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ReviewCite this article: Hazell PJ, Appleby-ThomasGJ, Wielewski E, Escobedo JP. 2014 The shockand spall response of three industriallyimportant hexagonal close-packed metals:magnesium, titanium and zirconium. Phil.Trans. R. Soc. A 372: 20130204.http://dx.doi.org/10.1098/rsta.2013.0204

One contribution of 11 to a Theme Issue ‘Shockand blast: celebrating the centenary ofBertram Hopkinson’s seminal paper of 1914(Part 2)’.

Subject Areas:materials science, mechanical engineering,mechanics

Keywords:anisotropy, texture, shock, spall

Author for correspondence:P. J. Hazelle-mail: p.hazell@adfa.edu.au

The shock and spall responseof three industrially importanthexagonal close-packedmetals: magnesium, titaniumand zirconiumP. J. Hazell1, G. J. Appleby-Thomas2, E. Wielewski3

and J. P. Escobedo1

1School of Engineering and Information Technology, UNSWCanberra at the Australian Defence Force Academy, UNSW Australia,Northcott Drive, Canberra, ACT 2600, Australia2Centre for Defence Engineering, Cranfield University, DefenceAcademy of the United Kingdom, Shrivenham, Swindon SN6 8LA,UK3Department of Physics, Carnegie Mellon University, Pittsburgh,PA 15213, USA

Magnesium, titanium and zirconium and their alloysare extensively used in industrial and militaryapplications where they would be subjected toextreme environments of high stress and strain-rate loading. Their hexagonal close-packed (HCP)crystal lattice structures present interesting challengesfor optimizing their mechanical response undersuch loading conditions. In this paper, we reviewhow these materials respond to shock loadingvia plate-impact experiments. We also discuss therelationship between a heterogeneous and anisotropicmicrostructure, typical of HCP materials, and thedirectional dependency of the elastic limit and, insome cases, the strength prior to failure.

1. IntroductionHexagonal close-packed (HCP) materials have seenincreasing use in structural applications. This has mainlybeen owing to their high specific strength relativeto traditional structural materials, but also owing tomore specialized properties, such as good resistance tocorrosion and a low absorption cross section for thermalneutrons.

2014 The Author(s) Published by the Royal Society. All rights reserved.

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This increased usage has led to a surge in research and development activities in the area ofHCP materials for structural applications. Research has primarily been focused on three mainelements and their alloys: magnesium, titanium and zirconium owing to their importance in theautomotive [1–3], aerospace [4–8], defence [9–14] and nuclear industries [15].

As a result, the previous deficit in understanding of the mechanical behaviour of HCPmaterials relative to face-centred cubic (FCC) and body-centred cubic (BCC) materials has beendrastically improved over the past 10 years [16]. Despite this, significant questions still remain—in particular with regards to how these materials behave under high strain-rate loading. Inparticular, there is a need to improve our understanding of the role of microstructure andcrystallographic texture during shock loading conditions to further exploit this unique classof materials.

Shock loading of materials (where the material is subjected to a discontinuity of stress in avery small time scale) invariably occurs through plate impact, explosive loading or by pulsedlaser. A good review of the various techniques available is provided by Field et al. [17]. Spallor dynamic fracture involves the generation of a plane of tensile damage within a dynamicallyloaded material; its effects can range from incipient spall where failure has just begun to break outto the creation of a detached spall plane. Measured spall strengths depend heavily upon loadingconditions [18,19]. There are a number of techniques that can be used to monitor the evolutionof spall inside materials. These include approaches to monitor the free surface of loaded systems,visual interferometer system for any reflector (VISAR), heterodyne velocimetry as well as usingembedded manganin gauges [20]. However, because such approaches monitor spall remote fromthe site of its evolution, the signal from the spall plane will inevitably evolve before detection,making interpretation of spall complex [18].

It should be noted that the contributing factors for materials spalling have been studied fordecades [21–27] and the phenomenon of spall was documented by Hopkinson [28]. Nevertheless,unlike FCC and BCC metals where the shock response has been reviewed [29,30], no such reviewexists for HCP metals. In this work, we focus primarily on three industrially important HCPmetals to review how they respond to shock and spall—with the addition of some recent resultsand analysis.

2. Overview of hexagonal close-packed materials

(a) Crystal structureThe distinguishing properties of magnesium, titanium and zirconium are a result of the uniquecrystallography of the HCP lattice structure. To highlight the hexagonal low symmetry of the HCPlattice, it is often represented by a hexagonal prism, as shown by the dashed lines in figure 1.However, the hexagonal prism is not a true unit cell and consists of three primitive unit cells,as shown by the bold lines in figure 1. The primitive hexagonal cell is described by the axesa1 = a2 �= c and by the corresponding angles α = β = 90◦ and γ = 120◦.

