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Effect of dynamic fragmentation on the reaction characteristics of a Zr-based metallic glass
Journal of Non-Crystalline Solids 515 (2019) 149–156
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Effect of dynamic fragmentation on the reaction characteristics of a Zr-based metallic glass ⁎
T
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Cheng Ji, Yong He , Chuan Ting Wang , Yuan He, Zhiping Guo, Lei Guo Departments of Mechanical Engineering, Nanjing University of Science & Technology, Nanjing, Jiangsu 210094, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Zr-based metallic glass Impact Quasi-static pressure Dynamic fragmentation Reaction
The reaction behavior and dynamic fragmentation of ZrCuNiAl bulk metallic glass (BMG) subjected to high velocity impact was investigated. ZrCuNiAl BMG specimens were launched into a quasi-sealed chamber filled with air or argon (Ar) under various velocities. The results demonstrated that the ZrCuNiAl metallic glass generated debris after impact, the debris reacted with oxygen in the air atmosphere. The combustion of Zr and Cu and the combination reaction of aluminum and nickel released heat, which caused significant over-pressure inside the chamber. This reaction was related to the fragmentation and the critical fragment size for reaction was determined by scanning electron microscope (SEM) images; In Ar atmosphere, the cumulative mass of debris of ZrCuNiAl BMG was following a near power function distribution. A model was established by combining the dynamic fracture distribution with chemical reaction of ZrCuNiAl BMG, which can predict the quasi-pressure inside the chamber under a certain range of velocities with acceptable accuracy.
1. Introduction Zr-rich metal alloy is a novel group of multifunctional energetic structural materials (MESMs) [1]. The Zr phase is combustible, can react with air to release high amounts of energy after impacting targets. Extensive studies have been performed to investigate the impact initiated reaction behavior of Zr-rich alloy [2–6]. Ren et al. performed dynamic compression tests of W/Zr alloys with split Hopkinson pressure bar (SHPB) platform, it was observed that W/Zr experienced violent reaction under shock-loading, while reaction products containing ZrO2 was observed on the residue surfaces [2]. The effect of impact velocity on the reaction behavior of W/Zr alloy was studied by using a quasi-sealed test chamber, the amount of released energy could be calculated quantitatively by measuring the pressure change inside the test chamber [3,4]. Wang et al. improved the design of the quasi-sealed test chamber for better accuracy, and investigated reaction behavior of Zr-based BMG under various impact velocities between 700 m/s and 1500 m/s [5]. The results showed that higher impact velocity led to higher reaction efficiency of Zr-based BMG. Huang et al. studied the impact response of Zr55Ni5Al10Cu30 alloy with a ballistic gun, it was indicated that Zr55Ni5Al10Cu30 alloy burned in the air according to the bright spark observation during impact [6]. Currently, the researches of reaction mechanism of MESMs have focused on energy releasing, widely neglecting the dynamic
⁎
fragmentation process [7–9]. Researches have been conducted to investigate the combustion times and temperatures, while the energy output of micron-sized metallic particles under shock-loading have not been well studied [10–13]. Actually, impact-initiated reactions of Zrrich metal alloy largely depends on the fragment size produced by loading impact. The small fragments generated from dynamic fragmentation with high temperature and large relative surface area are easy to combust and release energy in air, but the larger fragments even in hot state, due to the very small contact area with air, can not react and remain the original state after crushing. A similar pattern was gained by Ren at al on the W/Zr composites [2]. However, the reaction mechanism of MESMs associated with the theory of dynamic fragmentation has not been reported. This research was thus initiated to investigate the role of dynamic fragmentation on the reaction behavior of a Zr-based BMG. 2. Mateial and experiments The primary materials used in the study were commercial purity copper(99.9999% purity) plates, commercial purity nickel (99.96% purity) plates, commercial purity aluminum (99.9995% purity) bulks and commercial purity zirconium(99.7% purity) bulks. The primary materials were cut into small pieces by wire cut electrical discharge machining. Then the pieces were polished with SiC paper to remove the
Corresponding author. E-mail addresses: [email protected] (Y. He), [email protected] (C.T. Wang).
https://doi.org/10.1016/j.jnoncrysol.2019.04.022 Received 10 January 2019; Received in revised form 16 April 2019; Accepted 18 April 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Schematic illustration of the setup for quasi-sealed chamber test.
3. Results
surface oxide layers and weighed by high precision electronic balance according to the mass percentage. After that, the primary pieces were washed for 10–20 min by ultrasonic cleaning machine with alcohol to remove surface impurities and grease. The Zr55Cu30Ni5Al10 BMG (simply written as ZrCuNiAl BMG) was manufactured by arc melting and copper-mold vacuum suction casting. The ZrCuNiAl BMG was in form of rods with a diameter of 10 mm and height of around 60 mm. Generally, the cylinder samples with diameter of 10 mm and height of 10 mm were cut off from the BMG rod, the weight of each sample was around 5.4 g. An inert sample made of 45# steel with the same size and weight of around 6.1 g was prepared for comparison tests. The shock-induced fragmentation and reaction characteristics were investigated by means of a modified quasi-sealed test chamber. The schematic of the impact test is shown in Fig. 1. The quasi sealed chamber with volume of 20 L is made of hard steel and the inner diameter is around 440 mm. The quasi-sealed test chamber was sealed with a iron lid with thickness of 0.5 mm. A black powder ballistic gun was used to fire the samples into the test chamber. And the impact speed was controlled by adjusting the mass of black powder. The projectiles passed through the lid and impacted a steel target plate inside the chamber. The velocity of the samples was measured by a velocity measurement system at the shoot-line prior to penetrating the iron lid, which is very close to the target. Several sensors were placed in the test chamber to capture gas pressure change. Two series of impact experiments were conducted: Firstly, samples were shot into the chamber filled with air atmosphere to measure the over-pressure change inside the chamber caused by reaction; Secondly, in order to avoid the reaction of the BMG, the chamber was filled with argon to study the fragmentation of ZrCuNiAl BMG under impact loading. Argon was injected into the test chamber through the gas inlet valve as argon is denser than air. Meanwhile, the air was expelled through the gas outlet valve. This aeration process last about 10 min to ensure the chamber full of argon, then the two valves were closed to prepare for experiment. A box filled with argon was adjoined to the iron lid, which could prevent air from entering into the test chamber following the projectile. The fragments or reaction debris were respectively collected by an arc-shaped groove inside of the chamber. Scanning electron microscopy (SEM) equiped with energy dispersive spectrometer (EDS) was used to determine the morphology and element content of reaction products.
