Shock compression of $[10 1 ¯0]$-axis zinc single crystal

To solve most of the problems associated with the use of different materials, it is sufficient to know their properties, under static and quasi-static loading conditions, when the load changes slowly.¹ However, such studies do not reliably predict the behavior of materials under shock loading. In most cases, the response of a material is determined not only by the set of parameters of its internal structure (grain size, dislocations, solid inclusions, etc.), but also by the symmetry of the crystal lattice. With the high symmetry of the face-centered cubic lattice characteristic of materials, such as copper² and aluminum,³ it is difficult to expect significant changes in properties as a function of the direction of shock compression. Of interest are the studies of anisotropic hexagonal close-packed lattice (HCP) single crystals, where the behavior of each system can be studied separately depending on the orientation of the single crystal relative to the shock wave front.⁴ HCP metals can be divided into three isomechanical subgroups depending on the ratio of the crystal lattice parameters (c/a), where c and a represent the unit cell parameters⁴: (1) с/а < 1.633 (Ti, Zr, Hf, Be); (2) с/а ≈ 1.633 (Mg, Co); and (3) с/а > 1.633 (Zn, Cd). The role of crystalline anisotropy and the mechanisms of inelastic deformation of the first and second groups of shock-compressed single crystals, such as beryllium^5,6 and magnesium,^7–11 have been studied experimentally and by numerical modeling under shock loading. In the experiments with beryllium and magnesium, when loaded in the direction of a low-symmetry orientation at an angle of 45° to the crystal axis [0001], in addition to the elastoplastic transition, the phenomenon of multiple propagation of plastic waves moving at different velocities is observed. The amplitude of the Hugoniot elastic limit (HEL) of beryllium when compressed along the hexagonal axis [0001] is 7 ± 0.1 GPa and when compressed along the axis $[10 1 ¯0]$ is 0.64 GPa. The shear stress during basic sliding under 45° loading is 130 ± 10 MPa, which is significantly higher than the sliding stress under quasi-static conditions, which is about 10 MPa. During the shock compression of beryllium⁵ and magnesium,⁷ elastic precursors exhibit a characteristic velocity jump in the form of a “spike” due to intensive dislocation multiplication and the associated acceleration of shear stress relaxation.

In Refs. 12–14, the structure of shock waves in single crystals of zinc [0001] and $[10 1 ¯0]$ was recorded at different initial temperatures. The results have shown a significant difference in the response to shock compression. It has been found that shock compression of a zinc crystal in the [0001] direction does not form an elastoplastic wave due to the low modulus of elasticity of the material.¹² In this direction, the compressibility of the crystal is close to volumetric.¹⁵ In this regard, the increase in deviatory stresses during uniaxial compression of the crystal is extremely slow. Under the shock loading in the $[10 1 ¯0]$ direction, the compression wave acquires a two-wave structure and an elastic precursor with a characteristic “spike” is recorded. No effect of temperature was found during the loading of zinc single crystals in the $[10 1 ¯0]$ direction. Mathematical methods were used to simulate the experimental results with zinc single crystals in Ref. 16. For a more complete description of the properties of materials, additional information may be required on the effect of the structural state on the values of yield strength and strength at sub-microsecond load duration. Plastic deformation is the simplest and cheapest way of influencing the metal structure. The effect of pre-straining of 0.6% and 5.4% monocrystalline molybdenum [100] on the evolution of the wave profile was investigated in Ref. 17. It is shown that a small deformation of 0.6% leads to a tenfold decrease in the dynamic yield strength, while the tensile strength (spall strength) increases significantly. It has been found^18–22 that the initial dislocation density is the main parameter determining both strength and yield strength under shock compression. The behavior of single crystals is complex in some cases and requires both additional and new studies to investigate their responses in more detail.

This will make it possible in the future to create a universal, physically based model for the inelastic deformation of HCP metals. The studies of single crystals of zinc $[10 1 ¯0]$ in the directions of off-axis deformation under shock compression have not been carried out previously. In addition, the effect of small plastic deformations on the evolution of the elastic–plastic compression wave structure remains open. There are also uncertainties regarding the dependence of the spall strength of HCP single crystals on orientation. As the c/a axis ratio of zinc is 1.856, significant anisotropy of mechanical properties can be expected in planar shock waves under off-axis loading. The main purpose of this study is to investigate these aspects of high rate inelastic deformation and spall fracture of zinc single crystals.

