The dynamic compressive behavior of a hot pressed tungsten/zirconium (W/Zr) composite with a mass proportion of 34:64 (W:Zr) was experimentally investigated using a split Hopkinson pressure bar and a high-speed camera. The W/Zr composite has high strength but some brittle characteristics; when subjected to a strong enough impact loading, the sample is crushed, rapidly releasing high amounts of energy as a result. This impact-initiated reaction depends on the loading conditions, where a higher loading strain rate resulting a smaller fragment size. The Zr phase is involved in the reaction as the active component of the composite, and these fragments can be divided into small, medium, and large fragments with their reactions labeled as “fire ball,” “spark,” and “no react” respectively. A simple model is constructed to analyze the heat generated during plastic deformation based on yield stress, crack speed and the thermal properties of the brittle material. Our proposed model’s prediction of temperature increase at initiation may reach several hundred degrees Celsius.

Reactive materials that act as impact-induced energy materials are a new class of high efficiency damage materials with increased lethality. These reactive materials can crush, self-react or combust violently with air to rapidly release high amounts of energy under a strong impact loading due to the high temperature and pressure present, providing additional means of destruction.1–3 Reactive materials usually comprise two or more solid-state reactants, but unlike traditional energetic materials, these consist of thermites, intermetallics, metal/fluorine systems, metastable intermolecular composites (MIC), nano-laminates, and metal hydrides.2,4

Intermetallic-forming reactive materials are not only energy reactants, but can also act as structural components that can be applied to reactive liners and/or fragments. The most studied of these reactive materials are Al-based composite such as Al/Ni and Al/W owing to their high strength, high energy density, easy processing characteristics and rapid energy release properties.5–12 To improve their intercept efficiency, some high density reactive fragments have been proposed as alternatives to traditional steel fragments of anti-air warheads. For instance, tungsten/zirconium (W/Zr) composites have enough mechanical strength to maintain stability under overload during warhead detonation, and can penetrate targets and rapidly react. These fragments maintain their kinetic energy while increasing the damage capability, and ultimately improve the intercept efficiency.13,14 To date, most W/Zr research has concentrated on the formula, preparation methods, and ways to enhance the damage effects of warheads based on the impact initiation characteristics.15–17 However, studies of the relevant mechanical properties and reaction mechanism are seldom found in the literature. In this study, the mechanical properties of W/Zr composites are examined using a split Hopkinson pressure bar (SHPB) apparatus at different impact velocities.

The impact velocities used in these SHPB studies range from10–30 m/s at room temperature. The strain was measured by a strain gauge attached to the center of the sample surface. A high-speed camera (Photron FASTCAM SA5, USA) was used to record the impact and deforming process. The W/Zr composite used was prepared from an elemental powder of 34 wt% W (purity 99.9%, average particle size 3 μm) and 66 wt% Zr (purity 99%, average particle size 40 μm) using hot-pressing sintering; the resulting samples have identical initial dimensions of Φ2 mm × 2 mm with a density close to that of steel. In order to acquire accurate data, ramp loading was employed to facilitate a constant strain rate under dynamically equilibrated stresses using a copper sheet. To protect the end surfaces, two high-strength steel spacers with the same wave impedance as the bars were placed between the bars and the sample. A baffle plate was installed to reduce the influence of air flow from the barrel and experimental setup, as illustrated in Fig. 1. X-ray diffraction (XRD; Bruker D8 advance, Germany) and scanning electron microscopy (SEM; Hitachi S-4800, Japan) were used to determine the reaction products formed and investigate the failure mechanisms.

FIG. 1.

Schematic of experimental set up.

FIG. 1.

Schematic of experimental set up.