3.1. Reaction characteristics of ZrCuNiAl BMG subjected to impact under air atmosphere Impact tests were performed by shooting the ZrCuNiAl BMG specimens into the test chamber filled with air under various velocities. Fig. 2 shows the interior quasi-static pressure curves and video frames when ZrCuNiAl BMG specimens were hitting the target in air [5]. As Fig. 2a shows, the 45# steel caused moderate flash inside the chamber after impact due to donation of kinetic energy. Strong flash with venting of gas out of the chamber was observed after impact of ZrCuNiAl BMG samples, which indicated that the ZrCuNiAl BMG underwent chemical reaction in the air after impact. The pressure change inside the chamber was captured for each test. The over pressure curve contains two stages: the first stage is a blast pressure with duration of several micro seconds caused by impact process; the second stage is a quasistatic pressure with duration of several tens of milliseconds caused by kinetic and chemical energy [7–9]. The acquisition frequency of the data collector is 128 kHz in the pressure measurement system. In order to eliminate the noise, the quasi-static pressure can be obtained by filtering the original data with Matlab software, with a filtering cut-off frequency of 5000 Hz. After filter processing, the measured quasi-static pressure was plotted versus time, as shown in Fig. 2b. All the pressure curves increased dramaticly to a certain peak value after impact, and then dropped to zero gradually. Higher impact velocity led to higher peak value of quasi-static pressure inside the chamber. The debris generated by impact experiments was collected from the chamber and separated through varisized sieves. The morphology and composition of the debris are shown in Fig. 3. The SEM images indicate that the smaller debris with size less than around 20 μm are all sphere particles, the medium fragments (with size ranging from 20 μm to 220 μm) are mixed up with spherical particles and irregular debris, and there is almost no spherical fragment and all of them are irregular shape when the size is larger than 220 μm. In addition, the spherical particles are seen as hollow spheres from the enlarged photograph. The EDS results show that the irregular debris Zr, Cu, Ni, Al, with nearly none O, and the proportion of metal elements is similar to that of the Zr55Cu30Ni5Al10 bulk metallic glass. The spherical particles contain mainly Zr、O、Cu、Al、Ni and little Fe which may be derived from the steel target. Several conclusions can be drawn from the impact tests in air atmosphere: Firstly, the BMG specimen reacted with oxygen after impact, hollow spheres product was very possibly formed as a result of oxidation reaction. The process of reaction and cooling of fragments is short in time and small in scale, it is difficult to observe the spherical 150
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Fig. 2. The video frames and interior quasi-static pressure curves of steel and ZrCuNiAl BMG at various impact velocities in the air [5].
formation process. The material near the shear zone has a high temperature to form small droplets with a size of about ten microns instead of hollow spheres [14]. The hollow spheres are typical products of combustion and oxidation of micro metal powders. Similar hollow spheres products have been observed after combustion of Al, Ti and Zr [15]. Secondly, the impact formed debris with diameter < 20 μm underwent oxidation reaction, while the debris with diameter larger than 20 μm did not involve in reaction.
ZrCuNiAl BMG have similar shape like a power-law distribution. The slopes of the cumulative mass curves are from large to small with the increase of particle diameter. At a certain particle size level, the higher of the impact velocity, the higher is the cumulative mass value. This demonstrates that higher impact velocity tend to form smaller particle size of ZrCuNiAl BMG fragments after dynamic fragmentation.
3.2. Fragmentation of ZrCuNiAl BMG subjected to impact under Ar atmosphere
4.1. The critical fragment size related to the reaction of ZrCuNiAl BMG under shock-loading
Impact tests were also performed by shooting the ZrCuNiAl BMG specimens into the test chamber filled with argon under various velocities, aiming to study the effect of fragmentation on reaction behavior of ZrCuNiAl BMG by preventing oxidation after fragmentation. These tests were designed to study the distribution of debris of ZrCuNiAl BMG subjected to impact, as the oxidation react can be inhibited under Ar atmosphere. The debris was collected after impact tests and examined under SEM. As shown in Fig. 4, the debris consists of spherical particles and irregular shape fragments. The composition of spherical particles and irregular fragments are mainly Zr, Cu, Ni, Al, with nearly none O, according to the EDS results. As can be seen, the Zr-based BMG fragment did not experience oxidation reaction after impact in argon. The fragments produced by impact tests in argon atmosphere were separated through a series of sized sieving screens of different sizes and weighed within each size range by a high-precision electronic scale with an accuracy of 0.001 g. When the sample impact the target at a certain velocity, the fragmentation process and the debris forming mechanism is the same in argon and air. The difference caused by the different atmosphere is that: in air atmosphere, the debris will react with oxygen after impact due to its high temperature; in argon atmosphere, the formed debris will remain unreacted after impact. Therefore, the cumulative mass distribution of debris after impact in Ar atmosphere is used to quantitatively describe the fragmentation process of Zr-BMG samples. The result curves of cumulative mass distribution versus fragment size at different impact velocities in argon atmosphere are shown in Fig. 5. All the cumulative mass distribution curves of
Under loading conditions, fragments of different scales underwent various reaction phenomenon, described as “fire ball” “spark” and “no react” [2]. The energetic characteristics of HfZrTiTa0.53 alloy was studied by Zhang et al. with ballistic gun and armor chamber test [16], the results revealed that higher impact velocity brought around more severe fracture of the alloy and further lead to more violent reaction between the air and fragments causing more energy release. The expending ring experiments were designed in order to study the fragmentation process of three types of structural energetic materials [17], the results showed that the fragments generated by these MESMs are much smaller than those generated by ductile metals and combustion processes perhaps occur subsequent to the fragmentation process, however, the fragment combustion behavior was not well studied. The above studies have shown that the reaction of zirconium alloy under shock loading occurred after dynamic fragmentation and it was closely related to the fragment size. In this research, as the BMG projectiles hit the target anvil, cracks are generated and propagate rapidly inside the projectiles, which causes dynamic fragmentation of the BMG projectiles. In the air, the fragments dispread in the chamber and reacted with oxygen in the air. This combustion of Zr released heat and caused thermal expansion of the atmosphere inside the chamber. The expansion of the atmosphere finally led to a pressure change inside the chamber, which can be detected by sensors. As shown in Fig. 3, the SEM and EDS results indicate that not all of the ZrCuNiAl BMG debris reacted after impact in air atmosphere. Furthermore, the shock-induced reaction mechanism of
4. Discussion
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Fig. 3. Morphology and composition of the debris of ZrCuNiAl BMG specimen generated by the impact tests in air atmosphere, SEM images of products with different screening scales are (a) < 10 μm (b) 10–20 μm (c) 20–40 μm (d) 40–65 μm (e) 220–350 μm (f) 350–450 μm, (g) shows the elemental analysis of products.