Our studies were carried out on zinc single crystals $[10 1 ¯0]$ obtained by broaching the blank through the melt zone in a gradient tube furnace. The purity of the single crystals was 99.99%. The blanks were obtained in the form of a rectangular bar with dimensions of 120 × 15 mm² and a nominal thickness of 5 mm. The density ρ₀ of the samples measured by hydrostatic weighing was 7.130 g/cm³. The backscattered electron diffraction method was used to determine the orientation of the crystals in space. The plane-parallel samples were cut out using an electric discharge machine and then grinded and polished. The main search direction was the prism plane $[10 1 ¯0]$ perpendicular to the base plane [0001]. There was no more than 1° deviation from $[10 1 ¯0]$ orientation. The investigations have been carried out on monocrystalline samples whose plane (Fig. 1) was oriented at angle θ = 17°, 53°, and 64° to the main plane $[10 1 ¯0]$⁠.

To investigate the effect of the single crystal structure on the kinetic characteristics of deformation in plane shock waves, the studies were carried out on annealed samples. The annealing process was carried out in an automatic vacuum furnace for 3 h at a temperature of 260 °C. After annealing, the samples were subjected to plastic deformation by compression on a hydraulic press until the required degree of deformation was achieved. The longitudinal velocity of sound c_L was measured using the ultrasonic method with a 2.5 MHz frequency converter. The measurement error did not exceed ±5 m/s. In contrast to the plastic deformation, the annealing of the zinc single crystals had no effect on the values of the longitudinal sound velocity. Table I shows the values of the longitudinal sound velocity for annealed single crystals without deformation (0%) and the annealed single crystals with pre-strain (5% and 17%).

Shock wave loading of monocrystalline zinc was performed using a 50 mm gas gun. The shock waves in 12 × 20 mm² samples were generated by impact with a 1.45 ± 0.5 mm thick copper plate. The thickness of the samples varied between 4.0 and 4.9 mm. The experimental scheme is shown in Fig. 2. The main test was performed at a velocity of 350 ± 10 m/s and partially at velocities of 220 ± 10 and 470 ± 10 m/s. The impactor/sample misalignment (tilt) and the impact velocity were controlled by four pairs of electrically charged pins (one flush with the sample impact surface and three protruding 1 mm from the sample impact surface). In all impact tests, the tilt did not exceed 0.5 μrad, allowing uniaxial compression of the samples. The maximum compressive stress σ_shock achieved in the samples corresponded to the velocities of the impactors that were 2 ± 0.5, 5 ± 0.5, and 7 ± 0.5 GPa. The registration of the wave processes of compression and rarefaction wave processes in the sub-microsecond range of load duration was carried out using a VISAR (Velocity Interferometer System for Any Reflection)²³ with nanosecond time resolution.

The measured free surface velocity profiles are shown below. Table II shows the calculated values of σ_HEL/σ_spall, which relate only to the experiments obtained at impact velocities of 350 m/s.

Figure 3 shows the results of measurements of the free surface velocity profiles of annealed zinc single crystal samples at an impactor velocity of 350 ± 10 m/s. The wave profiles of zinc single crystals obtained under loading at angles of 1° and 17° relative to the principal orientation differ significantly from those obtained at angles of 53° and 64°. The results obtained clearly show the contribution of different deformation mechanisms, including both base sliding and prismatic sliding. These deformation features are typical of samples with an angle of 53° and 64°, which have a so-called low-symmetric (LS) orientation.¹⁰ LS is a “non-specific” direction, resulting in the plastic wave splitting into a “quasi-longitudinal wave” and a “quasi-shear wave” as it passes through the sample. The combination of low-symmetry directions and elastic–plastic deformation leads to the formation of multiple waves and a complex response during shock compression. An explanation of this phenomenon has been provided based on numerical modeling and theoretical analysis.^6,11

A velocity spike at the front of the elastic precursor wave generated in both cases is followed by a velocity minimum just behind the spike. The appearance of the spike-like precursor is usually associated with intense generation of the plastic deformation carriers (either dislocations or twins) immediately behind the precursor front.²⁵ In such a case, two HELs are usually considered, the first related to the velocity spike and the second to the post-spike velocity minimum. The wave profiles of the samples subjected to shock compression at an angle of 53° and 64° show the minimum amplitude of the HEL. This behavior could have been predicted as sliding along an inclined basal plane, which occurred at lower shear stresses. There is no sharp change in the velocity in the elastic precursor region of the wave profile, but there is a gradual increase in the velocity until the shock wave exits. The significant rise time of the elastic precursor wave front leads to an additional error in the determination of the value of σ_HEL.

