Combustion, Explosion, and Shock Waves, Vol. 38, No. 2, pp. 239 247, 2002
Evolution of the Microstructure of Dynamically Loaded Materials
M. P. Bondar 1 UDC 539.3 + 621.7.044.2
Translated from Fizika Goreniya i Vzryva, Vol. 38, No. 2, pp. 125 134, March April, 2002.
Original article submitted April 24, 2001.
The paper deals with the evolution of the microstructure in materials after explosive
loading by the method of a hollow thick-walled cylinder. The materials considered
differ in the type of crystal lattice and initial state (grain size and initial defect
density). The role of crystal structure in the formation of the microstructure of
single crystals and coarse-grain copper specimens formed under explosive deformation
is investigated. The microstructures formed are compared with the corresponding
strains. It is shown that during high-rate deformation, fragmentation of the structural
elements occurs at all scale levels. The fragmentation mechanism and the associated
properties depend on the initial structure and state of the material. The special
features of the microstructure evolution in materials revealed in this work are taken
into account in producing new materials by dynamic and quasidynamic methods.
INTRODUCTION thick-walled cylinder [4]. Transformation of the struc-
ture formed under increasing strain is analyzed with the
Special features of the microstructure evolution
use of the experimental results obtained in this work and
with increase in strain under static loading are described
those published previously [4 8].
in [1 3]. The formation of structures during deforma-
tion depends on the type of dissipative processes. Being
an energy-nonequilibrium system, a body is deformed
1. THE EFFECT OF CRYSTAL STRUCTURE
in such a manner that the most effective channels for
AND INITIAL STATE OF A MATERIAL ON
energy dissipation are activated. The degree and mech-
THE STRUCTURE EVOLUTION UNDER
anism of the dissipative processes and the formation of
DEFORMATION BY EXPLOSIVE
dissipative structures depend on the initial structure of
LOADING USING THE METHOD OF
the materials being deformed. Special features of the
HOLLOW THICK-WALLED CYLINDER
microstructure evolution under increasing strain and
dynamic loading have not been studied systematically,
To study the formation of a structure under high-
in particular, because of the variety of the experimen-
rate deformation, we used materials with different crys-
tal conditions, which makes it difficult to identify the
tal lattices: Cu with a face-centered cubic lattice (FCC),
results obtained. Extensive studies in this field are of
Ta with a body-centered cubic lattice (BCC), and Ti
considerable importance for both developing the theory
with a hexagonal close-packed lattice (HCP). The ini-
of plastic strain and designing new materials by quasi-
tial structures of the materials differed in defect density
dynamic and dynamic methods.
and grain size d (single crystal of Cu and polycrystal
In this work, we studied the microstructure evolu-
structures with d = 1000 and 30 �m for Cu, d = 60
tion and the critical parameters of unstable plastic flow
and 40 �m for Ta, and d = 140 and 25 �m for Ti).
(�r) in materials with different types of crystal lattice
High defect density was produced by plane-wave
and different initial states (grain size and initial defect
shock loading [6]. A distinguishing characteristic of
density) after explosive loading by the method of hollow
this loading is that it leads to high density of randomly
distributed defects, mostly dislocations, with residual
1
Lavrent ev Institute of Hydrodynamics, Siberian Division,
strain lower than 5%. High-rate deformation by ex-
Russian Academy of Sciences, Novosibirsk 630090;
[e-mail]. plosive collapse of a hollow thick-walled cylinder [4] al-
0010-5082/02/3802-0239 $27.00 � 2002 Plenum Publishing Corporation 239
240 Bondar
TABLE 1
1
Material d, �m State �r
Unhardened 0.26 0.30
1000
Hardened 0.6 0.7
2
Cu
Unhardened >2
30
Hardened 
Unhardened 1.2
60
Hardened 1.01
Ta 4
Unhardened >1.5
40
Hardened 
Unhardened 0.59
140
Hardened 0.3
3
Ti
Unhardened 0.22 0.26
25
Hardened <0.17
Fig. 1. Microstructure of collapsed single-crystal
specimens (�50).
lowed us to compare strains with the corresponding mi-
crostructures formed over a wide range of strains.