Assuming that atoms in the unit cell can be represented by hard spheres, the HCP crystalstructure has a close-packed stacking sequence of ABAB, with an ideal c/a ratio of 1.633. No puremetal has the ideal c/a ratio. The lattice parameters and c/a ratios of magnesium, titanium andzirconium are given in table 1.

A comprehensive review of the crystallography of the HCP lattice is given byPartridge [31].

(b) Plastic deformation(i) Crystallographic slip

As with most metals, magnesium, titanium and zirconium plastically deform principally bycrystallographic slip. The most commonly active slip systems observed in these materials are

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c

a2

a1

ab

g

Figure 1. Primitive hexagonal unit cell (bold lines) and hexagonal prism (dashed lines).

pyramidal

prismatic

·c + aÒ

·aÒ

a2

a1

basal

c

Figure 2. Slip systems in HCP magnesium, titanium and zirconium.

Table 1. Lattice parameters for magnesium, titanium [5] and zirconium.

material a (nm) c (nm) c/a

Mg 0.321 0.521 1.624. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Ti 0.295 0.468 1.586. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Zr 0.323 0.515 1.593. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table 2. Slip systems in magnesium, titanium and zirconium.

slip plane slip direction independent modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

basal (0002) 〈a〉 〈1120〉 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

prismatic {1010} 〈a〉 〈1120〉 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

pyramidal {1011} 〈a〉 〈1120〉 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

pyramidal {1122} 〈c + a〉 〈1123〉 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

listed in table 2, with a diagrammatic representation of the slip systems relative to the HCPprimitive unit cell and the hexagonal prism given in figure 2.

Broadly, the HCP lattice structure accommodates the easy glide of dislocations along the basal,prismatic and pyramidal planes in the 〈112̄0〉 directions, commonly referred to as 〈a〉 type slipsystems, as shown in figure 2. However, it has been shown that to accommodate compatibleplastic strains in a polycrystalline metal, a total of five independent slip systems are required[32,33]. Owing to the three easily activated 〈a〉 type slip systems having the same slip direction,they reduce to only four independent slip systems. Thus, to meet the criteria for compatible plastic

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c

a

a1

c

a1

a2

(a) (b)

Figure 3. Twinning systems in Zr, Ti and Mg. (a) {10 12} 〈1̄011〉 tensile twin and (b) {1122}〈1123〉 compressive twin.

Table 3. Twinning systems in magnesium, titanium and zirconium.

type K1 plane η1 direction K2 plane η2 direction

tension I {1012} 〈1011〉 {1012} 〈1011〉. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

tension II {1121} 〈1126〉 (0002) 〈1120〉. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

compression I {1122} 〈1123〉 {1124} 〈2243〉. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

compression II {1010} 〈1012〉 {1013} 〈3032〉. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

strains, a further non-〈a〉 type slip system must be activated. Typically, this is accommodatedby a so-called 〈c + a〉 type slip system, as shown in figure 2. However, it has been argued thatincompatible plastic strains in polycrystalline HCP metals can also be accommodated by theactivation of deformation twinning. Moreover, for some combinations of the loading axis andcrystallographic direction, twinning is the preferred mode for plastic deformation.

Crystallographic slip is driven by the shear stresses acting on a given slip plane. The shearstress required to activate a given slip system is referred to as the critically resolved shear stress(CRSS). The CRSS required to activate the different slip systems in magnesium, titanium andzirconium varies significantly depending on the temperature and composition of the material.However, generally, the CRSS of the 〈c + a〉 type slip system is higher than that of the 〈a〉 typeslip systems, leading to anisotropic plastic deformation behaviour at the single-crystal level. It iswell established that increasing the strain rate increases the CRSS by decreasing the time for agiven dislocation to overcome a barrier to its motion. At extremely high strain rates, the glide ofdislocations is further inhibited by mechanisms such as phonon drag [34,35].

(ii) Deformation twinning

Owing to the limited number of slip systems available in the HCP lattice, deformation twinningplays an important role in plastic deformation, and subsequently the ductility, of HCP materials[36,37]. Deformation twinning results in a reorientation of the crystal lattice around a given planeand in a given direction. This reorientation accommodates plastic strain and, more importantly,typically reorientates the crystal lattice for easier crystallographic slip.

