CrFeTi0.5 HEA and fine-grained oxide impurities [213]. The uniqueness of the precipitation strengthening in the Fe25Co25Ni25Al10Ti15 HEA is due to the spatial distribution of the fractional precipitate [219].
Diverse strengthening mechanisms of microstructures play a major role in the strength of metal materials. However, the formation of ASBs occurs through the deformation mechanisms of the material, which has a certain impact on the macroscopic failure modes. The failure of metal materials with layered microstructures generally occurs along the interlayer gaps, resulting in a brittle failure mode [60]. Moreover, when the deformation mechanism of a metal material is dislocation slip or its strengthening mechanism is the GB strengthening mechanism, the ductile failure mode is likely to be the only mode occurring under a high-speed impact [48]. In metal materials with nanoprecipitates, large slip dislocations tend to occur during plastic deformation, and the macroscopic failure is inclined to be brittle failure, albeit often in conjunction with ductile failure [14].
It can be seen from the above phenomena that the strength and toughness of a metal material are related to the material’s crystal structures and microstructures. Moreover, the material’s toughness is influenced by the deformation mechanism, and its strength is explained by the strengthening mechanism. The mechanisms work together to affect the evolution and formation of ASBs. The mechanical properties of a metal material depend on the material’s microstructures, which in turn depend on the processing and material composition.
To sum up, certain processing techniques can endow metal materials with specific microstructures. The microscopic characteristics of a metal material dominate its deformation and strengthening mechanisms. The strengthening mechanism determines the strength of the material, while the deformation mechanism is a key factor in the formation of ASBs. The two mechanisms jointly affect the failure modes of a metal material under high-speed penetration.
5. Simulation theory and actual simulations
5.1. Constitutive equations
Under high-speed impact, the pressure, density, and temperature of a metal material are subject to extreme changes. Therefore, defining a constitutive equation requires a comprehensive understanding of the processes and mechanisms of elastoplastic deformation, material fracture, flow stress, shock wave propagation, and heat conduction [220]. The early constitutive formulas were simple, only describing the relationship between elasticity, plasticity, and stress; thus, they could not correctly describe the effect of the work hardening dynamic parameters. Over the years, various plastic models have been presented and used to describe mechanical effects (e.g., the yield, work hardening, strain rate hardening, thermal softening) under dynamic loadings. Various constitutive models for metal materials have been developed in the field of numerical calculation of impact dynamics, such as the Zerilli-Armstrong (Z-A) [221], Arrhenius-type [222], and Preston-Tonks-Wallace (PTW) [223] models. Due to their cumbersome derivation process and complex expression forms, the Z-A, Arrhenius-type, and PTW models are not widely used in practical engineering applications.
Cowper and Symonds [224] presented the simplest and most widely used constitutive model to explain strain rate hardening:
where σy is the stress, $\dot{\varepsilon}$ is the strain rate, σy,0 is the yield stress, and P and Dh are hardening parameters obtained by fitting experimental data. This formula is widely used, but its applicability to complex models is limited.
The Johnson-Cook (J-C) constitutive model [225] is the most widely used method in engineering. This model comprehensively considers the effects of strain, strain rate, and temperature, and its description of the deformation laws of most metal materials is consistent with reality. Moreover, the model requires few measured parameters that can be obtained relatively easily. The model includes the effects of strain hardening, strain rate hardening, and thermal softening on material stress. It is a viscoelastic material model with high accuracy in describing material strength and ductility, even under high-speed impact loading.