4.2. A reaction model based on fragmentation of ZrCuNiAl BMG subjected to impact
ZrCuNiAl BMG was related to the particle size after fragmentation and a critical reaction size range was acquired. A schematic diagram of fragmentation and reaction process of ZrCuNiAl BMG subjected to impact is shown in Fig. 6. The small fragments (< 20 μm in size) produced by the BMG specimen could combust easily because of the large contact area with air. The large fragments (> 20 μm in size) did not react due to the small contact area with air and serious heat loss during flight. A similar pattern was gained by Ren at al about the W/Zr composites fragmentation and reaction [2]. Although there are many spherical particles in the medium fragments, the hollow structure is very possibly formed by ZrCuNiAl BMG debris with size smaller than 20 μm. Thus, 20 μm is taken as the critical size for the ZrCuNiAl BMG reaction with the air after impact. The fragments generated by dynamic fragmentation with diameter smaller than 20 μm are considered to react entirely in the air.
As for dynamic fragmentation of solids, the early seminal works were attributed to Mott et al. [18,19] The distribution of fragment size and the governing distribution length scale were predicted in the dynamic fragmentation theories by Mott. In subsequent work, Grady et al. developed the impact fragmentation theories to calculate the average fragment size and obtained the statistical distribution in fragment size by using of mechanics and energy balance methods [20,21]. In a recent study, Grady indicated that the energy-based fragmentation theory can be applied to describe nonequilibrium fragmentation mechanism of brittle materials [22]. The fragment distributions of brittle solids were observed to exhibit the power-law behavior required by the fractal nature of the breakup event other than the exponential distribution [23]. The characteristic fragment size λ governing the fragment distributions was determined by fracture properties of materials and ex• pansion strain rate (ε ) [22]. The characteristic fragment size λ can be 152
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Fig. 4. Morphology and composition of the debris of ZrCuNiAl BMG specimen generated by the impact tests in argon atmosphere, SEM images of products with different screening scales are (a) < 20 μm (b) 20–98 μm.
Γ=
(2)
where ρ is the density of the Zr55Cu30Ni5Al10 as 6.714 g/cm3, and E is the elastic modulus of the Zr55Cu30Ni5Al10 with the value of 81.6 GPa [24]. The value of the dynamic fracture toughness (Kc) is 50 MPam1/2 for calculation which is the average of 40–60 MPam1/2 obtained by Charpy impact test [25]. When a specimen impact the target right along the axis at normal incidence, a radial expansion strain rate is produced, which causes the radial dispersion velocity of the debris. The radial • expansion strain rate (ε ) is usually calculated via dividing the radial expansion velocity (vex) by the initial base radius of the ring or shell (r), • ε = vex / r , the expansion velocity is difficult to obtain but a strain rate representative for the impact velocity and sample size of the experiment can be approximated as it [23]. Hence the radial expansion strain rate • can be calculated as ε = vex / r ≈ v / h approximately, h is the height of specimen and v is the impact velocity. The characteristic fragment size, λ under various impact velocities can be calculated via solving Eq. (1) and Eq. (2). Fragment mass distribution is commonly described by a cumulative distribution function, instead of a probability density function, which is more sensitive to the fragment masses data scatter. In earlier theoretical studies, exponential functions were widely employed to determine fragment mass distributions [26,27]. Then, exponential distributions were found to be appropriate for predicting the dynamic fragmentation of ductile materials, however, highly brittle solids such as ceramic or glass were observed to be power-law [22,23]. The curves in Fig. 5 of cumulative mass distribution for ZrCuNiAl BMG approximately follows the shape of power function, hence the limiting form of Rosin-Rammler distribution attributed to Schuhmann is considered to describe the cumulative mass distributions of ZrCuNiAl BMG. It is assumed that the
Fig. 5. Experimental data of cumulative mass distribution for ZrCuNiAl BMG after dynamic fragmentation at different impact velocities in argon atmosphere.
expressed as 1/3
⎛ 48Γ ⎞ λ ≈ ⎜ •2 ⎟ ⎝ ρε ⎠
Kc2 2E
(1)
where Г is the fracture surface energy per unit area. The fracture energy is estimated by
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Fig. 6. Schematic diagram of fragmentation and reaction process of ZrCuNiAl BMG.
fragments are spherical, the total cumulative mass of fragments of equivalent diameter less than or equal to fragment diameter x in the form [28,29].
x k M (≤x ) = M0 ⎛ ⎞ ⎝λ⎠
(3)
where M0 equals to 5.4 g is the total mass of the test specimen before impact experiment. Commonly, the exponent k is not provided by the theory. In the Schuhmann relation ranges between around 0.5 and 1.5 according to empirical evidence [28]. Experimental observation suggests the range is 0.5 < k < 2.5 [22]. For the ZrCuNiAl BMG, it's also difficult to directly obtain the value of the index k from the experimental result plots because the error of individual data points will easily affect the results of the nonlinear fitting. Take the logarithm of both sides of the equation, and k is the slope of the linear function.
lg(M ) = k lg(x ) + lg
M0 λk
(4)
The function can be further constructed into a direct proportional function.
Y = kX
(5)
Y = lg(M ∗ λk / M0)
(6)
X = lg(x )
(7)
Fig. 7. Logarithm of characteristic fragment size normalized by cumulative mass of fragments plotted as a function of the logarithm of fragment diameter.
The exothermic energy of above chemical reactions are 1078.3 kJ/mol for Zr and 156.8 kJ/mol for Cu [30]. The mass of the ZrCuNiAl BMG fragments (≤20 μm in size) involved in the reaction at various impact velocities can be easily calculated by Eq. (3), then the amount of substance of zirconium in the reaction (n) can also be calculated according to the proportion of related elements of Zr55Cu30Ni5Al10. The chemical energy (ΔQ) released after dynamic fragmentation of ZrCuNiAl BMG can be calculated by the formula.
The experiment data of the relative cumulative mass and fragment size at different velocities are treated by the construction of logarithmic and proportional functions. The data points are shown in Fig. 7. The experiment data points processed by Eq. (4) and Eq. (5) are distributed near the direct line (y = 0.45x) unless the equivalent diameter of fragments is > 1 mm (that is lg(x) ≥ 0), for the reason that large irregular shape fragments cannot be assumed to be spherical and the error is inevitable. A k value of 0.45 ± 0.02 was obtained via data fitting for the ZrCuNiAl BMG. The character of the experimental distribution is in sensible agreement with the behavior predicted by the theory. The fragment distributions of ZrCuNiAl BMG are observed to follow power law in character and such trend was also predicted by the power function model about the ZrCuNiAl BMG dynamic fragmentation. Therefore, it is possible to calculate the mass of the fragments smaller than a certain size, by solving Eq. (1) to Eq. (7). The reaction of the ZrCuNiAl BMG mainly produced by the combustion of zirconium and copper occurs subsequent to the fragmentation process, aluminum and nickel of the metal glass are neglected because of their small content. The reaction equation of the combustion of zirconium and copper follows: Zr + O2 → ZrO2, Cu + 1/2O2 → CuO.