The most commonly active deformation twinning systems observed in magnesium, titaniumand zirconium are listed in table 3, with a diagrammatic representation of example twinningsystems relative to the HCP primitive unit cell and the hexagonal prism given in figure 3.

Deformation twinning is particularly important at high strain rates, where it has been observedthat twinning becomes more prevalent [38].

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2.0Mg alloy F 4.03 mm

Mg alloy F 6.02 mm

Mg alloy F 9.95 mm

Mg alloy F 11.54 mm

Mg alloy T5 12.00 mm

1.8

1.6

1.4

long

itudi

nal s

tres

s in

PM

MA

(G

Pa)

time (µs)

gauge

Mg

allo

y

PMM

A

1.2

1.0

0.8

0.6

0.4

0.2

0

0 0.5 1.0 1.5 2.0–0.2

Figure 4. Shock propagation in Elektron 675 in the F (as fabricated) condition and the T5 (artificially aged) condition showingdifferent behaviour in the elastic precursor. (Online version in colour.)

3. MagnesiumCompared with other metals such as copper and aluminium, where there is a wealth of data ontheir shock behaviour, magnesium and its alloys have received relatively little attention. This isdespite their extensive application in the defence and aerospace industries [3,8].

(a) Shock response of magnesiumEarly work on the elastic–plastic response of a magnesium alloy was carried out by Fuller &Price [39]. They studied the shock behaviour of several metals including ZW3—a high strengthmagnesium extrusion alloy (Zn 3.0, Zr 0.6—wt%). They repeatedly observed a relaxation instress behind the shock front prior to the arrival of the release wave that they attributed to sliponly occurring on the basal plane. They reported a Hugoniot elastic limit (HEL) of 0.24 GPa forthis alloy.

Figure 4 shows the shock traces of a Mg alloy (Elektron 675—an alloy based on themagnesium–yttrium–gadolinium ternary system) that has been subjected to shock loading toa stress of approximately 2.9 GPa. The experiments were conducted by launching 10 mm thickAl plates at 500 ± 30 m s−1 that impacted the Mg specimens. Here, the shock stress is recordedby means of a calibrated manganin gauge (type LM-SS-025CH-048), electrically insulated by25 μm of Mylar, and sandwiched between the specimen and a plate of poly(methyl methacrylate)(PMMA).

On the left-hand side, the elastic precursor is seen to diminish as the thickness of the specimenis increased, whereas on the right-hand side of the trace, it is seen that the magnitude of the elasticprecursor is maintained for 12 mm. Notably, a ‘hump’ in the trace is visible as the elastic wave isreflected back off the plastic shock wave [40]. Precursor decay has also been observed in annealedbar-stock magnesium alloy such as magnesium MA2–1 [41]; indicative signs of precursor decayhave also been seen in the alloy AZ61 [42].

The principal difference between these two sets of results is the processing of each material.The four traces in the left-hand side were for an alloy that has not undergone heat treatmentand is in the F condition (as fabricated) by hot extrusion. Whereas the alloy on the right has been

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artificially aged (T5) leading to the precipitation of alloying elements. These precipitates act to pindislocations. Similar comparisons in behaviour have also been seen when comparing relativelypure forms of aluminium to that of alloys where the alloys such as precipitation hardened AA6061-T6 show little-to-no precursor decay [43,44], whereas relatively pure forms of aluminiumshow moderate decay [44,45]. Further, Winey et al. [46] showed that thin (less than 600 μm) 1050Al samples exhibited attenuation of the elastic precursor, whereas the AA 6061-T6 targets didnot. As discussed by Gray III [47], this Mg alloy compares in a similar manner to the previouslydetailed work and it appears that a coherent conclusion can be garnered on its behaviour. Thatis, the ageing and consequential precipitation hardening that increases the strength of the alloyalso hinders precursor decay. That is, hindering dislocation source activation and/or evolutionreduces the propensity for the elastic precursor to attenuate.

Owing to its relatively low melting point (649◦C), a modest increase in testing temperaturehas also been shown to affect the shock response of Mg, primarily the elastic precursor [48]. Forinstance, large values of the elastic precursor wave were observed at temperatures approachingthe melting point. This was also seen in Al [48]. This was attributed to the Frenkel disorder [49],i.e. spontaneous nucleation of point defects at the elevated temperatures from their normallattice positions to interstitial positions. Theoretically, the end result is increased resistance toactivation and motion of dislocations. However, it is not clear that this process would occurquickly enough to result in the observed strengthening during shock loading. Similar behaviourhas been seen in heated single crystals of aluminium where the cause of the strength increasewas attributed to phonon drag on dislocations [50]. It has also been seen in stainless steels [51].In this case, it was thought to be owing to the formation of relatively hard intermetallics at thegrain boundaries.