Close modal

In dynamic tests, reaction sparks can be observed as long as the sample is broken. The higher the applied impact velocity, the more violent the reaction. Fig. 2 describes a typical ignition process, where some samples react to produce a fire ball during impact experiments. The original state is shown in Fig. 2(a), at t = 0 ms. The sample then deforms upon strong impact loading and is rapidly crushed into smaller particles and pieces, with a large amount of sparks produced (Fig. 2(b) and Fig. 2(c)). Along with fragment ejection, micron-sized particle mixtures drift and dust clouds were formed in local spaces. When the concentration reaches a critical level, the heat generated during fragmentation was sufficient to ignite the dust cloud; the ignition point is indicated by the white circle in Fig. 2(c). Once the dust cloud begins to burn, a fire ball is produced and rapidly spreads from the center to the outside, as shown in Fig. 2(d) and Fig. 2(e). The most intense reaction state (Fig. 2(f)) involves a fire ball 10 mm in maximum diameter. However, when the concentration or temperature decreased rapidly, the combustion did not propagate further and gradually disappeared (Fig. 2(g) and Fig. 2(h)). At the end of the reaction, only some sparks could be observed, as indicated in Fig. 2(i) with white circles. In addition, Fig. 3 shows some high-speed images of a spark from generation until it finally dissipates. A luminous halo, likely caused by oxidation of Zr vapor, is present only in the initial stage of burning (Fig. 3(a) and 3(b)). A compact oxidation layer on the fragment surface is formed, preventing any further reaction due to its high melting point (∼2680 °C). The components of a fragment not only have different thermal expansion coefficients, but a high amount of internal thermal stress is generated in the fragment interior under high heat. These oxide layers will disrupt and provide a greatly reduced barrier to combustion, leading to violent “microexplosion” reactions (Fig. 3(c) and 3(d)).

FIG. 2.

Selected frames from a high-speed imaging sequence of ignition and propagation following a SHPB test at 23.53 m/s. A record rate of 30000 frames/s and shutter speed of 1/40000 s were used. The timestamp of each frame is measured from the start of deformation.

FIG. 2.

Selected frames from a high-speed imaging sequence of ignition and propagation following a SHPB test at 23.53 m/s. A record rate of 30000 frames/s and shutter speed of 1/40000 s were used. The timestamp of each frame is measured from the start of deformation.

Close modal
FIG. 3.

Still frame images of sparking during the combustion of a fragment in air. Times of each frame (measured from the first clear frame): (a) 0 μs, (b) 66.6 μs, (c) 100 μs, (d) 133.3 μs .

FIG. 3.

Still frame images of sparking during the combustion of a fragment in air. Times of each frame (measured from the first clear frame): (a) 0 μs, (b) 66.6 μs, (c) 100 μs, (d) 133.3 μs .

Close modal

The threshold of W/Zr impact reaction producing fire balls was examined based on the drop height method for analyzing the impact sensitivity of explosives.18 The impact velocity of the striker bar is controlled by the gas gun pressure, with samples tested by SHPB at different pressures Pi; i increases with each pressure step of 0.02 MPa. If the sample creates a fire ball, the next sample will be tested at Pi-1; otherwise, it will be tested at Pi+1. P50 is the gas gun pressure with a fire ball probability of 50% as shown in Eq. (1)

P50=[A+B(iCiD12)]
(1)

where A, B, and D are the lowest pressure of all 20 experiments, the increment of pressure between the two adjacent tests, and the total number of fire ball occurrences in all experiments, respectively. Ci is the number of fire ball occurrences at the corresponding pressure. The reaction states of the impact testing results are presented in Table I, in which “✓” denotes a reaction fire ball state, and “✗” denotes reaction sparks.

TABLE I.

Summary of SHPB test results.

Expt. No.
iPressure (MPa)Impact velocity (m/s)1234567891011121314151617181920C
0.04 10.67 ✗                    
0.06 14.55 ✗                    
0.08 17.39 ✗                    
0.10 20.00 ✗    ✗                
0.12 22.22  ✗  ✓  ✗    ✗           
0.14 23.53   ✓    ✗  ✗  ✗      ✗  ✗  
0.16 25.80        ✓    ✗    ✓  ✓  ✓ 
0.18 26.67             ✗  ✓      
0.20 28.57              ✓       
Expt. No.
iPressure (MPa)Impact velocity (m/s)1234567891011121314151617181920C
0.04 10.67 ✗                    
0.06 14.55 ✗                    
0.08 17.39 ✗                    
0.10 20.00 ✗    ✗                
0.12 22.22  ✗  ✓  ✗    ✗           
0.14 23.53   ✓    ✗  ✗  ✗      ✗  ✗  
0.16 25.80        ✓    ✗    ✓  ✓  ✓ 
0.18 26.67             ✗  ✓      
0.20 28.57              ✓       

The values in Table I were substituted in Eq. (1), and the calculated value of P50 is 0.15 MPa, which corresponds to a threshold velocity of approximately 25 m/s.