ΔQ = n × ΔH
(8)
As Fig. 2 shows, the quasi-static pressure inside chamber increased from zero to the peak value within tens of milliseconds. The chamber can be regarded as a closed system and heat losses are neglected during this short period. ΔE is the energy input of the BMG projectile including chemical energy (ΔQ) and a quarter of the kinetic energy (0.25Ek) [5], which is according to the results of inert fragment experiment.
1 M0 v 2 2
(9)
ΔE = ΔQ + 0.25Ek
(10)
Ek =
The peak quasi-static pressure (ΔP) for BMG projectiles can be expressed as [5]. 154
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Fig. 9. The proportion contribution of chemical reaction to the overall overpressure rise (ΔPQ/ΔP) plotted as a function of the impact velocity.
Fig. 8. Experiment and calculation of quasi-static pressure in the chamber versus impact velocity for ZrCuNiAl BMG in air atmosphere.
mair − n × Moxygen ΔE ΔP = ×R+⎛ − ρair ⎞ × R × T V × Cp V ⎝ ⎠ ⎜
to the over-pressure rise in the chamber within the velocity range of this study (750–1500 m/s). It is possible that a large part of the kinetic energy during impact is consumed by the crushing process, the formation of the fragments surface and vibration of the system. The proportion contribution of chemical reaction to the over-pressure rise decreases approximately linearly with the increase of impact velocity. One possible reason is that the reaction rate of the ZrCuNiAl BMG under shock loading increases slowly as the impact velocity increases, so the proportion contribution of chemical reaction to over-pressure decreases and the proportion contribution of kinetic energy to over-pressure increases. It is reasonable to expect that the proportion contribution of kinetic energy to over-pressure will be more significant when the impact velocity is beyond velocity range of this study (> 1500 m/s).
⎟
(11)
where ΔP the peak quasi-static pressures are the peak values in Fig. 2 obtained by experiments, Cp = 717 J/(kg·K) is the specific heat of air, V = 20 L is the volume of the chamber, Moxygen = 32 g/mol is the molar mass of oxygen, mair, ρair and T are the mass, density and air temperature prior to impact, respectively. The value of the gas constant R is about 287 J/(kg·K) inside the chamber. ΔPQ is the over-pressure in the chamber contributed by chemical reaction only. By solving the Eq. (10) and Eq. (11), it is possible to calculate the energy deposition when a BMG projectile is hitting target with a certain velocity. And finally, the peak pressure can be obtained by solving Eq. (11). Experiment data and a calculation curve of peak pressure in the chamber are plotted versus impact velocity for ZrCuNiAl BMG, as shown in Fig. 8. The peak pressure increased with increasing of impact velocity. The experimental data points are in acceptable agreement with the theoretical calculation within a certain range of velocities (900–1400 m/s), which demonstrates that the dynamic fragmentation plays an important role on the reaction of ZrCuNiAl BMG in shock process. The model above could be used to predict the quasi-static pressure (or energy) when a Zr-BMG is impacting the target at a certain range of velocities. This model could be very useful to predict the damage effect of a Zr-BMG projectile when it is hitting the target inside a sealed space. Detailed calculation results of the peak pressure value in the chamber under various impact velocities are listed in Table 1. Fig. 9 shows the proportion contribution of chemical reaction to the overall over-pressure rise (ΔPQ/ΔP) plotted as a function of the impact velocity. It is demonstrated that the over-pressure rise in the chamber is mainly caused by chemical reaction, the kinetic energy contributes a small part
5. Conclusions The dynamic fragmentation and reaction characteristics of ZrCuNiAl metallic glass was investigated by the quasi-sealed test chamber filled with argon and air, respectively. Several conclusions are drawn as follows: 1. The ZrCuNiAl metallic glass reacted with oxygen in the air after impacting the target, such reaction generated heat and caused significant over-pressure rise inside the chamber. 2. The fragment distribution of ZrCuNiAl BMG is following a power function similar as other brittle materials. The cumulative mass distribution of ZrCuNiAl BMG is significantly affected by the impact velocity (or strain rate). 3. A model was built based on dynamic fragmentation mechanism, this model could be used to predict the quasi-static pressure (or energy) when a Zr-BMG is impacting the target at a certain range of velocities with acceptable accuracy.
Table 1 The calculation of quasi-static pressure in the chamber under various impact velocities. v (m/s)
λ (mm)
M(≤20μm) (g)
Q (J)
ΔPQ (kPa)
ΔE (J)
ΔP (kPa)
750 850 986 1100 1200 1328 1500
2.573 2.367 2.144 1.993 1.881 1.758 1.621
0.595 0.618 0.647 0.668 0.686 0.708 0.734
5100.781 5297.719 5541.129 5727.692 5880.537 6063.724 6291.417
102.016 105.954 110.823 114.554 117.611 121.274 125.828
5480.469 5785.407 6197.361 6544.442 6852.537 7254.144 7810.167
109.077 115.156 123.372 130.296 136.444 144.460 155.561
Acknowledgements This work was supported by the National Natural Science Foundation of China [NSFC51601095] and the National Natural Science Foundation of Jiangshu China [BK20160832].