(b) Spall response of magnesiumExamination of the spall behaviour of various magnesium alloys has been of interest to anumber of researchers [52,53]—particularly at elevated temperatures [48,54,55]. Schmidt et al.[56] measured the spall strength of AZ31B-H24 and reported a value of 1.5 GPa for the onset ofincipient spall at room temperature. They reported a rapid drop in spall strength as the internalenergy was increased and approached 0.2 GPa at incipient melt. Similarly, the spall strength ofMg95 (99.95 wt% Mg) has been studied by Kanel et al. [48] at various initial temperatures. Inthis work, they showed that the spall strength dropped off as the temperature approached themelting point of the metal. Similar behaviour has been observed in magnesium alloys [41,57].Ordinarily, this might appear unsurprising. However, it is reported that when various metalshave been shocked to a high stress, and where the temperature increase approaches melt for thematerial (owing to shock heating), the spall strength remains unaffected [48].

Limited studies have been carried out on the microstructural effects on the shock and spallbehaviour of magnesium alloys. One of the more promising types of magnesium alloys forstructural applications are the rare-earth alloys. However, processing of rare-earth Mg alloysgenerally results in a heterogeneous and anisotropic microstructure. For instance, figure 5c showsthe microstructure of the Mg alloy Elektron 675-T5 where striations of relatively small grains(indicated by the arrows) are observed. These striations can affect both the spall strength and theHEL [58]. In a recent study, Mg alloy samples possessing the microstructure depicted in figure 5cwere shocked either along the extrusion direction or perpendicular to it. Figure 5a shows theeffect of the microstructural features of the alloy on its shock response; both the HEL and thespall strengths are lower in samples that were shocked perpendicular to the extrusion direction.Notably, their reload of the spall signal from the dip also appears sharper. This is indicative ofa faster rate of damage accumulation, presumably owing to a separation between the hardersmaller grains and softer larger grains. Similar to these findings, Rinehart in his seminal 1964paper [22] discussed the spalling of materials and structures such as laminates, highly texturedor rolled plates. In these cases, the heterogeneity acts as planes of weakness that can be separatedduring a tensile pulse.

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600

500

(a)

(c)

(b) 3plate-impact

samples

101–0

21–1–00001

1

extu

sion

dir

ectio

n

extu

sion

dir

ectio

n

300

400

200

100

free

sur

face

vel

ocity

(m

s–1)

T5-F1

T5-F3

0 2 4 6

100 µm

time (µs)

Figure 5. (a) Free surface velocity response of two Mg-alloy (T5 temper) targets shocked along the extrusion direction (T5-F3)and perpendicular to it (T5-F1), (b) location of where plate-impact samples originated and (c) orientation map of the virginmicrostructure indicating the columns of small grains. (Online version in colour.)

4. TitaniumTitanium alloys have been extensively used in aerospace applications owing to their highspecific strength and good resistance to corrosion. Despite these favourable properties, titaniumalloys have found limited use as monolithic armour materials, with high production costsand a propensity to fail owing to adiabatic shear banding/spall being limiting factors to theiradoption. However, new low-cost variants of traditional titanium alloys and advances in low-costproduction methods have resulted in renewed interest in titanium alloys for armour applications.

(a) Shock response of titaniumThe equation of state for the most widely used titanium alloy, Ti–6Al–4V, has been wellestablished by numerous studies using longitudinal stress gauges, with the HEL shown to varybetween 2.1 and 2.8 GPa [59–61]. It is well known that oxygen content significantly increases theyield strength of titanium alloys owing to the formation of coherent α2 particles [5,62]. Razorenovet al. [63] have studied the shock behaviour of three Ti–6Al–4V alloys of different oxygen contentsand measured a marked increase in the HEL with increasing oxygen content; the spall strengthappeared largely unaffected by increasing the oxygen content from 0.105% up to 0.24%. Moreover,Ren et al. [64] tested an extra-low interstitial Ti–6Al–4V and found that the HEL was 1.7 GPa,significantly lower than the previous results for Ti–6Al–4V. Again, it was concluded that this wasdue to the low oxygen content.