Fig. 4 shows a typical waveform for a pulse-shaped SHPB test with a strike velocity of 23.53 m/s. Note that the incident stress pulse is nearly a linear ramp (A-B) and the reflected strain pulse has a flat slope for about 20μs (C-D), which indicate that stress uniformity and a constant strain rate are achieved in the sample. Thus, the data obtained from the pulse-shaped SHPB experiment is valid, and the stresses and strains in the sample can be calculated using one-dimensional stress wave theory. Fig. 5 gives dynamic and quasi-static stress-strain data for the W/Zr samples, the compressive strength with an average strain rate of 600 s–1 is 2607 MPa, which is higher than in the quasi-static test (∼1860 MPa). The failure stain of the W/Zr composite exhibits a significant strain-rate hardening effect, but the values are still very small (less than 2%) and reveal that the composite is a typical brittle material. The dynamic Young’s modulus for this composite is almost the same as in the quasi-static results or approximately 186 GPa, indicating the absence of strain rate sensitivity.

FIG. 4.

Typical strain-time signals for a pulse shaped SHPB experiment with a W/Zr sample.

FIG. 4.

Typical strain-time signals for a pulse shaped SHPB experiment with a W/Zr sample.

Close modal
FIG. 5.

Compression stress-strain curves for W/Zr at quasi-static and dynamic strain rates.

FIG. 5.

Compression stress-strain curves for W/Zr at quasi-static and dynamic strain rates.

Close modal

The dominant factor influencing the fragment size is the loading strain rate, the higher the loading strain rate, the brighter the light because a more complete reaction occurs. Fragments with different sizes have different reaction behavior, as shown in Fig. 6. Cracks will propagate rapidly and form net-like patterns under strong impacts, greatly influencing the interfaces in the W/Zr composite and leading to sample disorganization and formation of numerous fragments. Smaller fragments (<100 μm in size) will easily ignite and sustain burning, reacting violently to form a fire ball. The maximum adiabatic flame temperature of Zr in air is approximately 3400 °C,19 and these fire balls can ensure targeted destruction but reduce hazards to innocent bystanders, due to having low kinetic energy and a small effective kill radius. Medium fragments (100200μm in size) will react by sparking, as shown in Fig. 3. Large fragments (>200 μm in size) will not react during the entire impact process, even in the hot detonation products, due to the very small contact area of the reactants and air, and significant heat loss during flight. These fragments will travel until they reach a solid surface and may react upon impact.

FIG. 6.

Fragmentation and reaction schematic for W/Zr composites.

FIG. 6.

Fragmentation and reaction schematic for W/Zr composites.

Close modal

In order to analyze the reaction mechanism of the W/Zr composites, some residues are collected after testing and examined by SEM and XRD. Fig. 7(a) shows a SEM image of the residues after quasi-static tests and a zigzag crack propagation path in the composite can be observed, which appeared in the crystal grains and along the grain boundaries. This observation implies that these interactions absorb the energy of crack propagation during fracturing. A similar crack can be observed in the residues after SHPB tests, as shown in Fig. 5(b). However, the difference between Fig. 5(a) and Fig. 5(b) is that the dynamic residues surfaces are covered with the powders, which are simply produced by the reaction between small fragments and air. Fig. 5(c) shows a relatively low magnification view of the dynamic residues morphology, where the surface is covered with more combustion product in a highly-porous sponge-like form. Some small spherical ZrO2 particles are also present, as indicated by the circles in Fig. 5(c), which formed from the melting oxide under high combustion temperatures and surface tension.