A common feature of all the collapsed materials is In the case of explosive loading, where stresses exceed
that collapse of the cylindrical cavity is accompanied the value of �max, the activity of slip systems depends
by localization of the strain, which degenerates into a weakly on m. Whether slip traces are present or absent
system of cracks near the central part of the specimen in the plane of a metallographic section depends on the
[4 9]. The strain �r attained before the onset of local- angle they make with the (134) plane. The center of
ized plastic flow are listed in Table 1 for the materials the section is the point of intersection of the directions
considered. [128Ż [2443], and [62Ż which are the medians of the
3], 3],
In these experiments, copper single crystals shaped (134) plane and coincide with the direction of the radial
like tubes of inner diameter 11 mm and wall thickness load for collapse of the cylinder. The minimum angle
3 mm were subjected to collapse. The single crystal equal to 16ć% is made by intersection of the [128Ż di-
3]
was oriented in such a manner that the axis of the tube rection  cylinder radius (position 1 in Fig. 1)  with
(cylinder) was directed along the [134] crystallographic the close-packed direction [Ż The [128Ż direction
110]. 3]
direction. Figure 1 shows shear bands in the metallo- is close to the [110] angle of the stereographic triangle
graphic section that coincides with the (134) crystal- and determines multiple slippage. For close-packed slip
lographic plane. The distinct symmetry of the shear systems (1Ż [Ż and (Ż [101], the Schmid factor
11) 101] 111)
bands is seen. Some of the bands reach the outer sur- reaches maximum values (0.39 and 0.48, respectively)
face of the crystal, and there are bands whose origin is relative to the [128Ż direction and the corresponding
3]
located within the surface of the metallographic section planes make minimum angles (25ć% and 48ć%) with the
or near the cavity center. In addition, there is a sector (134) section. For these reasons, the traces of the slip
in which localized shear bands are absent. systems belonging to the (1Ż and (Ż appear as two
11) 111)
It is known that in static tests, shear occurs over families of bands directed at different angles to [128Ż
3]
close-packed slip systems, i.e., planes and correspond- (position 1 in Fig. 1) with their origin located on the pe-
ing directions in these planes. For FCC copper, these riphery of the single crystal. The other shear bands refer
systems are planes of the type (111) and directions of to the directions of slip systems relative to the loading
the type {110}. In this case, the priority in the activ- directions that determine single slip. In the metallo-
ity of the slip systems depends on the reduced shear graphic section, they are located at different distances
stress � determined by the Schmid factor m, which is from the center and are easily identified in accordance
equal to the product of the sine of the angle between the with the crystallographic orientation of the single crys-
loading direction and the close-packed plane into the tal. One can see from Fig. 1 that the density of the
cosine of the angle between the loading direction and shear bands increases toward the center, which is deter-
the close-packed slip direction lying in this plane. For mined by the geometry of loading. As the shear bands
the maximum reduced stress (�max), m is equal to 0.5. merge, their width increases and they become cracks.
In Fig. 1, one can see traces of almost all close-packed There is a sector (4) in which shear bands are absent in
slip systems, which is a result of axisymmetric loading. the metallographic section. The location of shear bands
Evolution of the Microstructure of Dynamically Loaded Materials 241
Fig. 2. Shear macroband in the collapsed specimen
from coarse-grain copper (�50).
in the adjacent regions (2 and 3) determines the rigid-
�m
3
body motion of the sector toward the center, which is
seen in Fig 1.
Thus, the single crystal is fragmented by shear Fig. 3. Intragranular block structure in collapsed
fine-grain copper specimens.
bands, which develop in close-packed systems according
to the crystallographic orientation of the single crystal
<" <"
relative to the direction of applied stresses. Near the ranges � 0.1 3 and � 104 105 sec-1, the formation
= Ł =
cavity of the collapsed specimen there are narrow re- of the microstructure is determined mainly by the rela-
gions of the recrystallized structure. These regions are tionship between the processes occurring at the micro-
arranged irregularly in accordance with the inhomoge- and mesolevels. Observation of the microstructure on
neous shear-band pattern. a scanning electron microscope shows that the defor-
In coarse-grain copper specimens (d = 1000 �m), mation is uniform within each grain of the collapsed
localized shear bands appear at different distances from fine-grain specimen. Each grain is divided into blocks
<"
the center of the collapse; in some grains they appear of size 1 �m (Fig. 3). The change in the orientation of
=
in regions where �r <" 0.26 (Fig. 2). As the strain in- the block structure from grain to grain is compensated