Declaration of interest statement None. 155
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Credit author statement
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Data curation: C.J. and C.T.W.; Formal analysis: C.J. and C.T.W.; Funding acquisition: Y.H. and C.T.W.; Investigation: C.J. and Z.P.G.; Methodology: Y.H. and L.G.; Project administration: Y.H.; Supervision: Y.H. and C.T.W.; Validation: Y.H., Z.P.G. and L.G.; Roles/Writing original draft: C.J. and C.T.W.; Writing - review & editing: Y.H. and L.G. References [1] R.G. Ames, Energy release characteristics of impact-initiated energetic materials, Mater. Res. Soc. Symp. Proc. 896 (2005) (0896-H03-08). [2] H.L. Ren, X. Liu, J. Ning, Impact-initiated behavior and reaction mechanism of W/ Zr composites with SHPB setup, AIP Adv. 6 (2016) 115205. [3] X.F. Zhang, A.S. Shi, L. Qiao, J. Zhang, Y.G. Zhang, Z.W. Guan, Experimental study on impact-initiated characters of multifunctional energetic structural materials, J. Appl. Phys. 113 (2013) 1156–2129. [4] P.G. Luo, Z.C. Wang, C.L. Jiang, L. Mao, Q. Li, Experimental study on impact-initiated characters of W/Zr energetic fragments, Mater. Des. 84 (2015) 72–78. [5] C.T. Wang, Y. He, C. Ji, Investigation on shock-induced reaction characteristics of a Zr-based metallic glass, Intermetallics 93 (2018) 383–388. [6] C. Huang, S. Li, S. Bai, Quasi-static and impact-initiated response of Zr55Ni5Al10Cu30 alloy, J. Non-Cryst. Solids 481 (2018) 59–64. [7] H.F. Wang, Y.F. Zheng, Q.B. Yu, Z.W. Liu, W.M. Yu, Impact-induced initiation and energy release behavior of reactive materials, J. Appl. Phys. 110 (2011) 074904. [8] W. Xiong, X.F. Zhang, Y. Wu, Influence of additives on microstructures, mechanical properties and shock-induced reaction characteristics of Al/Ni composites, J. Alloys Compd. 648 (2015) 540–549. [9] C. Ji, Y. He, C.T. Wang, Y. He, X.C. Pan, J.J. Jiao, L. Guo, Investigation on shockinduced reaction characteristics of an Al/Ni composite processed via accumulative roll-bonding, Mater. Des. 116 (2017) 591–598. [10] C. Badiola, E.L. Dreizin, Combustion of micron-sized particles of titanium and zirconium, Proc. Combust. Inst. 34 (2013) 2237–2243. [11] Q.H. Wang, J.H. Sun, J. Deng, H. Wen, Y. Xu, Combustion behaviour of Fe2O3coated zirconium particles in air, Energy Procedia 66 (2015) 269–272. [12] S. Mohan, M.A. Trunov, E.L. Dreizin, Heating and ignition of metallic particles by a CO2 laser, J. Propuls. Power 24 (2015) 199–205. [13] H.Y. Wei, C.S. Yoo, Kinetics of small single particle combustion of zirconium alloy,
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Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol
Effect of dynamic fragmentation on the reaction characteristics of a Zr-based metallic glass ⁎
T
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Cheng Ji, Yong He , Chuan Ting Wang , Yuan He, Zhiping Guo, Lei Guo Departments of Mechanical Engineering, Nanjing University of Science & Technology, Nanjing, Jiangsu 210094, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords: Zr-based metallic glass Impact Quasi-static pressure Dynamic fragmentation Reaction
The reaction behavior and dynamic fragmentation of ZrCuNiAl bulk metallic glass (BMG) subjected to high velocity impact was investigated. ZrCuNiAl BMG specimens were launched into a quasi-sealed chamber filled with air or argon (Ar) under various velocities. The results demonstrated that the ZrCuNiAl metallic glass generated debris after impact, the debris reacted with oxygen in the air atmosphere. The combustion of Zr and Cu and the combination reaction of aluminum and nickel released heat, which caused significant over-pressure inside the chamber. This reaction was related to the fragmentation and the critical fragment size for reaction was determined by scanning electron microscope (SEM) images; In Ar atmosphere, the cumulative mass of debris of ZrCuNiAl BMG was following a near power function distribution. A model was established by combining the dynamic fracture distribution with chemical reaction of ZrCuNiAl BMG, which can predict the quasi-pressure inside the chamber under a certain range of velocities with acceptable accuracy.
1. Introduction Zr-rich metal alloy is a novel group of multifunctional energetic structural materials (MESMs) [1]. The Zr phase is combustible, can react with air to release high amounts of energy after impacting targets. Extensive studies have been performed to investigate the impact initiated reaction behavior of Zr-rich alloy [2–6]. Ren et al. performed dynamic compression tests of W/Zr alloys with split Hopkinson pressure bar (SHPB) platform, it was observed that W/Zr experienced violent reaction under shock-loading, while reaction products containing ZrO2 was observed on the residue surfaces [2]. The effect of impact velocity on the reaction behavior of W/Zr alloy was studied by using a quasi-sealed test chamber, the amount of released energy could be calculated quantitatively by measuring the pressure change inside the test chamber [3,4]. Wang et al. improved the design of the quasi-sealed test chamber for better accuracy, and investigated reaction behavior of Zr-based BMG under various impact velocities between 700 m/s and 1500 m/s [5]. The results showed that higher impact velocity led to higher reaction efficiency of Zr-based BMG. Huang et al. studied the impact response of Zr55Ni5Al10Cu30 alloy with a ballistic gun, it was indicated that Zr55Ni5Al10Cu30 alloy burned in the air according to the bright spark observation during impact [6]. Currently, the researches of reaction mechanism of MESMs have focused on energy releasing, widely neglecting the dynamic
⁎
fragmentation process [7–9]. Researches have been conducted to investigate the combustion times and temperatures, while the energy output of micron-sized metallic particles under shock-loading have not been well studied [10–13]. Actually, impact-initiated reactions of Zrrich metal alloy largely depends on the fragment size produced by loading impact. The small fragments generated from dynamic fragmentation with high temperature and large relative surface area are easy to combust and release energy in air, but the larger fragments even in hot state, due to the very small contact area with air, can not react and remain the original state after crushing. A similar pattern was gained by Ren at al on the W/Zr composites [2]. However, the reaction mechanism of MESMs associated with the theory of dynamic fragmentation has not been reported. This research was thus initiated to investigate the role of dynamic fragmentation on the reaction behavior of a Zr-based BMG. 2. Mateial and experiments The primary materials used in the study were commercial purity copper(99.9999% purity) plates, commercial purity nickel (99.96% purity) plates, commercial purity aluminum (99.9995% purity) bulks and commercial purity zirconium(99.7% purity) bulks. The primary materials were cut into small pieces by wire cut electrical discharge machining. Then the pieces were polished with SiC paper to remove the
Corresponding author. E-mail addresses: [email protected] (Y. He), [email protected] (C.T. Wang).
https://doi.org/10.1016/j.jnoncrysol.2019.04.022 Received 10 January 2019; Received in revised form 16 April 2019; Accepted 18 April 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.
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Fig. 1. Schematic illustration of the setup for quasi-sealed chamber test.