FIG. 7.

SEM micrographs of (a) residues after quasi-static testing, (b) residue after SHPB testing, (c) a relatively low magnification view of (b).

FIG. 7.

SEM micrographs of (a) residues after quasi-static testing, (b) residue after SHPB testing, (c) a relatively low magnification view of (b).

Close modal

Based on the analysis presented previously, the W/Zr composite is extremely brittle and susceptible to impact-induced reactions. It is well known that inelastic deformation occurs at the tip of a moving crack during dynamic fracturing, producing heat as a consequence.20 Here, heat at the crack tip as a mechanism for “hot spot” formation is used to analyze the impact-induced reaction phenomenon of W/Zr composites under SHPB testing. In the theoretical analysis, a simple model based on the slip-line theory and the J integral is used to predict the maximum temperature generated at the crack tip. If we assume that the crack velocity and heat-generation zone size are constant, then the crack propagation process can be viewed as a small thermal heat source fixed at the tip of the crack moving in the material (Fig. 8).

FIG. 8.

Sketch of the plastic zone and heat-production zone at a moving crack tip.

FIG. 8.

Sketch of the plastic zone and heat-production zone at a moving crack tip.

Close modal

If the loading rate is high enough, the crack tip conditions are nearly adiabatic and the temperature field T is given by

ρcT˙=ηW˙P
(2)

where ρ is the mass density, c is the specific heat and η is the work rate to heat rate conversion fraction (∼0.9 in metals).21 For small-scale yield at a stationary crack tip, Rice and Levy22 give the plastic work rate W˙P as

ω=3(1ν)2(2+π)(KI2τ0)2
(4)

where τ0 is the shear yield stress and G is the shear modulus. A polar coordinate system (r, θ) is chosen at the tip with θ=0 being the line ahead of the crack, ω is the maximum dimension of the plastic zone, ν is the Poisson’s ratio and KI is the far field stress intensity factor. Thus, the temperature rise near the crack tip at initiation can be predicted as

ΔT=3η(1ν)KI242(2+π)ρcGr
(5)

Weichert et al.23 estimated that half the width of the heat-production zone at the crack tip is δ2D/νc , and in this investigation we simply assume that the value of r is equal to δ. Here D=k/ρc is the thermal diffusivity, νc is the crack tip speed and k is the conductivity. We can use quasi-static fracture theory to determine KI since the samples are deformed nearly uniformly at a constant strain rate under dynamically equal stress until being crushed, with this value given by24,25

KI=2aτsinαπ(l+l0)
(6)
τ=12σsin2α12μ[σσcos2α]
(7)

where 2a and l are the length of initial micro-cracks and each tension cracks, τ is the shear stress on the pre-existing micro-crack, μ is the coefficient of friction and α is the angle between direction of tensile crack propagation and initial crack plane. Here l0 = 0.27a is estimated and σ can be directly obtained from the SHPB test.17,26 The maximum running speed of the crack (νcmax) is limited by the Rayleigh wave speed CR; in practice νcmax= 0.4 – 0.6 CR,27 and the detailed parameters for the composite used here are listed in Table II.

TABLE II.

Material parameters for heat calculation of W/Zr.

ρ (kg/m3)k (W/m K) νE (GPa)vc (m/s) 2a(μm)α (°) μ ησ (MPa)
8410 45 0.228 186 1100–1650 40 45 0.3 0.9 2450–2690 
ρ (kg/m3)k (W/m K) νE (GPa)vc (m/s) 2a(μm)α (°) μ ησ (MPa)
8410 45 0.228 186 1100–1650 40 45 0.3 0.9 2450–2690 