=
creases, localization bands appear in other grains. This for by intermediate adjustment of conjugate blocks, as
is responsible for the saw-tooth boundary of the begin- can be seen from Fig. 3 (three grains are shown). The
ning of development of shear strains relative to the cen- highly homogeneous block structure in each grain with
ter of collapse. Harren et al. [3] determined �r for single a small scatter in the size and direction of the blocks
crystals of an Al 0.5% Cu alloy of various orientations and compensated transition into adjacent grains indi-
subjected to plane static compression: �r = 0.26 0.95. cate that the plastic flow is stable. Resistance to rota-
The values of �r obtained in our tests on coarse-grain tions at the grain contacts leads to heat release, which
copper are in the indicated range. Shear bands are favors dynamic recrystallization. The latter is respon-
formed in individual grains with different values of �r, sible for a decrease in the average grain size from 30 to
which is explained by their orientation relative to the 22 �m in the region of 0.3 < � < 0.7. Near the cavity
plane of the metallographic section. This was shown surface, where deformation is most severe (� > 0.7 and
above in considering the formation of a microstructure � increases), the grains are extended toward the cen-
Ł
in a single crystal. The beginning of the macroband ter [4]. This shows that as the strain rate increases (and
depends on the extent to which neighboring grains are hence, the duration of the process decreases), a grain of
disoriented with respect to one another and to the radial size 30 �m can no longer be a structural element that
load. As the strain increases, the macrobands formed in implements the rotational mode of deformation. Un-
coarse-grain specimens propagate along a slightly bro- der these conditions, texturing proceeds actively. This
ken line toward the center of the collapse. During prop- is supported by the results obtained in [5], where it is
agation, the macrobands are deflected from the radial shown that during explosive welding of internally oxi-
direction, and in some places they leave the plane of dized copper plates with a fine-grain structure (30 �m),
metallographic section (see Fig. 2). a strong melt-free bond is formed at the contact sur-
In collapsed specimens of fine-grain copper (d = face for high velocity of the contact point under col-
30 �m), no localized plastic strain bands were de- lision (>1.5 � 107 sec-1). The velocity of the contact
tected [4]. Near the central cavity there is a recrys- point depends directly on the strain rate at the contact
tallized microcrystal structure indented by thin radial boundary. The bond is formed owing to the developed
cracks. The transformation of the microstructure in compatible strain for spreading grains. During welding
copper with variation in grain size indicates that in the of plates with a coarse-grain structure, no strong bonds
242 Bondar
TABLE 2
r, mm ("a/a) � 103 D, �m r, mm ("a/a) � 103 D, �m
Action
Copper Tantalum
Shock-wave
 1.42   0.94 
loading
Shock-wave 1 3 0.95 0.11 1 3 0.94 0.11
loading and collapse >5 0.35 0.6 0.15 0.18 >5 0.75 0.15
Collapse without 1 3 0.7 0.2 1 3 0.11

preloading >5 0.3 0.6 0.22 >5 0.11 0.15
Notes. r is the distance from the center of the cylinder, ("a/a) � 103 is the variation in the lattice
parameter, and D is the size of the blocks.
are formed under these conditions because of the early tively large strains [7]. The formation of block structure
development of localized-shear bands accompanied by in these materials (see Fig. 3), was supported by studies
melts and cracking on the contact boundaries. of changes in the residual microstrain of the crystal lat-
In materials with 30-�m grains, the absence of in- tice and in the dispersity of the intragranular structure
stability of plastic flow can be explained by the fact that after all types of loading by analyzing x-ray diffraction
for the loading parameters used, a grain of size 30 �m line broadening. The results are given in Table 2.
itself is the structural element that implements the ro- Microstrains are determined by randomly dis-
tational mode of deformation. tributed defects of the crystal lattice, and the dispersity
The presence of localization bands in coarse-grain of the block structure characterizes the number of sub-
copper for �r = 0.26 is evidence of translation instability boundaries which are sufficiently disoriented that neigh-
at the microlevel. boring regions of the crystal participate incoherently in
In collapsed BCC-tantalum specimens with a grain the dissipation.
of size 60 �m at �r = 0.65, closely spaced shear-strain Preliminary loading, which led to the development
bands are observed in some grains [6]. The deformation of the substructure during the subsequent collapse, is
proceeds in such a manner that in some grains, slip responsible for delay of strain localization to large val-
bands make up a grid to form mesovolumes consisting ues of �r in both coarse- and fine-grain specimens (see
of several grains. The initial direction of the grid sides Table 1).