The J–C constitutive model is the product of three functions: the strain hardening term f1(ε), strain rate hardening term $f_{2}(\dot{\varepsilon})$, and thermal softening term f3(T); that is,$ \bar{\sigma}=f_{1}(\varepsilon) f_{2}(\dot{\varepsilon}) f_{3}(T)$. Its specific form is as follows [225]:
where Ay is the initial yield stress, By is the strain strengthening parameter, nt is the strain strengthening coefficient, Cy is the strain rate strengthening parameter, $\bar{\varepsilon}^{\mathrm{P}}$ is the equivalent plastic strain, and $\dot{\varepsilon}^{*}=\dot{\bar{\varepsilon}}^{\mathrm{P}} / \dot{\varepsilon}_{0}$ is the strain rate of dimension 1, where $\dot{\bar{\varepsilon}}^{\mathrm{P}}$ is the equivalent plastic strain rate, and $\dot{\varepsilon}_{0}$ is the reference strain rate. T* = (T − Tr)/(Tm − Tr), where T* is the normalized temperature and T is the temperature; Tr and Tm are the room temperature and the melting temperature of the material, respectively. mt is the thermal softening index of the material.
The J-C failure model includes the effects of stress triaxiality, strain rate, and temperature on the mechanical properties of materials. Its specific form is as follows [226]:
where εfs is the equivalent plastic fracture strain.$ \sigma^{*}=p_{\mathrm{h}} / \sigma_{\mathrm{eq}}=-\eta_{\mathrm{s}}$, where ph is the hydrostatic pressure, σeq is the equivalent stress, ηs is the stress triaxiality, and D1–D5 are undetermined parameters.
This model uses cumulative damage to describe the failure process of the material, and the failure variable is
where Df is the damage parameter, which varies between 0 and 1, with an initial value of 0. When Df = 1, the material fails. Δεeq is the equivalent plastic strain increment within a time step, and εfs is the equivalent plastic fracture strain calculated at the current time step.
Because of the differences in the microstructures of different materials and the internal microstructure state, which determine the plastic deformation, targeted improvements need to be made to the J-C model for different materials. In order to use suitable J-C constitutive models for numerical simulation, researchers have built different J-C constitutive models for different materials. Most of the improvements involve making a corresponding modification to a certain term or recalibrating the parameters in the model.
Another crucial constitutive model of the metal impact process was presented by Steinberg et al. [227] and is expressed as follows:
where Yh is the yield strength of the material, ph is the pressure of the material, εpl is the equivalent plastic strain, ρh is the material density, Gh is the shear modulus of the material. Yh0 is the yield strength in the reference state, Tf is the temperature in the reference state, εpl0 is the equivalent plastic strain in the reference state, ρh0 is the material density in the reference state, and Gh0 is the material shear modulus in the reference state; Yh0[1 + βh(εpl0 + εpl)]nh ≤ Ymax, where βh and nh are the working hardening parameters; When T > Tm, Yh and Gh are zero. This model is usually limited to very high strain rates ($\dot{\varepsilon}_{0}$≥ 105 s−1); therefore, the above constitutive relationship does not include strain rate correlation terms, where the yield strength caused by the strain rate effect is saturated, and the relevant parameters are determined within the range of extreme strain rates [227].
Studies have suggested that the above two constitutive equations have different scopes of application. Eq. (21) is a typical constitutive equation for modeling metal materials under high-speed impacts, whereas Eq. (24) is the first choice for ultra-high speed impacts. Different experimental techniques can be used to determine the parameters of the above material models, depending on the strain rate [228]: Universal testing machines can be used to perform quasi-static tensile compression tests (10−4-101 s−1); dynamic tensile compression tests can be performed using split-Hopkinson pressure bars (102-104 s−1) [229]; and higher strain rates can be achieved through improved Taylor impact tests (105-106 s−1), reverse plane plate impact tests (106-109 s−1) [230], and light gas gun tests.
5.2. Numerical simulations
The penetration time of the high-speed impact is short, making it difficult to perform detailed experimental studies on the penetration angle and structural change process. The main reasons for these difficulties are as follows:
(1) The time-scale issue: The high-speed impact penetration process usually occurs at the millisecond or microsecond level, so the duration is extremely short. It is difficult for experimental equipment to capture detailed information—such as changes in the penetration angle and the evolution of the structure—in such a short time.
(2) High-speed dynamic effects: The high-speed impact penetration process involves a high velocity and high strain rates, making the dynamic response of the material incredibly complex. Under a high-speed impact, the mechanical properties, deformation behavior, and structural changes of a material may vary significantly from those under static or low-speed conditions, which makes it even more challenging to experimentally investigate the penetration angle and structural changes during a high-speed impact penetration process.
