Combustion, Explosion, and Shock Waves, Vol. 38, No. 4, pp. 484 487, 2002
Spalling Kinetics over a Wide Range
of Shock-Wave Amplitude and Duration
V. A. Ogorodnikov1 UDC 532.593
Translated from Fizika Goreniya i Vzryva, Vol. 38, No. 4, pp. 119 123, July August, 2002.
Original article submitted September 13, 2001.
The paper reports results of metallographic studies of specimens of St. 3 steel and
<"
M1 copper loaded by shock waves of various intensity (p 2 30 GPa) and duration
=
<"
(� 10-6 10-7 sec). The kinetics of spalling fracture of materials under these con-
=
ditions is discussed.
Key words: metals, shock waves, fracture, kinetics, modeling.
It is commonly assumed that spalling fracture con- ters as the loading duration decreases (Fig. 1). A simi-
sists of the following stages: nucleation of defects, lar effect caused by a decrease in loading duration was
growth of the defects under tensile stresses, coalescence observed in specimens of 12Kh18N10T steel and PT-
of neighboring developed defects accompanied by for- 3V titanium alloy [11]. In this case, the characteristic
mation of a macrocrack, and delamination of the ma- impactor velocities for which defect nucleation was ob-
terial resulting in formation of free surfaces [1]. To served increase substantially with decrease in the thick-
construct a physicomathematical model for the fracture ness of the impactors. This is an experimental justifica-
process taking into account these stages, it is important tion of the statement that the stresses initiating smaller
to have information on the function of defect distribu- sites of fracture nucleation increase [12]. Furthermore,
tion in parameters characterizing the size, shape, and this is the most probable reason for a sudden increase in
orientation of defects [2 4]. This information can be ob- the spall strength of materials with decrease in charac-
tained by studying the state of tested specimens which teristic loading duration compared to quasistatic load-
were loaded by a shock wave (SW) of various ampli- ing conditions [13].
tude and duration before unloading and spalling frac- It is worth noting that the spalling fracture kinet-
ture. The results of metallographic and fractological ics has been studied, as a rule, for the cases where the
studies [5 9] show that over a wide range of tempera- SW front pressure amplitudes in specimen materials be-
tures (from -196 to 800ć%C), the nature of fracture of fore unloading were close to their dynamic yield points,
some metals is essentially the same as in the case of which, for example, for metals, do not exceed several gi-
static uniaxial extension. Based on this fact, Seaman et gapascals. To solve some practical problems, it is neces-
al. [3] used a kinematic model to describe spalling. sary to describe spalling phenomena for the case where
However, a spall fracture analysis for some met- unloading of materials is preceded by shock-wave load-
als and alloys, using geometrically similar  impactor ing with an amplitude of several tens or even hundreds
<"
target systems or for various loading duration (� of gigapascals. Therefore, to justify the applicability of
=
10-6 10-7 sec) shows that the fracture kinetics de- kinetic models of spalling, one needs information on the
pends on loading duration [10, 11]. For example, for fracture kinetics under exactly these loading conditions.
a characteristic duration � = (1 5) � 10-6 sec, frac- In this connection, of interest are the experimental stud-
ture defects, for example, in copper [10] are ellipsoidal ies of [14, 15], in which two boundaries of the spalling
pores with characteristic sizes of tens to hundreds of fracture zone of specimens of fixed thickness "specimen
micrometers oriented in the loading direction, whereas were determined. These boundaries correspond to sub-
for � d" 7 � 10-7 sec, the defects are spherical micropores stantially different pressure amplitudes at the SW front
whose characteristic size decreases to several microme- before unloading.
1
Russian Federal Nuclear Center, Institute of Experimental
Gas Dynamics and Physics of Explosion, Sarov 607190;
[e-mail].
484 0010-5082/02/3804-0484 $27.00 � 2002 Plenum Publishing Corporation
Spalling Fracture Kinetics 485
a b c d e
g
f h i
Fig. 1. Photographs of longitudinal microsections of specimens (�50): frames a e refer to copper specimens of thickness
15, 10, 5, 2.5, and 1.5 mm, respectively, frames f and g refer to 12Kh18N10T steel specimens of thickness 10 and 2 mm,
respectively, and frames h and i refer to specimens of PT-3V titanium alloy of thickness 10 and 2 mm, respectively.
the specimen was loaded by a gliding detonation wave
induced by a thin charge of a high explosive (HE) of
thickness "HE or by normal impact of a thin plate of
thickness "imp through a softening spacer of thickness
"spacer (or a thin HE layer). In both cases, for a cer-
tain ratio "HE/"specimen or "imp/("spacer+"specimen),
the SW decayed substantially in the specimen and its
reflection from the free surface produced the follow-
ing conditions for the absence or nucleation of spalling
in the specimen: �ten d" �sp (Fig. 2a). Under these
loading conditions, the lower boundary of the spalling
fracture zone was studied for small HE thicknesses
("HE = "low) and low pressure amplitudes at the SW
HE
<"
front (p plow).
=
With increase in HE thickness, the pressure ampli-
tude at the front of the SW that arrived at the free sur-
face of the specimen increased and macroscopic spalling
occurred in a certain cross section of the specimen.