coincides with the direction of maximum shear strains. The special features of formation of the structure
As the strain increases, the grid sides become closer in titanium with an HCP lattice differ markedly from
to each other and the mesovolumes are distorted. For those established for FCC copper and BCC tantalum. A
�r = 1.2, the bands developed in separate grains merge characteristic feature of titanium is that localized shear-
into macrobands, which radiate through many grains strain bands are adiabatic-shear bands [8]. In coarse-
toward the center; for � = 2, the macrobands become a grain titanium, these bands are formed for �r = 0.59;
system of cracks. in fine-grain titanium, they are formed for �r = 0.22
In collapsed specimens with grains of size 45 �m, (see Table 1) [8, 9]. Figure 4 shows the microstruc-
neither a structure developed at the mesolevel nor mac- ture evolution in coarse-grain titanium with increase in
robands of strain localization [6] were detected; as in the strain, which is manifested in an increase in the twin-
case of fine-grain copper, a system of cracks is formed ning density. Fragmentation, which occurs mainly by
in the neighborhood of the central cavity. twinning, does not determine uniform deformation at
Fragmentation of the structure in copper and the microlevel. In collapsed pre-hardened specimens
tantalum becomes more pronounced after preliminary of coarse-grain and fine-grain titanium, adiabatic-shear
shock-wave loading, which increases the defect density. bands are formed for �r = 0.3 and �r < 0.17, respec-
The defect structure formed by shock-wave loading de- tively.
termines the conditions under which an intragranular Thus, the value of �r decreases as the degree of
block structure is formed under subsequent plastic de- imperfection in the structure of titanium increases due
formation. The block structure developed ensures uni- to a decrease in grain size and due to the density of the
form deformation in prehardened specimens to rela- defects formed by preliminary shock-wave loading.
Evolution of the Microstructure of Dynamically Loaded Materials 243
a b
2 �m 2 �m
c d
2 �m
2 �m
e f
2 �m
2 �m
Fig. 4. Change of the twinning microstructure in collapsed specimens of coarse-grain titanium versus strain:
� = 0.17 (a), 0.18 (b), 0.19 (c), 0.5 (d), 0.59 (e), and >0.59 (f) (microstructure between adiabatic-shear bands
with microcracks).
244 Bondar
Fig. 5. Microhardness versus strain along the radii of collapsed cylinders, for single crystal: curves 1 4 refer to the
positions 1 4 shown in Fig. 1; for polycrystalline copper and titanium, curves HV0, HVh, HVc, and HVh+c refer to
the microhardnesses of the initial, prehardened, collapsed, and collapsed prehardened specimens, respectively.
The evolution of the deformation microstructure shear bands, the microhardness varies slightly with in-
with increase in strain is traced by variation of the mi- crease in strain, and the region of position 4 moves as
crohardness HV along the radius of collapsed specimens. a rigid body toward the center. The motion of this
The microhardness is measured along a broken line in position is determined by the location of shear bands
such a manner that the projections of the prints onto in adjacent regions. The region of position 1 refers to
the radius close up with one another. Figure 5 shows the neighborhood of radius [128Ż where deceleration
3],
the dependence of microhardness on strain for coarse- is caused by counter shears. In this region, the curve
and fine-grain titanium subjected to different actions. of HV(�) is similar to the curve of �(�) [10] and it is of
For comparison, curves of HV(�) for copper specimens a multistage nature typical of single crystals. Curves 2
are also shown in Fig. 5. and 3 refer to the regions located between positions 1
Of interest are also the curves of variation of mi- and 4.
crohardness along the radii of collapsed single-crystal For titanium, curves of HV(�) (see Fig. 5) show that
specimens that refer to regions with the characteristic each loading stage contributes to hardening. Curves of
pattern of shear bands. It is clear that for a single variation of microhardness for specimens that collapsed
crystal, the shape of the curves HV(�) is determined after prehardening (HV ) show relaxation structures
h+c
by the special features of strain variation in different most clearly. In the deformation of coarse-grain tita-
positions of the cross section (Fig. 1): position 4 dif- nium, the quantity HV initially decreases somewhat
h+c
fers from position 1 in that it refers to a sector without relative to the microhardness of pre-hardened specimen
Evolution of the Microstructure of Dynamically Loaded Materials 245
HV owing to the beginning of intense twinning [9], 2. PRODUCING A STRONG
h
which produces relaxation structures. After the limiting MICROCRYSTALLINE MATERIAL
density of twins is attained for � = 0.3, and with further BY THE QUASIDYNAMIC METHOD
increase in strain, the values of HV exceed HV . For
h+c h
specimens of fine-grain titanium, HV > HV over the It was shown above that during high-rate severe
h+c h
entire range of �.
plastic deformation, fragmentation of the structure oc-
For copper specimens, the relationship between
curs most actively in FCC materials with highly imper-
HV and HV is different [4]: curves of HV are
fect initial structure upon reaching values � = 0.3 0.7.
h+c h h+c
lower than curves of HV (see Fig. 5) for all values of �.