Pan et al. indicated that ramp loading typically produces valid SHPB experiments on brittle material at strain rates from 10–1000 s–1.28 In this investigation, the temperature increases presented in Fig. 9 are predicted as a function of strain rate (300–1000 s–1) with values predicted as high as 400–726 °C being clearly visible. We provide a curve fitting analysis based on the red-square experimental data, and this curve can predict the temperature within the scope of the upper limit of this strain rate range. Recent dynamic experiments on materials such as PMMA, 4340 steel and glass show high generated temperatures (102–103 °C), as shown in Fig. 10. For non-metal materials, the crack tip temperature increases with increasing brittleness. As W/Zr is a brittle alloy, the predicted temperature increases are slightly higher than that of Ti-10V-2Fe-3Al, 4340 steel and Beta-C Ti.29–34 Cooper et al.35 revealed that layers of Zr dust with particle diameters of 106μm can be ignited at 222 °C in air, indicating that Zr dust can react at lower temperatures owing to its large surface area. These fragments rapidly disperse in air with the high temperatures generated by dynamically propagating cracks. Within 2 ms (the time from beginning to ignition, Fig 2(a) and Fig 2(c)), the temperature will decrease only slightly. Thus, the combustible cloud formed by fine fragments can easily be ignited.

FIG. 9.

Calculated temperature of W/Zr as a function of strain rate.

FIG. 9.

Calculated temperature of W/Zr as a function of strain rate.

Close modal
FIG. 10.

Temperature increases at a moving crack tip in different materials.

FIG. 10.

Temperature increases at a moving crack tip in different materials.

Close modal

The impact-initiated processes of reactive materials are commonly analyzed using Taylor tests and chamber tests. However, in this paper we used a low-speed impact test platform-SHPB apparatus with a constant strain rate loading to accurately measure the mechanical properties of W/Zr composites and study the reaction mechanism present. Impact-initiated reactions depend on the loading conditions, which strongly influence the fragment size. The Zr as the reactive component of the W/Zr composite mainly reacted with oxygen, different from the Zr dust layer which combusts in air. Based on the assumptions that the crack begins to propagate and rapidly grows in a stable manner at high speeds, a simple model was developed to predict the maximum temperature of a crack tip generated during dynamically propagation. By setting a reasonable crack speed and other parameters, the predicted temperature could reach several hundred degrees higher than necessary to ignite the combustible cloud formed by the fine fragments.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11572049).