Hopkins and Brar inserted manganin gauges into sectioned discs of Ti–6Al–4V to investigatethe shear response of the material. They found evidence of shear-hardening with increasing shockstress [61]. Whereas Arrieta & Espinosa [65] investigated the effect of temperature on the HELand showed that the HEL decreased with increasing temperature; similar results were found byKruger et al. [66] for the titanium alloy Ti–6–22–22S.

Millett et al. [67] studied the effects of crystallographic texture on the shock response of Ti–6Al–4V by loading material with a strong texture in the longitudinal and radial directions. Novariation in the equation of state was found between the two conditions, but it was shown that

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the shear strength (again, by using embedded manganin gauges in sectioned targets) was lowerin the radial direction which was attributed to the orientation of the HCP unit cell relative to theloading direction.

Titanium and its alloys have been shown to undergo phase transformations during shockloading [53]. At high pressures, the HCP α-phase of titanium undergoes a martensitic phasetransformation to a new HCP structure, known as the ω phase, with a c/a ratio of approximately0.61 [68]. Owing to a large hysteresis, the ω phase is retained after the high-pressure loading isremoved [69]. This phase transformation was first observed by Jamieson [70] and has since beenextensively studied under various high-pressure conditions [68] and alloy compositions [71,72].During shock loading of high-purity titanium, Razorenov et al. [73] noted an anomalous shockwave structure at approximately 2–5 GPa, which was attributed to the α–ω phase transition.Arrieta & Espinosa [65] investigated the effect of temperature on the α–ω phase transition inTi–6Al–4V and found that increasing temperature suppresses the transition, but that increasingstrain rate had the opposite effect. Indications of phase transformations have also been seenin Ti–6Al–4V by Rosenberg et al. [60] and in α-Ti by Christman et al. [74] at around 10 GPa.More recently, Cerreta et al. [75] studied the role of oxygen content in the α–ω phase transition.It was found that the α–ω phase transition occurred at 10.4 GPa in the high-purity titanium,whereas the addition of 3700 ppm of oxygen completely suppressed the onset of the α–ω

phase transition.

(b) Spall response of titaniumThe spall strength of Ti–6Al–4V has been studied by Dandekar & Spletzer [76], Church et al. [77]and Tyler et al. [78], all of which report a marked increase in spall strength with increasing pulseduration, indicating significant microstructural and/or dislocation structure evolution during theinitial compressive loading stage.

Me-Bar et al. [20] investigated the spall strength of two Ti–6Al–4V materials with a well-developed bimodal microstructure and a lamellar microstructure. Post-experiment microscopyof recovered specimens showed that spall occurred by the nucleation, growth and coalescence ofvoids parallel to the main spall plane. It was suggested that they had nucleated simultaneously,owing to the similar size of the voids, with nucleation occurring at α grain boundaries inthe bimodal material and at the prior β grain boundaries in the lamellar material. It wassuggested that these voids grow and coalesce into facets, connected by intergranular andtransgranular shear or cleavage cracks. Microstructural analysis of recovered specimens byTyler et al. [78] showed that voids seemed to nucleate at the interface between the α and β

phase. Boidin et al. [79] also observed that voids nucleated at the interface between the α

and β phase in Ti–6Al–4V with a lamella-based microstructure. The voids were observed tocoalesce owing to highly localized plastic bridging between facets. Based on these observations,Boidin et al. proposed a two-stage fracture model consisting of an initial quasi-brittle failuremode (void nucleation), followed by a ductile failure mode (void growth and coalescence).Similarly, Arrieta & Espinosa [65] investigated the effects of temperature on the spall behaviourof Ti–6Al–4V, where it was shown that the spall strength reduced as the temperature increased.Post-impact microscopy on recovered specimens once again showed that spall occurred viathe nucleation of voids at the boundaries between α grains and propagated via coalescencethen bridging.

McDonald et al. [80] probed the three-dimensional nature of spall in Ti–6Al–4V using X-raymicrotomography and showed that the volume fraction of voids/cracks increased with increasingshock stress, but that the spall strength was effectively strain-rate independent.