Under shock loading along the basal [0001] and prismatic $[10 1 ¯0]$ planes of the crystal, shear stresses in the plane of easy sliding are zero. Shock compression along the LS axis dominates due to basal sliding, with prismatic and pyramidal compression playing lesser roles. Deviation of the crystal by an angle of 17° results in the activation of a basal slip, leading to a decrease in the HEL from max 2.63 (min 1.8) GPa to max 1.17 (min 0.7) GPa relative to the crystal with 1° deviation from the plane $[10 1 ¯0]$⁠. The results obtained are in agreement with the previously published data for beryllium^5,6 and magnesium.^7,9,10 For zinc single crystals, a similar phenomenon is observed for the first time, as all the previous studies^12–14 were carried out by loading samples along the highly symmetric axes [0001] and $[10 1 ¯0]$⁠. Shock loading along these axes cannot activate the densely packed basal slip plane.

Figure 4 shows the frontal parts of the wave profiles of zinc single crystals before and after annealing. It can be seen that annealing a single crystal leads to an increase in the elastic–plastic transition parameters and an increase in the compressive stress in the first plastic wave during the formation of a two-wave structure. In the study of single crystals of molybdenum¹⁷ and titanium alloy VT1-0,¹⁸ an increase in the HEL parameter was found, followed by relaxation after annealing. It can be assumed that the samples in the as-received state have an increased initial density of twins and dislocations, allowing plastic deformation at lower stresses. Annealing results in a decrease of mobile defects, such as twins and dislocations. In fact, the increase in stress results from the need to generate new dislocations to ensure plastic deformation when the mobility of the existing dislocations is insufficient to compensate for the deformation.

Figure 5 shows the results of measurements of the free surface velocity profiles of annealed and pre-strained samples by 0.6% and 5%. In the annealed state, there is an abrupt increase in the elastic wave parameters with a rise time of 2–3 ns. The rise time of the plastic wave parameters is 100–150 ns and is directly dependent on the viscosity of the material. The irregular oscillations present on the wave profiles can be explained by concomitant twinning⁷ in the shock wave. A change in the deformation kinetics is observed on the wave profiles after 0.6% and 5% pre-strain, which is manifested in a change in the shape and amplitude of the jump in the elastic precursor. A pre-strain of 0.6% resulted in a doubling of the HEL due to an increase in the density of deformation defects, such as twins and dislocations. The amplitude of the dynamic elastic limit is not significantly affected by a subsequent 5% plastic deformation.

Figure 6 summarizes the free surface velocity profiles of annealed samples and after pre-straining for shock wave loading at 64° to the $[10 1 ¯0]$ axis. It can be seen that for single crystals in the initial state, no two-wave structure is formed at the front of the plastic wave. Similar behavior was observed by the authors⁵ for beryllium in off-axis impact at an angle of 65°. The deformation mechanism of the annealed crystal shows qualitative differences from the unannealed crystal. The presence of many structural defects that prevent sliding in the basal plane is the most likely explanation for this phenomenon. In order to verify the assumption about the effect of the defect concentration on the transformation of the wave profile, a process of plastic deformation of the crystal with an intensity of 5% and 17% was carried out. Unannealed and 17% deformed crystals show almost identical deformation behavior in a plastic wave under shock compression. A pre-strain of 5% does not lead to any significant changes in the deformation behavior compared to a single annealed crystal. If only the basal slip is taken into account, there is no evidence of the formation of a multi-wave structure in a plastic wave. Prismatic and pyramidal slips play an important role in the plastic deformation along the LS axis, and the relationship between longitudinal and shear deformation during shock compression along the LS axis is due to the activation of prismatic and pyramidal slips. The analysis of deformation mechanisms^5,6,9,10 can probably be applied to interpret the results obtained in the study of annealed and pre-deformed zinc single crystals. By acting on the crystal structure through annealing, pyramidal and prismatic sliding can be activated and also blocked through significant deformation, in our case 17%, ensuring only the basic basal sliding.

Additional information on high strain rate resistance can be obtained by measuring the compression rate in a plastic shock wave.^26,27 Figures 7 and 8 show the results of measuring the free surface velocity profiles for annealed samples oriented at 17 and 53 with respect to the surface $[10 1 ¯0]$⁠. The total strain rate $ε ˙ x$ in a stationary plastic wave is determined by differentiating the corresponding portion of the velocity profile $u p(t)$ and dividing by the wave propagation velocity $U S$⁠: $ε ˙ x= u ˙ f s / 2 U S$⁠, where $u ˙ f s$ is the maximum acceleration of the surface in a plastic shock wave.