We used these results to produce a material from chips
h
This is most pronounced for fine-grain copper.
of internally oxidized Cu 0.4% Al alloy based on FCC
For high-rate deformation, the degree of harden- copper. The structure of internally oxidized copper al-
ing [increase in HV(�)] and the values of parameters
loys is highly stable [11], which ensures high strength of
for which the plastic flow becomes unstable (�r) are
this material up to temperatures of 800ć%C.
determined by the character of the corresponding dis- Chips of the internally oxidized alloy 150 �m thick
sipative processes. Dissipative (relaxation) structures
were pressed at room temperature to produce a briquet
are formed by a mechanism such that the internal en- with open porosity. The final material having the shape
ergy of the material tested is minimized and the degree
of bars was obtained by double punching. The first
of hardening is the higher the harder the development
punching was performed at T = 1000ć%C and � = 0.5,
of irreversible changes in the structure that decrease
and the second punching was performed at T = 20ć%C
the internal energy of the system. These structural
and � = 0.4. In both cases, the strain rate was 0.5 sec-1
changes occur in titanium when an additional defor- (quasidynamic regime) and the values of � lied in the
mation mechanism (twinning) begins to work, which is
interval of strains for which the structure fragmentation
illustrated by the example of structural transformation
was maximal.
in coarse-grain titanium (see Fig. 4). An analysis using a scanning electron microscope
After shock-wave loading, the state of the mate- shows that the microstructural elements are frag-
rial is characterized by a high density of randomly dis- mented. After the first punching, micrograins were of
tributed defects and high energy; therefore, this state
size 1 10 �m. In Fig. 6, they have different deformation-
is unstable. The nature of relaxation processes in cop- shear orientation.
per and tantalum is determined by their crystal struc-
Figure 7 shows the fracture structure after the first
ture, responsible for defect mobility. Under subsequent
and second punching. An analysis of the structures
high-rate plastic deformation, defects are redistributed
of the fractured specimens shows that the fracture of
in copper and tantalum, i.e., low-energy dislocation
doubly-punched specimens is tougher (Fig. 7b) than
(block) structures are formed. As a result, intragran- that of single-punched specimens (Fig. 7a). The size of
ular fragmentation of the structure occurs, which shifts the fracture cells is determined by the size of the final-
the critical instability parameters of plastic flow toward
the region of larger strains and leads to softening of the
material.
It should be noted that the structure fragmentation
in titanium due to twinning does not create conditions
for preservation of the uniform plastic flow up to large
values of � and does not lead to substantial softening
and increase in internal energy. In contrast to the dis-
sipative structures formed in copper, twins are not the
structural elements capable of activating the rotational
component of deformation.
Thus, in strained materials with FCC and BCC
lattices, relaxation processes are accompanied by for-
mation of dissipative structures (strain carriers). The
high initial defect density (dislocations and small grain
3 �m
size) favors the formation of microstructures that en-
sure uniform deformation up to large values of �. These
Fig. 6. Microstructure of a compact of internally ox-
results were taken into account in designing a material
idized copper after the first punching by the quasi-
by the quasidynamic method.
dynamic method.
246 Bondar
a
b
1 �m 1 �m
Fig. 7. Microstructure of fracture of bars produced by the quasidynamic method: (a) first punching; (b) second punching.
structure fragments. One can see from Fig. 7 that after mined by the nature and initial state of the material:
the second punching, the structure of the specimens be- the degree of development of the subgrain microstruc-
comes more dispersed. This is possibly responsible for ture in FCC and BCC metals, determined by rearrange-
the tougher fracture despite the fact that the second ment of the dislocation structure, ensures uniform plas-
punching was performed at room temperature. tic flow up to large values of �r, and the structure frag-
The characteristics of the material show that the mentation in HCP titanium by the twinning mechanism
results established for the dynamic loading regime leads to a decrease in �r.
are applicable to the pressing (quasidynamic) loading The special features of microstructure evolution in
regime. materials are taken into account in designing new ma-
Along with heat-resistant materials, internally oxi- terials by dynamic and quasidynamic methods. The
dized copper obtained by double punching was tested structure and properties of the material obtained from
as inserts in nozzles of a wind tunnel [12]. Prelim- internally oxidized copper of fine fraction (150 �m)
inary studies show that internally oxidized copper is by multiple punching in a hummer mode (� =
Ł
promising for operation under severe cyclic temper- 10 sec-1 refers to quasidynamic mode) are studied. The
ature and force conditions (T = 1300 1600 K and properties of the specimens obtained under pulsed high-
p0 = 600 750 MPa) [12]. temperature and force cyclic loads show that the use of
high-rate deformation is promising for the production
of high-strength materials.
CONCLUSIONS
An analysis of the shear-band pattern in the cross
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