CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
MACRO - MESO ENERGY EXCHANGE IN
DYNAMICALLY DEFORMED STEELS
Yuri I. Mescheryakov
Institute of Problems of Mechanical Engineering RAS, St.Petersburg 199178, Russia
Abstract. Dependence of spall-strength on the intensity of the energy exchanges between macroscopic
and mesoscopic scale levels is experimentally studied for four kinds of steels having different chemical
composition and thermal treatments. For all the kinds of steel the spall-strength is shown to be
maximum when velocity dispersion at the mesolevel equals velocity loss at the plateau of compressive
pulse, which corresponds to equilibrium state of energy exchange between scale levels.
structure re-arrangement of a dynamically deformed
material reveals via the shock-induced change of
the particle velocity dispersion D and velocity loss
Au [3,4]:
BACKGROUND
Commonly used approaches to microstructure
description of response of material to impact link the
resulting macroscopic
behavior with the
microstructure data obtained after dynamic loading.
In reality, adequate modeling of dynamic processes
should be based on the microstructure kinetics data
obtained in real time, i.e. during dynamic processes.
To date the only possibility for obtaining in-sit data
on the kinetics of microstructure is a measuring of
time-dependent velocity dispersion at the free
surface of targets in planar shock experiments. The
velocity dispersion (or diffusion velocity) can be
measured with the laser interference technique and
has a statistical meaning [1,2].
In considering the microstructure aspects of
dynamic deformation it should be ascertained that
experimentally determinable kinetic characteristics
obtained with interference technique are those
belonging to the mesoscopic scale level which
occupies an intermediate position between atomdislocation and macrolevel. In this connection it
should be noticed that as distinct from the
quasistatic situation, in a dynamically loaded
medium mesolevel is not a completed structure. It is
a specifically transient structure where both a scale
of structure elements and energy capacity of
mesolevel currently change. The specifics of
Au= cm(dD/du)
(1)
Here cm = dE/ dD is the mesolevel specific
energy capacity. This equation asserts that mass
velocity loss is proportional to rate of change of the
velocity dispersion in the velocity space. It
disappears when the rate of change of dispersion is
invariable. The "loss", or decrease of mass velocity,
is a quantitative characteristic of the energy
exchange between mesoscopic and macroscopic
scale levels in non-equilibrium processes. The
energy balance in this case [4]:
= AuSU-cmD
(2)
Here AE is the change of internal energy due to
non-equilibrium
energy
exchange
between
macrolevel and mesolevel. The first term on the
right hand side is the energy proportional
transportation of the velocity loss over the plastic
front. When dispersion at the mesolevel grows
faster than the mean mass velocity, AE goes on
mesostructure formation. In this situation, energy
balance supports owing to decrease of elastic stored
energy and scheme of the process is thought to be:
267
W, m/s
strain rate increase —+ velocity dispersion growth
—» onset of energy exchange —> wave amplitude
loss —> decrease of the elastic energy.
In opposite situation initially large dispersion
decreases and AE goes on increase of mean mass
velocity.
To check above consideration, four kinds of
steel having different chemical composition and
thermal treatment have been tested. They have been
loaded under uniaxial strain conditions within
impact velocity range of 200-550 m/s.
< c>, u, m/s
250
248
246
10
EXPERIMENTS AND RESULTS
Experiments on shock loading of plane targets
were performed by using a light gas gun facility of
37 mm bore diameter. Thickness of targets and
impactor were adjusted to provide a spallation. Free
surface velocity profiles were recorded using a twochannel velocity interferometer [2]. The technique
allows, besides the free surface velocity profile, to
determine also a diffusion velocity (c) (or square
root of the velocity dispersion) and velocity loss Au.
400
FIGURE 2. Pull-back velocity (1), diffusion velocity (2),
velocity loss (3) versus impact velocity (40XCHMA steel, 2-set)
a). Results of shock tests for the first set of targets
are presented in Fig. 1 which shows that pullback
velocity W = f (Uimp), diffusion velocity (c) = f
(Uimp) and velocity loss Aw = / (Uimp) dependencies
monotonically grow with the impact velocity. It is
also seen that within impact velocity range 211-437
m/s diffusion velocity remains being smaller than
velocity loss, i.e. (c) « Au. At the same time, it
may be noticed that dependencies Au = f(Uimp) and
(c) -f(Uimp) have different inclination. Intersection
of the curves would happen at the impact velocity of
700 m/s where the pullback velocity is expected to
be equal to 250 m/s. The special shot at the impact
velocity of 695 m/s has been performed to check
that conclusion, which showed the pullback velocity
of 247 m/s. Thus, it may be concluded that within
impact velocity range of 211-437 m/s this steel
does
not
have
optimum
spall-strength
characteristics. Its thermal treatment corresponds to
maximum dynamic strength at the velocity of « 700
m/s.
b). Results of shock test for the second set of
targets in the form of dependencies W = f (Uimp),
(c) =f(Uimp) and Au =f(Uimp) are provided in Fig.