The obtained values of the exponents of power dependence α vary strongly with the direction of the crystal axis during shock compression. The compression rate from pressure (Figs. 9 and 10) increases for low-symmetry orientations (17°, 53°, and 64°). The main contribution to acceleration is probably due to the increasing role of a basal slip, as the angle of propagation of the shock wave increases (Fig. 1). Obviously, the data can be described by a universal power dependence with an exponent equal to four, as proposed in the well-known work²⁸ exclusively for single crystals oriented at angles of 53° and 64° in the first shock wave. The deceleration of the compression rate in the second wave can be explained by the significant contribution of a prismatic slip under the load of the second plastic wave (Fig. 6). The role of deformation twinning does not contribute significantly.⁶ 

After reflection of the compression pulse from the free surface, tensile stresses are generated in the sample, leading to the initiation of its failure—the spall. The dynamic “spall” strength is calculated from the magnitude of the velocity drop from the maximum value to the value before the front of the reflective pulse. As a result of the analysis of the obtained wave profiles, the values of the critical failure stresses during spalling of σ_sp were determined for all the samples of zinc single crystals studied.²⁹ 

Figure 11 shows the results of the dependence of spall strength on a strain rate for the zinc single crystals investigated in this work. The strain rate prior to spall fracture did not exceed 10⁵ s⁻¹ in all cases. During the study, it was found that annealing and pre-strain have virtually no effect on the values of the spall fracture of a zinc single crystal. In this respect, Fig. 11 shows only the results obtained for annealed crystals.

To investigate the effect of anisotropy on inelastic deformation under plane shock compression, the wave profiles of zinc single crystals loaded along the high symmetry axis $[10 1 ¯0]$ and low-symmetry axes at 17°, 53°, and 64° were recorded and analyzed. The effect of annealing and pre-strain on the dynamics of the deformation and fracture processes was also investigated. The experiments carried out in this study allow us to confirm the basic mechanisms and kinetic characteristics of the deformation of single crystals with a HCP lattice, previously discovered for beryllium and magnesium. In the process of plane shock compression along the $[10 1 ¯0]$ axis, the maximum value of the HEL is observed, which is due to the difficulty of deformation in pyramidal slip and twinning systems at a given crystal orientation. A 17° change in the tilt angle of the plane $[10 1 ¯0]$ relative to the shock wave front results in the inclusion of a basal slip in the deformation process. The activation of the primary basal slip system leads to a more than twofold decrease in the amplitude of the HEL. Experiments with single crystals oriented at an angle of more than 45° to the plane $[10 1 ¯0]$ have confirmed the formation of a two-wave structure of the plastic front, previously found in beryllium and magnesium. Prismatic and pyramidal slip systems are included in the process of inelastic deformation during compression along a low-symmetry axis. The effect of pre-strain on monocrystalline samples was found to cause the transformation of the initial defective structure, including dislocations and twins.

The effect is most pronounced at the initial stage of the formation of an elastic–plastic wave. At this point, there is either a sharp increase in the parameters of the elastic wave or their gradual increase until the release of the plastic compression wave. During the formation of the two-wave structure of the plastic front, annealing leads to an increase in the amplitude of the second plastic compression wave. The spall strength of zinc single crystals varies depending on the direction of loading. Comparison of the experimental results with the literature data allowed us to establish that at a strain rate not exceeding 10⁵ s⁻¹, the greatest value of the spall strength is achieved along the [0001] direction and is 2.1 GPa. The mechanism of fracture along the highly symmetrical axes of the zinc crystals is different due to high anisotropy. In the volume of the sample, there is an intense twinning of the structure during loading, which precedes the process of fracture along the axis $[10 1 ¯0]$ and the inclined planes. It can be assumed that the twinning process leads to a violation of the integrity of the crystal, creating areas of increased stress concentration and other structural inhomogeneities and defects, which, in turn, reduces its strength. The spall strength of zinc single crystals increases in all cases with increasing strain rate and can be approximated by a power function.

This work was performed within the framework of Study No. 17706413348210001380/226/3464-D, as well as under the programs within the framework of the state assignment for basic scientific research with Registration No. FFSG-2024-0001 (“Comprehensive study of physico-chemical properties and processes occurring with a substance under high energy conditions”); and No. 075-00270-24-00 (with the support of the Ministry of Science and Technical Higher Education of the Russian Federation) and No. 122021000033-2 (“Structure”).

The authors have no conflicts to disclose.

G. V. Garkushin (Геннадий Гаркушин): Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). A. S. Savinykh (Андрей Савиных): Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). S. V. Razorenov (Сергей Разоренов): Conceptualization (equal); Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Supervision (equal); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). I. G. Brodova (Ирина Бродова): Investigation (equal); Methodology (equal); Validation (equal). D. Yu. Rasposienko (Дмитрий Распосиенко): Investigation (equal); Methodology (equal); Validation (equal). D. I. Devyaterikov: (Денис Девятериков) Investigation (equal); Methodology (equal); Validation (equal). P. E. Panfilov (Петр Панфилов): Investigation (equal); Methodology (equal); Validation (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.