(3) Limitations of experimental equipment: To conduct detailed research on the high-speed impact penetration process, it is necessary to use experimental equipment with high accuracy, speed, and resolution. These devices are usually very expensive and complex, and various technical challenges caused by high-speed impacts, such as measurement errors, data collection, and processing, need to be overcome in the experiments.
(4) Interaction of multiple factors: The high-speed impact penetration process involves the interaction of multiple factors, such as the impact speed, penetration angle, and mechanical properties of the target material. The complex interactions between these factors make it even more difficult to study the penetration angle and process of structural changes through experiments.
Therefore, to better study the penetration angle and structural changes during the high-speed impact penetration process, it is usually necessary to combine various methods such as theoretical analysis, numerical simulation, and experimental research. Numerical simulations can simulate the high-speed impact process, providing more detailed information and insight, which helps in the design and interpretation of experimental research. With developments in computers, numerical simulations using the finite-difference method or finite-element method can play an important role in penetration research. Since the 1970s, various relevant computer software programs have emerged, and research on the penetration process has further developed using software. The Autodyn calculation program (finite-difference method) developed by Birnbaum et al. of Century Dynamics [231] and the Dyna calculation program (finite-element method) developed under the leadership of Hallquist of Lawrence Livermore National Laboratory are mature [232].
The large-scale practical finite-element computational procedure that has been developed thus far can be summarized as two essential methods—namely, control equation methods based on either the Lagrange or the Euler reference systems. The Lagrange method (Fig. 17(a)) [25] is characterized by simple control equations and an efficient solution. However, in the simulation of a high-speed impact process, problems such as mesh element distortion caused by large deformation are prone to occur, resulting in solution termination. The Euler method (Fig. 17(b)) [233] can overcome this problem and has advantages for calculations concerning high-speed impact explosions, and so forth. However, it also has drawbacks such as an inability to track strain and unclear material interfaces. The essential equations in finite-element analysis software using elastic (viscos) plastic constitutive relationships are written relative to the Lagrange reference system; examples include Marc, Ansys, Forge, and Forge3. The essential equations in finite-element analysis software using rigid (viscos) plastic constitutive relationships are written relative to the Euler reference system, with examples including ALPID, DEFORM, and MAEAP. Over the years, the finite-element method has played a crucial role in the numerical simulation of the penetration process.
Even though the finite-element method has become mature and is widely used, it still has some problems, as follows:
(1) The finite-element method has been developed based on continuum mechanics, and it cannot effectively converge when used for discontinuous problems. For example, when it comes to displacement in the deformation of materials, the finite-element method can only represent the displacement caused by plastic deformation; the displacement after material fracture or damage cannot be effectively simulated and predicted. Furthermore, finite-element stimulation requires continuous deformation between the elements to be maintained and, during the loading process, neither disconnection nor overlap is allowed. Therefore, there may be problems in studying doping, micro defects, and damage accumulation in the internal structure of materials.
(2) A calculation program written using the theory of continuum mechanics assumes that the material is homogeneous in terms of its properties; however, this assumption may differ significantly from the fact, resulting in inaccurate simulation results, particularly in cases of mass loss and target plate collapse and damage during penetration under high-speed impact.
In summary, a non-continuum calculation method is needed that not only describes the state changes of the interface during the loading process but also reflects the impact of the discontinuity of the interface displacement on the structural load-bearing capacity. In this regard, discrete-element methods built on the basic method of non-continuum mechanics have their advantages. One such method is the smooth particle hydrodynamics (SPH) discrete-element method (Fig. 17(c)) [8], which was first proposed by Lucy in the 1970s [234]. Petschek and Libersky [235] applied the SPH method to solid mechanics based on the conservation equation. Since 1993, the LS-DYNA software has been rapidly developed after incorporating the SPH method. This method is now widely used to simulate large deformation and dynamic fracture in solids. However, its calculation accuracy depends on the arrangement of the lattice. Moreover, its application accuracy in thermal coupling problems has not been widely verified by experiments and, once particles exceed the control domain, they cannot be controlled, which is inconsistent with the facts. Table 4 summarizes the advantages and disadvantages of several commonly used numerical simulation calculation methods.