3. Results
surface oxide layers and weighed by high precision electronic balance according to the mass percentage. After that, the primary pieces were washed for 10–20 min by ultrasonic cleaning machine with alcohol to remove surface impurities and grease. The Zr55Cu30Ni5Al10 BMG (simply written as ZrCuNiAl BMG) was manufactured by arc melting and copper-mold vacuum suction casting. The ZrCuNiAl BMG was in form of rods with a diameter of 10 mm and height of around 60 mm. Generally, the cylinder samples with diameter of 10 mm and height of 10 mm were cut off from the BMG rod, the weight of each sample was around 5.4 g. An inert sample made of 45# steel with the same size and weight of around 6.1 g was prepared for comparison tests. The shock-induced fragmentation and reaction characteristics were investigated by means of a modified quasi-sealed test chamber. The schematic of the impact test is shown in Fig. 1. The quasi sealed chamber with volume of 20 L is made of hard steel and the inner diameter is around 440 mm. The quasi-sealed test chamber was sealed with a iron lid with thickness of 0.5 mm. A black powder ballistic gun was used to fire the samples into the test chamber. And the impact speed was controlled by adjusting the mass of black powder. The projectiles passed through the lid and impacted a steel target plate inside the chamber. The velocity of the samples was measured by a velocity measurement system at the shoot-line prior to penetrating the iron lid, which is very close to the target. Several sensors were placed in the test chamber to capture gas pressure change. Two series of impact experiments were conducted: Firstly, samples were shot into the chamber filled with air atmosphere to measure the over-pressure change inside the chamber caused by reaction; Secondly, in order to avoid the reaction of the BMG, the chamber was filled with argon to study the fragmentation of ZrCuNiAl BMG under impact loading. Argon was injected into the test chamber through the gas inlet valve as argon is denser than air. Meanwhile, the air was expelled through the gas outlet valve. This aeration process last about 10 min to ensure the chamber full of argon, then the two valves were closed to prepare for experiment. A box filled with argon was adjoined to the iron lid, which could prevent air from entering into the test chamber following the projectile. The fragments or reaction debris were respectively collected by an arc-shaped groove inside of the chamber. Scanning electron microscopy (SEM) equiped with energy dispersive spectrometer (EDS) was used to determine the morphology and element content of reaction products.
3.1. Reaction characteristics of ZrCuNiAl BMG subjected to impact under air atmosphere Impact tests were performed by shooting the ZrCuNiAl BMG specimens into the test chamber filled with air under various velocities. Fig. 2 shows the interior quasi-static pressure curves and video frames when ZrCuNiAl BMG specimens were hitting the target in air [5]. As Fig. 2a shows, the 45# steel caused moderate flash inside the chamber after impact due to donation of kinetic energy. Strong flash with venting of gas out of the chamber was observed after impact of ZrCuNiAl BMG samples, which indicated that the ZrCuNiAl BMG underwent chemical reaction in the air after impact. The pressure change inside the chamber was captured for each test. The over pressure curve contains two stages: the first stage is a blast pressure with duration of several micro seconds caused by impact process; the second stage is a quasistatic pressure with duration of several tens of milliseconds caused by kinetic and chemical energy [7–9]. The acquisition frequency of the data collector is 128 kHz in the pressure measurement system. In order to eliminate the noise, the quasi-static pressure can be obtained by filtering the original data with Matlab software, with a filtering cut-off frequency of 5000 Hz. After filter processing, the measured quasi-static pressure was plotted versus time, as shown in Fig. 2b. All the pressure curves increased dramaticly to a certain peak value after impact, and then dropped to zero gradually. Higher impact velocity led to higher peak value of quasi-static pressure inside the chamber. The debris generated by impact experiments was collected from the chamber and separated through varisized sieves. The morphology and composition of the debris are shown in Fig. 3. The SEM images indicate that the smaller debris with size less than around 20 μm are all sphere particles, the medium fragments (with size ranging from 20 μm to 220 μm) are mixed up with spherical particles and irregular debris, and there is almost no spherical fragment and all of them are irregular shape when the size is larger than 220 μm. In addition, the spherical particles are seen as hollow spheres from the enlarged photograph. The EDS results show that the irregular debris Zr, Cu, Ni, Al, with nearly none O, and the proportion of metal elements is similar to that of the Zr55Cu30Ni5Al10 bulk metallic glass. The spherical particles contain mainly Zr、O、Cu、Al、Ni and little Fe which may be derived from the steel target. Several conclusions can be drawn from the impact tests in air atmosphere: Firstly, the BMG specimen reacted with oxygen after impact, hollow spheres product was very possibly formed as a result of oxidation reaction. The process of reaction and cooling of fragments is short in time and small in scale, it is difficult to observe the spherical 150
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Fig. 2. The video frames and interior quasi-static pressure curves of steel and ZrCuNiAl BMG at various impact velocities in the air [5].
formation process. The material near the shear zone has a high temperature to form small droplets with a size of about ten microns instead of hollow spheres [14]. The hollow spheres are typical products of combustion and oxidation of micro metal powders. Similar hollow spheres products have been observed after combustion of Al, Ti and Zr [15]. Secondly, the impact formed debris with diameter < 20 μm underwent oxidation reaction, while the debris with diameter larger than 20 μm did not involve in reaction.
ZrCuNiAl BMG have similar shape like a power-law distribution. The slopes of the cumulative mass curves are from large to small with the increase of particle diameter. At a certain particle size level, the higher of the impact velocity, the higher is the cumulative mass value. This demonstrates that higher impact velocity tend to form smaller particle size of ZrCuNiAl BMG fragments after dynamic fragmentation.
3.2. Fragmentation of ZrCuNiAl BMG subjected to impact under Ar atmosphere
4.1. The critical fragment size related to the reaction of ZrCuNiAl BMG under shock-loading
Impact tests were also performed by shooting the ZrCuNiAl BMG specimens into the test chamber filled with argon under various velocities, aiming to study the effect of fragmentation on reaction behavior of ZrCuNiAl BMG by preventing oxidation after fragmentation. These tests were designed to study the distribution of debris of ZrCuNiAl BMG subjected to impact, as the oxidation react can be inhibited under Ar atmosphere. The debris was collected after impact tests and examined under SEM. As shown in Fig. 4, the debris consists of spherical particles and irregular shape fragments. The composition of spherical particles and irregular fragments are mainly Zr, Cu, Ni, Al, with nearly none O, according to the EDS results. As can be seen, the Zr-based BMG fragment did not experience oxidation reaction after impact in argon. The fragments produced by impact tests in argon atmosphere were separated through a series of sized sieving screens of different sizes and weighed within each size range by a high-precision electronic scale with an accuracy of 0.001 g. When the sample impact the target at a certain velocity, the fragmentation process and the debris forming mechanism is the same in argon and air. The difference caused by the different atmosphere is that: in air atmosphere, the debris will react with oxygen after impact due to its high temperature; in argon atmosphere, the formed debris will remain unreacted after impact. Therefore, the cumulative mass distribution of debris after impact in Ar atmosphere is used to quantitatively describe the fragmentation process of Zr-BMG samples. The result curves of cumulative mass distribution versus fragment size at different impact velocities in argon atmosphere are shown in Fig. 5. All the cumulative mass distribution curves of
Under loading conditions, fragments of different scales underwent various reaction phenomenon, described as “fire ball” “spark” and “no react” [2]. The energetic characteristics of HfZrTiTa0.53 alloy was studied by Zhang et al. with ballistic gun and armor chamber test [16], the results revealed that higher impact velocity brought around more severe fracture of the alloy and further lead to more violent reaction between the air and fragments causing more energy release. The expending ring experiments were designed in order to study the fragmentation process of three types of structural energetic materials [17], the results showed that the fragments generated by these MESMs are much smaller than those generated by ductile metals and combustion processes perhaps occur subsequent to the fragmentation process, however, the fragment combustion behavior was not well studied. The above studies have shown that the reaction of zirconium alloy under shock loading occurred after dynamic fragmentation and it was closely related to the fragment size. In this research, as the BMG projectiles hit the target anvil, cracks are generated and propagate rapidly inside the projectiles, which causes dynamic fragmentation of the BMG projectiles. In the air, the fragments dispread in the chamber and reacted with oxygen in the air. This combustion of Zr released heat and caused thermal expansion of the atmosphere inside the chamber. The expansion of the atmosphere finally led to a pressure change inside the chamber, which can be detected by sensors. As shown in Fig. 3, the SEM and EDS results indicate that not all of the ZrCuNiAl BMG debris reacted after impact in air atmosphere. Furthermore, the shock-induced reaction mechanism of
4. Discussion
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Fig. 3. Morphology and composition of the debris of ZrCuNiAl BMG specimen generated by the impact tests in air atmosphere, SEM images of products with different screening scales are (a) < 10 μm (b) 10–20 μm (c) 20–40 μm (d) 40–65 μm (e) 220–350 μm (f) 350–450 μm, (g) shows the elemental analysis of products.