Fig. 2. Diagrams of specimen loading: (a) near the
With further increase in "HE, the SW pressure pro-
lower boundary of the spalling fracture zone (p d"
file became nearly rectangular (Fig. 2b). In this case,
plower); (b) near the upper boundary of the spalling
the conditions for the absence or occurrence of spalling
fracture zone (p e" pupper); RW stands for rarefaction
in a specimen (�ten d" �sp) were formed for greater HE
wave.
thicknesses ("HE = "upper) and higher pressure am-
HE
<"
plitudes at the SW front (p pupper), i.e., the upper
=
We consider schematically two regimes of loading
boundary of the spalling fracture zone was studied un-
of a specimen by a shock wave with a triangular pres-
der these conditions.
sure profile (Fig. 2). The first regime occurred when
486 Ogorodnikov
a b cd
e g h
f
Fig. 3. Photographs of longitudinal sections of specimens: the top and bottom photographs refer to loading near the
lower and upper boundaries of the spalling fracture zone, respectively; frames a, b, e, and f refer to steel (�50) and
frames c, d, g, and h refer to copper (�100) in form bar (a, e, c, and g) and plate (b, f, d, and h).
Usually, in the literature, the spalling kinetics near recovered by smooth deceleration in sawdust. Then,
the lower boundary (in the sense mentioned above) has the specimens were cut, and their matallographic anal-
been studied. It follows from the reasoning given above ysis was performed. Figure 3 shows photographs of mi-
that taking special recovery measures, it is possible to crosections of steel and copper specimens made from
study the kinetics of spalling at the upper boundary. In bars and plates after loading near the lower and upper
this paper, we give results on the spalling fracture kinet- boundaries of the spalling fracture zone.
ics of specimens of St. 3 steel and M1 copper of thickness In steel specimens made from bars and loaded near
"specimen = 5 mm. The specimens were made from bars the lower boundary (plower <" 2 3 GPa), fracture de-
=
and plates and loaded by a plastic-bounded HE layer fects (sites) shaped like ellipsoidal pores with size of
(density 1.51 g/cm3 and detonation rate 7.8 km/sec) of several tens of micrometers are located in the direc-
various thicknesses in the regimes of gliding and nor- tion of tensile stresses or SW propagation direction of
mally incident detonation waves. The loading condi- (Fig. 3a). Under increasing load, these pores are con-
tions near the lower or upper boundary of the spalling nected by microcracks normal to the direction of load-
fracture zone were produced by varying the HE charge ing. When these specimens are loaded near the upper
thickness and by taking special measures, for exam- boundary (pupper <" 20 30 GPa), the fracture defects
=
ple, installing a screen on the outer surface of the HE are shaped like nearly spherical pores with diameter of
charge for gliding detonation or exciting a normal deto- several micrometers and are arranged as microflows di-
nation wave by an impactor. In the experiments, using rected along the tensile stresses and separated by a dis-
<"
manganin gauges, we measured the pressure profiles of tance � 100 �m (Fig. 3e). With further increase in
=
the SW arriving at the free surface of specimens and load, these defect microflows merge by means of micro-
checked constant strain rate in the plane of spalling cracks propagating normally to the loading direction.
<"
(� 105 sec-1). After loading, the specimens were
Ł =
Spalling Fracture Kinetics 487
For steel specimens made from plates and loaded 5. V. K. Golubev, S. A. Novikov, Yu. S. Sobolev, and
near the lower and upper boundaries of the spalling frac- N. A. Yukina,  Critical conditions for microdamage ini-
ture zone, the shape and size of defects are almost the tiation in a spalling metal, J. Appl. Mech. Tech. Phys.,
same as for specimens made from bars but their orienta- No. 4, 586 591 (1983).
tion changes. The defects are normal to the loading di- 6. V. K. Golubev, S. A. Novikov, Yu. S. Sobolev, and
N. A. Yukina,  Nature of fracture of aluminum and
rection and localized in a narrower zone (Fig. 3b and f).
its alloys D16 and AMG-6 in the temperature range
These special features are due to technological factors.
(-196) (+600)ć%C, Probl. Prochn., No. 2, 53 59
For copper specimens made from bars and plates
(1983).
and loaded near the lower and upper boundaries of the
7. V. K. Golubev, S. A. Novikov, Yu. S. Sobolev,
spalling fracture zone, the defects are shaped like nearly
and N. A. Yukina,  Nature of fracture of copper,
spherical pores with characteristic size of several tens of
nickel, titanium, and iron in the temperature range
micrometers (Fig. 3c, d, g, and h). The larger pores in
of (-196) (+800)ć%C, Probl. Prochn., No. 3, 78 84
specimens made from bars (Fig. 3c and g) are due to
(1983).
the coarser grains of this material. Moreover, a decrease
8. M. F. Ashby, C. Gandhi, and D. M. R. Taplin,  Frac-
in the pore size is observed in going over to the upper
ture  mechanism maps and their construction for f.c.c.
boundary of the spalling fracture zone (Fig. 3g and h).
metals and alloys, Acta Met., 27, No. 3, 699 729
The results obtained suggest that the spalling frac-
(1979).
ture kinetics of metals and their alloys depends on the
9. V. V. Rybin and V. A. Likhachev,  Statistics of mi-
individual properties of materials and shock-wave load-
crocracks at tough (cap-shaped) fractures, Fiz. Metal.
ing duration and rate. These factors should be taken
Metalloved., 44, No. 5, 1085 1092 (1977).
into account in constructing kinetic models for spalling
10. V. A. Ogorodnikov, A. G. Ivanov, V. I. Luchinin, et al.,
fracture.
 Scale effect in high-rate (spall) failure, Combust. Expl.
Shock Waves, 29, No. 6, 750 754 (1993).
11. V. A. Ogorodnikov, A. G. Ivanov, V. I. Luchinin, et al.,
 Effect of the scale and technological factors and pre-
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