Atomic models based on molecular dynamics are expected to reveal the microscopic mechanisms of the high-speed penetration process. The scaled atomic model [236], [237] is conducive to the study of high-speed penetration, as it can assist in understanding high-speed impact problems at the atomic scale and fundamentally explaining various phenomena [238], [239].
Many problems related to the deformation mechanism have been explored through molecular dynamics simulations. For example, Jiang et al. [15] used experiments and large-scale molecular dynamics simulations to successfully reproduce the entire plastic process of an Al0.1CrCoFeNi HEA under various extreme conditions when subjected to uniaxial tension; they deeply analyzed the reasons for changes in the phase transition to a BCC structure and even amorphous changes, so as to gain a deeper understanding of the phase change mechanism. Researchers have further explored the factors affecting the deformation mechanism and strengthening mechanism through molecular dynamics. For example, Zhao et al. [240] conducted a tension molecular dynamics simulation of a CrCoNi alloy and confirmed that localized chemical fluctuations can significantly affect dislocation activity [241] and vacancy dynamics in HEAs [242], thereby affecting their impact resistance. With the further development of simulation technology and the advancement of experimental means, researchers have found that the short-range order (SRO) is an important characteristic of HEAs. Using Monte Carlo methods, molecular dynamics simulations, and density functional theory calculations, Chen et al. [107] studied a CoCuFeNiPd HEA and found that this kind of HEA is energetically favorable for forming SRO, and that the SRO will generate a pseudo-composite microstructure; surprisingly, this greatly improves the HEA’s ultimate strength and ductility.
However, due to the limitations of geometric size and time scale, as well as the cumbersome process required to obtain potential functions of complex materials, there are still many shortcomings in the numerical simulation of atomic models that have not yet been extensively explored in large-scale models.
6. Outlook and future perspectives
In recent years, significant progress has been made in research on the penetration resistance of metal materials. However, further exploration is still needed in the following aspects.
First, although a great deal of work has been done on the relationships between macroscopic failure modes and micro-mechanisms, there is still a lack of quantitative descriptions and explicit expressions of these relationships, such as the relationship between the strength, stiffness, plasticity, ballistic limit, and penetration depth; the relationship between the lattice arrangement in the microstructure and the mechanical properties of strength and stiffness; and the specific quantitative relationships between the material microstructure, strengthening mechanism, macroscopic failure modes, and so forth.
In the study of microscopic mechanisms, atomic and small-scale in situ dynamic photography techniques could be used to more intuitively and clearly demonstrate the microscopic mechanisms under impact. At present, the rare research in this area only focuses on low strain rates, making it impossible to systematically and comprehensively reveal the microscopic mechanisms in metal materials; in situ research under a high-speed impact is even rarer.
Finally, molecular dynamics simulations are still limited by the influence of computation time and model scale. At present, relevant research can only be performed on models below the nanoscale and at the microsecond level. Whether such research can accurately describe macroscopic models and their relationship with the microscopic models has not been revealed yet, and further exploration is needed.
In summary, whether it is research on the mechanism of the impact penetration resistance of metallic materials or simulation research, the ultimate goal is to design materials with superior anti-penetration performance. In future design research on metal anti-penetration materials, the following aspects can be explored in depth.
(1) Materials design and manufacturing: Future research may pay increased attention to the design and manufacturing of novel metallic materials by manipulating factors such as the microstructure, crystal structure, and chemical composition in order to enhance the materials’ anti-penetration performance. This includes developing alloy materials with high strength, high toughness, and superior fatigue resistance, as well as searching for new types of metal-based composite materials.