4.2. A reaction model based on fragmentation of ZrCuNiAl BMG subjected to impact
ZrCuNiAl BMG was related to the particle size after fragmentation and a critical reaction size range was acquired. A schematic diagram of fragmentation and reaction process of ZrCuNiAl BMG subjected to impact is shown in Fig. 6. The small fragments (< 20 μm in size) produced by the BMG specimen could combust easily because of the large contact area with air. The large fragments (> 20 μm in size) did not react due to the small contact area with air and serious heat loss during flight. A similar pattern was gained by Ren at al about the W/Zr composites fragmentation and reaction [2]. Although there are many spherical particles in the medium fragments, the hollow structure is very possibly formed by ZrCuNiAl BMG debris with size smaller than 20 μm. Thus, 20 μm is taken as the critical size for the ZrCuNiAl BMG reaction with the air after impact. The fragments generated by dynamic fragmentation with diameter smaller than 20 μm are considered to react entirely in the air.
As for dynamic fragmentation of solids, the early seminal works were attributed to Mott et al. [18,19] The distribution of fragment size and the governing distribution length scale were predicted in the dynamic fragmentation theories by Mott. In subsequent work, Grady et al. developed the impact fragmentation theories to calculate the average fragment size and obtained the statistical distribution in fragment size by using of mechanics and energy balance methods [20,21]. In a recent study, Grady indicated that the energy-based fragmentation theory can be applied to describe nonequilibrium fragmentation mechanism of brittle materials [22]. The fragment distributions of brittle solids were observed to exhibit the power-law behavior required by the fractal nature of the breakup event other than the exponential distribution [23]. The characteristic fragment size λ governing the fragment distributions was determined by fracture properties of materials and ex• pansion strain rate (ε ) [22]. The characteristic fragment size λ can be 152
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Fig. 4. Morphology and composition of the debris of ZrCuNiAl BMG specimen generated by the impact tests in argon atmosphere, SEM images of products with different screening scales are (a) < 20 μm (b) 20–98 μm.
Γ=
(2)
where ρ is the density of the Zr55Cu30Ni5Al10 as 6.714 g/cm3, and E is the elastic modulus of the Zr55Cu30Ni5Al10 with the value of 81.6 GPa [24]. The value of the dynamic fracture toughness (Kc) is 50 MPam1/2 for calculation which is the average of 40–60 MPam1/2 obtained by Charpy impact test [25]. When a specimen impact the target right along the axis at normal incidence, a radial expansion strain rate is produced, which causes the radial dispersion velocity of the debris. The radial • expansion strain rate (ε ) is usually calculated via dividing the radial expansion velocity (vex) by the initial base radius of the ring or shell (r), • ε = vex / r , the expansion velocity is difficult to obtain but a strain rate representative for the impact velocity and sample size of the experiment can be approximated as it [23]. Hence the radial expansion strain rate • can be calculated as ε = vex / r ≈ v / h approximately, h is the height of specimen and v is the impact velocity. The characteristic fragment size, λ under various impact velocities can be calculated via solving Eq. (1) and Eq. (2). Fragment mass distribution is commonly described by a cumulative distribution function, instead of a probability density function, which is more sensitive to the fragment masses data scatter. In earlier theoretical studies, exponential functions were widely employed to determine fragment mass distributions [26,27]. Then, exponential distributions were found to be appropriate for predicting the dynamic fragmentation of ductile materials, however, highly brittle solids such as ceramic or glass were observed to be power-law [22,23]. The curves in Fig. 5 of cumulative mass distribution for ZrCuNiAl BMG approximately follows the shape of power function, hence the limiting form of Rosin-Rammler distribution attributed to Schuhmann is considered to describe the cumulative mass distributions of ZrCuNiAl BMG. It is assumed that the
Fig. 5. Experimental data of cumulative mass distribution for ZrCuNiAl BMG after dynamic fragmentation at different impact velocities in argon atmosphere.
expressed as 1/3
⎛ 48Γ ⎞ λ ≈ ⎜ •2 ⎟ ⎝ ρε ⎠
Kc2 2E
(1)
where Г is the fracture surface energy per unit area. The fracture energy is estimated by
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Fig. 6. Schematic diagram of fragmentation and reaction process of ZrCuNiAl BMG.
fragments are spherical, the total cumulative mass of fragments of equivalent diameter less than or equal to fragment diameter x in the form [28,29].
x k M (≤x ) = M0 ⎛ ⎞ ⎝λ⎠
(3)
where M0 equals to 5.4 g is the total mass of the test specimen before impact experiment. Commonly, the exponent k is not provided by the theory. In the Schuhmann relation ranges between around 0.5 and 1.5 according to empirical evidence [28]. Experimental observation suggests the range is 0.5 < k < 2.5 [22]. For the ZrCuNiAl BMG, it's also difficult to directly obtain the value of the index k from the experimental result plots because the error of individual data points will easily affect the results of the nonlinear fitting. Take the logarithm of both sides of the equation, and k is the slope of the linear function.
lg(M ) = k lg(x ) + lg
M0 λk
(4)
The function can be further constructed into a direct proportional function.
Y = kX
(5)
Y = lg(M ∗ λk / M0)
(6)
X = lg(x )
(7)
Fig. 7. Logarithm of characteristic fragment size normalized by cumulative mass of fragments plotted as a function of the logarithm of fragment diameter.