1.
N. N.
Thadhani
,
J. Appl. Phys.
76
,
2129
(
1994
).
2.
National Research Council
,
Advanced Energetic Materials
(
National Academies Press
,
2004
), Vol. 32.
3.
H. F.
Wang
,
Y. F.
Zheng
,
Q. B.
Yu
,
Z. W.
Liu
, and
W. M.
Yu
,
J. Appl. Phys.
110
(
7
),
074904
(
2011
).
4.
X. F.
Zhang
and
X. N.
Zhao
,
Chin. J. Energetic Mater.
17
(
6
),
731
(
2009
).
5.
D. E.
Eakins
and
N. N.
Thadhani
,
Int. Mater. Rev.
54
,
181
(
2009
).
6.
B. B.
Aydelotte
,
C. H.
Braithwaite
, and
N. N.
Thadhani
,
J. Phys.: Conf. Ser.
500
(
13
),
132001
(
2014
).
7.
D. E.
Eakins
and
N. N.
Thadhani
,
Appl. Phys. Lett.
92
,
111903
(
2008
).
8.
B. A.
Mason
,
L. J.
Groven
, and
S. F.
Son
,
J. Appl. Phys.
114
,
113501
(
2013
).
9.
K. L.
Olney
,
V. F.
Nesterenko
, and
D. J.
Benson
,
Appl. Phys. Lett.
100
,
191910
(
2012
).
10.
C. T.
Wei
,
E.
Vitali
,
F.
Jiang
,
S. W.
Du
,
D. J.
Benson
,
K. S.
Vecchio
,
N. N.
Thadhani
, and
M. A.
Meyers
,
Acta Mater.
60
,
1418
(
2012
).
11.
B. B.
Aydelotte
and
N. N.
Thadhani
,
Mater. Sci. Eng. A
570
,
164
(
2013
).
12.
X. F.
Zhang
,
A. S.
Shi
,
L.
Qiao
,
J.
Zhang
,
Y. G.
Zhang
, and
Z. W.
Guan
,
J. Appl. Phys.
113
,
083508
(
2013
).
13.
A.
Coverdill
,
C.
Delaney
,
A.
Jennrich
,
H.
Krier
, and
N.
Glumac
,
J. Energetic Mater.
32
,
135
(
2014
).
14.
G. T.
Liu
,
D.
Liang
,
W. T.
Zhao
,
W. Y.
Ge
,
T.
Liu
, and
M.
Chen
,
Ordnance Mater. Sci. Eng.
35
(
2
),
73
(
2012
).
15.
W.
Chen
,
W. T.
Zhao
,
J.
Wang
,
D.
Liang
,
W. Y.
Ge
, and
X. S.
Xiong
,
Ordnance Mater. Sci. Eng.
32
(
2
),
108
(
2009
).
16.
P. G.
Luo
,
Z. C.
Wang
,
C. L.
Jiang
,
L.
Mao
, and
Q.
Li
,
Mater Design.
84
,
72
(
2015
).
17.
H. L.
Ren
,
X. J.
Liu
, and
J. G.
Ning
,
Mater. Sci. Eng. A
660
,
205
(
2016
).
18.
W. J.
Dixon
and
A. M.
Mood
,
J. Am. Stat. Assoc.
43
(
241
),
109
(
1948
).
19.
C.
Badiola
and
E. L.
Dreizin
,
Proc. Combust. Inst.
34
,
2237
(
2013
).
20.
J. E.
Field
, “
Hot spot ignition mechanisms for explosives
,”
Acc. Chem. Res.
25
,
489
(
1992
).
21.
G. I.
Taylor
and
H.
Quinney
,
Proc. R. Sot. A
143
,
307
(
1934
).
22.
J. R.
Rice
and
N.
Levy
, “
Local heating by plastic deformation at a crack tip
,” in
The Physics of Strength and Plasticity
, edited by
A. S.
Argon
(
MIT
,
Cambridge, MA
,
1969
), pp.
227
293
(1969).
23.
R.
Weichert
and
K.
Schönert
,
J. Mech. Phys. Solids.
26
,
151
(
1978
).
24.
ASTM E24.03. 03
, “
Proposed standard methods of test for instrumented impact testing of precracked charpy specimen of metallic materials
,”
Draft 2d
(
American Society for Testing and Materials
,
Philadelphia, U. S. A
,
1981
).
25.
G.
Ravichandran
and
G.
Subhash
,
Int. J. Solids Struct.
32
(
17/18
),
2627
(
1995
).
26.
H.
Horii
and
S.
Nemat-Nasser
,
Phil. Trans. R Soc. A
319
,
337
(
1986
).
27.
K.
Ravi-Chandar
and
W. G.
Knauss
,
Int. J. Fract.
25
,
247
(
1984
).
28.
Y.
Pan
,
W.
Chen
, and
B.
Song
,
Exp. Mech.
45
(
5
),
440
(
2005
).
29.
K.N.G.
Fuller
,
P.G.
Fox
, and
J.E.
Field
,
Proc. R. Soc. Lond. A
341
,
537
(
1975
).
30.
J. T.
Dickinson
,
L. C.
Jensen
,
S. C.
Langford
, and
R. P.
Dion
,
J. Polym. Sci., Part B: Polym. Phys.
32
,
779
(
1994
).
31.
J. J.
Mason
, Ph.D. thesis,
California Institute of Technology
,
Pasadena
,
1993
.
32.
A. T.
Zehnder
and
A. J.
Rosakis
,
J. Mech. Phys. Solids.
39
(
3
),
385
(
1991
).
33.
J. A.
Kallivayalil
and
A. T.
Zehnder
,
Int. J. Fracture.
66
,
99
(
1994
).
34.
J. D.
Hogan
,
J. G.
Spray
,
R. J.
Rogers
,
S.
Boonsue
,
G.
Vincent
, and
M.
Schneider
,
Int. J. Impact Eng.
38
,
931
(
2011
).
35.
T. D.
Cooper
,
Review of Zirconium-Zircaloy Pyrophoricity
Rockwell International
, RHO-RE-ST-31P,
1984
.