(2) Numerical simulation and modeling: With the continuous progress in computing technology, numerical simulation and modeling will play an increasingly important role in research on metal anti-penetration performance. By creating more accurate mathematical and physical models, the dynamic responses and failure behaviors of metallic materials under high-speed impact conditions can be better understood, which will provide powerful guidance for material design and optimization.
(3) Multiscale research methods: Future research on the anti-penetration performance of metals may introduce multiscale research methods, cleverly integrating research at the atomic, microscopic, and macroscopic levels. This approach can delve into the relationship between the microstructure of metallic materials and the materials’ performance, providing more comprehensive information for the optimization and modification of metal materials.
(4) Machine learning and data-driven research: The rapid development of artificial intelligence and machine learning has opened up new possibilities for the study of metal anti-penetration performance. By utilizing a large amount of experimental data and numerical simulation results, more accurate predictive models can be trained to accelerate the research and optimization processes of materials.
(5) Experimental techniques and testing methods: To study the anti-penetration performance of metallic materials more deeply, it is necessary to continuously improve and optimize experimental techniques and testing methods. This may involve developing high-precision, high-speed testing equipment and exploring innovative experimental methods, such as in situ observation technology and multi-physics field-testing technology.
(6) Interdisciplinary research: The study of metal anti-penetration performance involves multiple disciplinary fields, including materials science, mechanics, physics, and computer science; thus, it calls for interdisciplinary research. Future research directions may put more emphasis on interaction and cooperation between different disciplines to promote the advancement of metal anti-penetration technology.
7. Conclusions
This study reviewed the impact and penetration resistance behaviors of metal materials at the macro and micro levels, summarized the relationship between the micro and macro mechanisms, and systematically discussed the application of numerical simulation in this field. An outline of this article is provided in Fig. 18. At the macro level, the indicators that can directly characterize the anti-penetration performance of metal materials are the ballistic limit velocity and penetration depth, with penetration failure modes as their manifestation. At the micro level, metal materials are subject to plastic deformation under high-speed impact and form ASBs.
The macroscopic failure mode and anti-penetration performance indicators of metal materials are closely related to the materials’ mechanical properties, such as strength and toughness. The strength and toughness of metal materials depend on their crystal structures and microstructures. Toughness is affected by the deformation mechanism, whereas strength is defined by the strengthening mechanism. These mechanisms jointly affect the evolution and formation of ASBs. The mechanical properties of metal materials depend on the materials’ microstructures, which depend on the processing technology and material composition.
From a macro perspective, this study summarized nine common penetration failure modes of metal targets and discussed the ductile reaming penetration process of intact blunt-nose projectiles. Microscopic differences in the ASBs formed in metal materials with different crystal structures were compared, and the reasons for the formation of the ASBs in metal materials with various crystal structures were explained.
In the field of numerical calculation of impact dynamics, the three common constitutive models for metal materials are the strain hardening, J-C, and Steinberg models, which have differing adaptation ranges. The strain hardening model is simple in form and is widely used without considering the influence of complex temperatures and other factors. The J-C model is a typical constitutive model for the modeling of metal materials at high speed, whereas the Steinberg model is the preferred constitutive model for metal materials at ultra-high speed. Commonly used numerical simulation methods include the Lagrange, Euler, and SPH methods, which have different application conditions. Atomic models based on molecular dynamics are expected to reveal the microscopic mechanisms of high-speed penetration; however, owing to the limitations of geometric size and time scale, such models still need to be developed.
In the future, with the development of nanotechnology and related technologies, the anti-penetration performance of metal materials will be significantly improved. The relevant mechanisms and the connections between the micro and macro levels will be clearer, providing better guidance for the processing and design of metal materials and more possibilities for researchers and practical applications.
Acknowledgments
This research was funded by Qin Chuang Yuan Talent Project in Shaanxi Province, China (QCYRCXM-2022-274).
Compliance with ethics guidelines
Jialin Chen, Shutao Li, Shang Ma, Yeqing Chen, Yin Liu, Quanwei Tian, Xiting Zhong, and Jiaxing Song declare that they have no conflict of interest or financial conflicts to disclose.
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