The exothermic energy of above chemical reactions are 1078.3 kJ/mol for Zr and 156.8 kJ/mol for Cu [30]. The mass of the ZrCuNiAl BMG fragments (≤20 μm in size) involved in the reaction at various impact velocities can be easily calculated by Eq. (3), then the amount of substance of zirconium in the reaction (n) can also be calculated according to the proportion of related elements of Zr55Cu30Ni5Al10. The chemical energy (ΔQ) released after dynamic fragmentation of ZrCuNiAl BMG can be calculated by the formula.
The experiment data of the relative cumulative mass and fragment size at different velocities are treated by the construction of logarithmic and proportional functions. The data points are shown in Fig. 7. The experiment data points processed by Eq. (4) and Eq. (5) are distributed near the direct line (y = 0.45x) unless the equivalent diameter of fragments is > 1 mm (that is lg(x) ≥ 0), for the reason that large irregular shape fragments cannot be assumed to be spherical and the error is inevitable. A k value of 0.45 ± 0.02 was obtained via data fitting for the ZrCuNiAl BMG. The character of the experimental distribution is in sensible agreement with the behavior predicted by the theory. The fragment distributions of ZrCuNiAl BMG are observed to follow power law in character and such trend was also predicted by the power function model about the ZrCuNiAl BMG dynamic fragmentation. Therefore, it is possible to calculate the mass of the fragments smaller than a certain size, by solving Eq. (1) to Eq. (7). The reaction of the ZrCuNiAl BMG mainly produced by the combustion of zirconium and copper occurs subsequent to the fragmentation process, aluminum and nickel of the metal glass are neglected because of their small content. The reaction equation of the combustion of zirconium and copper follows: Zr + O2 → ZrO2, Cu + 1/2O2 → CuO.
ΔQ = n × ΔH
(8)
As Fig. 2 shows, the quasi-static pressure inside chamber increased from zero to the peak value within tens of milliseconds. The chamber can be regarded as a closed system and heat losses are neglected during this short period. ΔE is the energy input of the BMG projectile including chemical energy (ΔQ) and a quarter of the kinetic energy (0.25Ek) [5], which is according to the results of inert fragment experiment.
1 M0 v 2 2
(9)
ΔE = ΔQ + 0.25Ek
(10)
Ek =
The peak quasi-static pressure (ΔP) for BMG projectiles can be expressed as [5]. 154
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Fig. 9. The proportion contribution of chemical reaction to the overall overpressure rise (ΔPQ/ΔP) plotted as a function of the impact velocity.
Fig. 8. Experiment and calculation of quasi-static pressure in the chamber versus impact velocity for ZrCuNiAl BMG in air atmosphere.
mair − n × Moxygen ΔE ΔP = ×R+⎛ − ρair ⎞ × R × T V × Cp V ⎝ ⎠ ⎜
to the over-pressure rise in the chamber within the velocity range of this study (750–1500 m/s). It is possible that a large part of the kinetic energy during impact is consumed by the crushing process, the formation of the fragments surface and vibration of the system. The proportion contribution of chemical reaction to the over-pressure rise decreases approximately linearly with the increase of impact velocity. One possible reason is that the reaction rate of the ZrCuNiAl BMG under shock loading increases slowly as the impact velocity increases, so the proportion contribution of chemical reaction to over-pressure decreases and the proportion contribution of kinetic energy to over-pressure increases. It is reasonable to expect that the proportion contribution of kinetic energy to over-pressure will be more significant when the impact velocity is beyond velocity range of this study (> 1500 m/s).
⎟
(11)
where ΔP the peak quasi-static pressures are the peak values in Fig. 2 obtained by experiments, Cp = 717 J/(kg·K) is the specific heat of air, V = 20 L is the volume of the chamber, Moxygen = 32 g/mol is the molar mass of oxygen, mair, ρair and T are the mass, density and air temperature prior to impact, respectively. The value of the gas constant R is about 287 J/(kg·K) inside the chamber. ΔPQ is the over-pressure in the chamber contributed by chemical reaction only. By solving the Eq. (10) and Eq. (11), it is possible to calculate the energy deposition when a BMG projectile is hitting target with a certain velocity. And finally, the peak pressure can be obtained by solving Eq. (11). Experiment data and a calculation curve of peak pressure in the chamber are plotted versus impact velocity for ZrCuNiAl BMG, as shown in Fig. 8. The peak pressure increased with increasing of impact velocity. The experimental data points are in acceptable agreement with the theoretical calculation within a certain range of velocities (900–1400 m/s), which demonstrates that the dynamic fragmentation plays an important role on the reaction of ZrCuNiAl BMG in shock process. The model above could be used to predict the quasi-static pressure (or energy) when a Zr-BMG is impacting the target at a certain range of velocities. This model could be very useful to predict the damage effect of a Zr-BMG projectile when it is hitting the target inside a sealed space. Detailed calculation results of the peak pressure value in the chamber under various impact velocities are listed in Table 1. Fig. 9 shows the proportion contribution of chemical reaction to the overall over-pressure rise (ΔPQ/ΔP) plotted as a function of the impact velocity. It is demonstrated that the over-pressure rise in the chamber is mainly caused by chemical reaction, the kinetic energy contributes a small part
5. Conclusions The dynamic fragmentation and reaction characteristics of ZrCuNiAl metallic glass was investigated by the quasi-sealed test chamber filled with argon and air, respectively. Several conclusions are drawn as follows: 1. The ZrCuNiAl metallic glass reacted with oxygen in the air after impacting the target, such reaction generated heat and caused significant over-pressure rise inside the chamber. 2. The fragment distribution of ZrCuNiAl BMG is following a power function similar as other brittle materials. The cumulative mass distribution of ZrCuNiAl BMG is significantly affected by the impact velocity (or strain rate). 3. A model was built based on dynamic fragmentation mechanism, this model could be used to predict the quasi-static pressure (or energy) when a Zr-BMG is impacting the target at a certain range of velocities with acceptable accuracy.
Table 1 The calculation of quasi-static pressure in the chamber under various impact velocities. v (m/s)
λ (mm)
M(≤20μm) (g)
Q (J)
ΔPQ (kPa)
ΔE (J)
ΔP (kPa)
750 850 986 1100 1200 1328 1500
2.573 2.367 2.144 1.993 1.881 1.758 1.621
0.595 0.618 0.647 0.668 0.686 0.708 0.734
5100.781 5297.719 5541.129 5727.692 5880.537 6063.724 6291.417
102.016 105.954 110.823 114.554 117.611 121.274 125.828
5480.469 5785.407 6197.361 6544.442 6852.537 7254.144 7810.167
109.077 115.156 123.372 130.296 136.444 144.460 155.561
Acknowledgements This work was supported by the National Natural Science Foundation of China [NSFC51601095] and the National Natural Science Foundation of Jiangshu China [BK20160832].
Declaration of interest statement None. 155
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Credit author statement
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