As noted previously, crystallographic slip in HCP materials at a single-crystal (orgrain-by-grain) level is highly anisotropic, owing to 〈c + a〉 type slip having a higher CRSSrelative to 〈a〉 type slip. This results in the ease of activation of plastic deformation in agiven grain being highly dependent on its orientation relative to the loading conditions.Recently, Wielewski et al. [81] investigated the role of microtexture in the activation of

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(a) (b)

(c)

10 µm 10 µm

10 µm 10 µmTaylor factor

0 3

Taylor factor

rollingdirction

through-thickness

0 3

(d)

101–0

21–1–00001

101–0

21–1–00001

Figure 6. (a) High magnification orientation map of a void nucleation site; (b) a Taylor factor map of the same area; (c) lowmagnification orientation map of a void coalescence site; and (d) a Taylor factor map of the same area. (Online versionin colour.)

spall in Ti–6Al–4V by electron backscatter diffraction analysis of recovered specimens fromplate-impact experiments. Interestingly, it was found that voids nucleated at the interfacebetween plastically hard (high Taylor factor) and soft (low Taylor factor) α grains, shown infigure 6a,b. Further, it was shown that the hard/soft grain interaction sites could be foundat the corners of a facet that had formed via the nucleation and coalescence of voids, asshown by the circles in figure 6d. This closely mirrors the results of Dunne et al. [82,83] andRugg et al. [84] under fatigue loading conditions, where it was shown that facets nucleateat boundaries between plastically hard and soft α grains. This failure mechanism is yet tobe probed in other HCP metals. Notably, no twins were evident in the recovered plate-impact specimens, which was contrary to observations of the same material loaded in aTaylor test [38].

5. ZirconiumOwing to its relatively high ductility, good corrosion resistance and low absorption of neutrons,Zr has received considerable attention from a variety of industries. Thus, the number of studiesto understand the mechanical response of Zr subjected to various loading conditions is the mostprolific out of the three materials discussed herein.

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(a) Shock response of zirconiumOne of the primary areas of research in Zr subjected to shock loading is the investigation ofthe complex series of phase transformations with increasing temperature or pressure/stress. It isknown that Zr moves from the HCP α phase through a hexagonal with a three atom basis/hex-3ω phase to the BCC β phase at elevated pressures [85–87]. Greeff [86] established a high strain-ratephase diagram and Hugoniot equation of state which clearly illustrated the transition throughthese three phases. In particular, under shock loading conditions, zirconium has been observedto undergo an α–ω phase transformation across a range of pressures from 2.3 to 8.5 GPa. Thisphase transformation has also been shown to display a hysteretic behaviour. That is to say, highfractions of metastable ω phase are retained in specimens that were shock-loaded to stresses inexcess of the threshold for phase changes and then unloaded to ambient pressure.

Cerreta et al. [87] conducted a series of one-dimensional plate-impact experiments using asingle-stage gas-gun to impact Zr samples of 3 mm thickness. Via choice of one high-purity(35 ppm Hf; less than 50 ppm O) and two low-purity (350/14 000 ppm Hf and 390/1200 ppm O,respectively) metals, they were able to investigate the effects of interstitial oxygen on the shockresponse of Zr. They found that the α–ω phase transition increased from 7.1 to 8.3 GPa as theoxygen content increased from less than 50 to 350 ppm, with this transition entirely inhibitedfor an oxygen content of 14 000 ppm. This response was attributed to the fact that the oxygenatoms were located at octahedral sites within the HCP lattice rather than the tetragonal sites.Consequently, the presence of these large interstitial oxygen atoms displaced space within theHCP α-Zr lattice required for the α–ω phase transformation. Recent work by Rigg et al. [85] usedplate impact as well as a Z pinch machine to quasi-isentropically load similar Zr materials as thoseused by Cerreta et al. The α–ω phase transition was again observed to be heavily dependent onimpurity content, with no difference observed with regards to the stress at which this transitionoccurred with sample thickness. However, it was observed that the 1200 ppm O grade of Zrshowed a much more pronounced phase-change signal using the Z pinch machine than wheredata were gained by the plate-impact experiments.

In a more complex shock loading condition, Martinez et al. [88] and Escobedo et al. [89] studiedthe effects of high strain rates on a highly textured Zr via a series of impact experiments usinga modified Taylor cylinder system. Zr bullet-shaped projectiles were accelerated at velocitiesranging from 400 to 600 m s−1 and impacted into a steel anvil with a tapered central section, whichextruded the incident projectiles, inputting peak stresses of ca 3.5 GPa. Post-mortem examinationof recovered specimens showed that deformation occurred by a combination of slip and twinning,with the precise sequence of deformation mechanisms dictated by the initial texture. The endresult was a larger ductility exhibited by the material whose texture had the higher number ofreadily available slip systems.

(b) Spall response of zirconiumIn one of the most complete works available, Gray III et al. [90] have recently studied the effectof both crystallographic and microstructural anisotropy on spall in a variety of BCC and HCPmaterials. In particular, they undertook a study looking at incipient spall in crystalline Zr plate(clock rolled and annealed to produce an equiaxed ca 25 μm grain size with a strong basal texturealong the through-thickness direction of the plate). The Zr chosen was high purity, with only54 ppm of Hf and 40 ppm O, suggesting that the α–ω phase transition should occur at a stress ofaround 7 GPa. A 50 mm bore gas-gun was used to impact metallurgically pure 10 mm diametersamples of Zr encased in annular lower purity Zr rings. These samples were then nominally softcaptured in loose rags. A pair of shots was carried out at 330 m s−1 using Cu flyers (giving a peakstress of 5 GPa, below the expected phase change on this material) on samples cut both in-planeand transverse to the rolling direction of the plate. The resultant free surface velocity traces, shownin figure 7, were broadly similar. The main difference between the traces lay in the initial elasticbehaviour, with a more ramped response and higher HEL apparent in the through-thickness

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0.3

0.2 reloading

u fs (

mm

µs–1

)

0.1in-plane direction

through-thicknessdirection

00 0.4 0.8 1.2 1.6

time (µs)

Figure 7. VISAR profiles illustrating spall in two perpendicular directions in 10 mm diameter sections of clock rolled Zr plate.(Adapted from fig. 8 in Gray et al. [90].)

direction. The pullback signal seemed relatively unaffected by loading orientation; further, in bothcases, the subsequent reloading as the tensile releases reflected off the back of the spalled regionwas comparable with a two-stage response attributed elsewhere to elastic–plastic behaviour(figure 7).

Interestingly, as highlighted in figure 7, there are different reloading gradients for thetwo loading directions—suggestive of different spallation mechanisms. Chen et al. [91] havepreviously linked a ‘shoulder-like’ feature to a transition between ductile and brittle-like failure;this explanation has been adopted by several other authors [81], whereas others have put thisdown to the rate of damage accumulation [92,93]. This supposition is backed here by opticalmicrographs presented by Gray III et al. which showed a slight difference in tensile failure.In both the in-plane and transverse orientations, ductile voids were apparent. However, in thetransverse case, these voids had begun to coalesce with some microcracking apparent. This effectwas attributed to the textural differences in these two orientations, with the Zr behaving in a‘softer’ manner orthogonal to the transverse direction resulting in faster void coalescence.

These results tie in with recent work by the authors of this paper. Plate-impact experimentswere conducted on commercially pure 19 mm diameter Zr rod sourced from GoodfellowCambridge Ltd (UK) and of composition (in ppm): 2500 Hf; 1000 O; 250 C; 200 Cr; 200 Fe; 100 N;10 H. The relatively high oxygen content is necessary to preserve strength [94,95], but as discussedpreviously will likely have influenced any phase changes while under test. The supplied materialhad an equiaxed microstructure, with a grain size of ca 25 μm—broadly similar to that of the Zrstudied by Gray III et al. [90].

A series of five plate-impact shots were carried out with a 50 mm bore single-stage gas-gunusing approximately 50 mm diameter, 2.5 mm thick Al 6082-T6 flyer plates to impact 5.0 mm thicksections of the as-supplied Zr rod. This configuration was chosen such that spall occurred withinthe bulk of the material; typically, the spall plane formed approximately 1–2 mm from the rear ofthe target—allowing spall evolution, along with rapid transmission of reloading data. The freesurface of the Zr targets was monitored using a single heterodyne velocimetry channel. Resultantfree surface velocity traces are presented in figure 8a.

The general form of these traces is very similar to that observed in [90]. The HEL is clearlyapparent and appears to be relatively independent of the impact conditions. Applying the Zrmaterial properties (ρ0 = 6.506 g cm−3, cL = 4.77 mm μs−1) presented by Marsh [96], this HEL is

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0800

shock stress = 9.46 GPa

(a) (b)

–50

1.0 1.5 2.0 2.5

600

700 shock stress = 7.64 GPashock stress = 5.31 GPashock stress = 3.94 GPa

shock stress = 9.46 GPa

shock stress = 7.64 GPa

shock stress = 5.31 GPa

shock stress = 3.94 GPa

shock stress = 2.63 GPa

–100400

500

–200

–150

200

300

free

-sur

face

vel

ocity

(m

s–1)

free

-sur

face

vel

ocity

(m

s–1)

–250

100

0 1.0 2.0 3.0time (µs)

time (µs)

Figure 8. (a) Free-surface velocity histories for five plate-impact shots using a 2.5 mm Al flyer to impact 5 mm Zr targets and(b) variation of velocity drop with impact stress.

calculated to be 0.60 ± 0.02 GPa. For comparison, the HEL values extracted from [90] are 0.62and 1.24 GPa, for the in-plane and through-thickness directions, respectively. The in-plane HELmatches the value found along the extrusion direction of the Zr rod considered here withinexperimental error. However, the substantial differences in the HEL for the two directions clearlyillustrate the importance of microstructure and anisotropy with regards to the high strain-rateresponse of Zr—as previously discussed with Mg.

Of particular note in figure 8a is the relatively short duration of the velocity plateaus. Todiscount the influence of release waves from the periphery affecting the shock duration, acalculation of the time of release arrival from the radial periphery of the target was carried out.This calculation used the ‘worst-case scenarios’ of the elastic sound speed and a shortened releasepath assuming a sample with an 8 mm radius. This suggests that releases from the sample edgecould not arrive before an absolute minimum of 1.68 μs after impact (i.e. 0.5 μs in figure 8a); thisis significantly beyond the post spall-minimum reloading data in all cases.

The shapes of the pullback spall signals are shown in figure 8b. Overall, a linear decrease inpullback magnitude with increasing impact stress is apparent for the Zr rod tested here. To theauthors’ best knowledge, this strain-rate softening behaviour has not been explicitly highlightedfor Zr elsewhere; however, it is consistent (although more marked) with the known responseof other HCP materials such as Ti64 and a Mg alloy [58]. It is also interesting to note that thefree-surface velocity drop measured from figure 7 lies below the new experimental data (approx.155 m s−1). This is despite the similarities in the measured HEL values.

Optical micrographs highlighting the extent of damage around the resultant spall planes arepresented in figure 9; these micrographs are taken from the central section of the spalled targets.These micrographs clearly show the classical evolution of ductile voids, which coalesce withincreasing impact stress to form defined spall planes by the 544 m s−1 shot.

The amount of damage in the micrographs presented in figure 9 appears to increase withimpact stress up to an impact velocity of 5.3 GPa (figure 9c). Figure 9e shows evidence of voidcoalescence to form extended damage zones (indicated by the arrows); at 7.6 GPa, however,the spall damage appears more diffuse with less evidence of void coalescence (figure 9f ).Furthermore, this change in behaviour occurs at an impact stress between 5.3 GPa and 7.6 GPawhich is consistent with the observed α–ω phase change threshold of 7.1–8.3 GPa for Zr. Cerretaet al. [97] have shown that the hardness of shocked Zr increases substantially at stresses abovethe threshold for phase change. It is well known that high strength materials resist the growthof cavities during ductile spall [25,98], and thus it is possible that the harder ω phase inhibits thevoid coalescence and this may explain the reduction in damage evolution.

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400 µm 400 µm

400 µm

×150 100 µm ×150 100 µm

400 µm

(a) (b)

(c) (d)

(e) ( f )

Figure 9. Optical micrographs showing spall damage for shock stress: (a) 2.6; (b) 3.9; (c) 5.3; (d) 7.6 GPa. Scanningelectron micrographs of the spall damage at (e) 5.3 and (f ) 7.6 GPa. The shock direction in all micrographs is from bottomto top.

6. ConclusionWe have reviewed the shock and spall response of three industrially important HCP metals andtheir alloys, with emphasis on how microstructure and crystallographic texture affect the dynamicmechanical behaviour. The most salient features of their shock response are as follows. (i) Theoxygen content affects the stress threshold for both the elastic–plastic transition and the phasechanges. (ii) The commercially available materials exhibit a highly heterogeneous and anisotropicmicrostructure, which in turn causes a directional dependency of the elastic limit and, in somecases, the spall strength. (iii) For the case of Zr, the shock-induced phase change seems to alter thedamage evolution during spall.

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All these effects are inherently related to the processing of these materials. This leavesthe following questions open: can we tune the microstructure through commercial/industrialprocessing to optimize their mechanical behaviour under shock loading conditions? Specifically,can we tailor the oxygen content; generate an optimum amount of metastable high-pressurephases; minimize the morphological and texture anisotropy; and ultimately control the numberof ‘directionally’ hard and soft grains to increase the spall strength of these materials? If so, anincrease in the use of this unique class of materials for industrial applications that involve shockloading should be expected.

Acknowledgements. The authors thank Mr Andrew Roberts, Mr Adrian Mustey and Mr Stefano Cademartori forsupport in producing the experimental data used in this paper.

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