2.
Maximum spall-strength (W « 250 m/s)
corresponds to the impact velocity of « 490 m/s.
Just at that impact velocity the curves (c) -f(Uimp)
and Au =f(Uimp) intersect, so that (c) = Au.
This is complex alloyed steel, which was studied
for two sets of targets of different thermal treatment
[5].
u , m/s
50
0 -f—————————I——————————————I- -5
200
250
300
350
400
impact velocity, m/s
500
impact velocity, m/s
40XCHMA steel (HRc 55)
m/s
450
450
FIGURE 1. Pull-back velocity (1), diffusion velocity (2) and
velocity loss (3) versus impact velocity (40XCHMA steel, 1-set)
268
Microstructure investigations of post-shocked
specimens show that in the first set of steel targets
spalling looks as a totality of cracks parallel to the
free surface of target. This kind of fracture is known
to be cleavage.
Microstructure mechanisms of dynamic fracture in
the second set of 40XCHMA steel turns out to be
different at different regions of impact velocity.
- Uimp < 500 m/s: (c) > Au. Spall crack has a steplike shape with identical longitudinal and transverse
length of step.
- Uimp = 500 m/s: (c) = Au. Within the spall zone
there is a dense network of short adiabatic shear
bands.
- Uimp > 500 m/s: (c) < Au. Spall fracture in the
form of cleavage.
Thus, for both sets of 40XCHMA steel maximum
spall-strength corresponds to the strain rate where
(c) = Au. On the basis of spall tests of two sets of
40XCHMA steel one can conclude that behavior of
diffusion velocity and velocity loss provides
information whether the thermal treatment of steel
corresponds to the maximum value of dynamic
strength.
W,
u, <c>, m/s
250
200
150
100
180
230
280
330
impact velocity, m/s
Figure 3. Fullback velocity (1), velocity loss (2), diffusion
velocity (3) versus impact velocity (38XH3M&A st, 2-set)
criterion (c) = Au is fulfilled for the entire range
of
impact velocities under investigation.
Accordingly, the pullback velocity is also practically
constant.
The structural mechanism of dynamic fracture for
this steel can be classified as growth of voids
within overall range of impact velocities.
On comparing two sets of 38XH3M0A steel
targets we can conclude that thermal treatment of
the second set provides an optimization of dynamic
strength properties within more wide range of the
impact velocities. However, the value of spallstrength is decreased.
38XH3MOA steel (HRc 39)
This is a complex-alloyed Cr-Ni-Mo steel having
optimum combination of quasistatic plastic and
strength characteristics. To determine its dynamic
plasticity and strength characteristics, two sets of
targets have been tested under planar conditions.
The first set has been prepared from the material as
supplied and the second, after thermal treatment,
providing a homogenization of structure.
a). Results of test for the first set of 38XH3M&A
steel targets are provided in Fig. 3. This set of steel
targets reveals a non-monotonic behavior of spallstrength on the strain rate. At the impact velocity of
~ 300 m/s, the quantities Au = f(Uimp) and (c) =
f(UimP) intersect each other, which corresponds to
the criterion (c} = Au. This impact velocity
corresponds to the maximum spall-strength of the
steel.
b). The diffusion velocity (c) =f(Uimp) and velocity
loss Au = f(Uimp) lie close to each other, so that,
within the limits of scatter of experimental data, the
30XH4M steel (HRc 40)
The quantities (c) =f(Uimp)and Au = f (Uimp)
lie close to each other within the overall range of
impact velocities, so the criterion (c) = Au is
fulfilled everywhere while pull-back velocity is
invariable (see Fig.4). This means that 30XH4M
steel has optimum thermal treatment. Behavior of
this steel is similar to that for the second set of
38XH3M0A steel.
However this steel has different mechanisms of
dynamic plasticity at the mesolevel, mesorotations.
As for the mechanism of fracture,
269
W , < c>,
a, m/s
CONCLUSIONS
250
Together with well-known quasistatic strength
characteristics of material an important role in
dynamic fracture belongs to kinetic characteristics
of microstructure at the mesolevel.
The first kinetic characteristic is the velocity
dispersion D = c 2 at the mesolevel or diffusion
velocity (c), which is a measure of the velocity
heterogeneity of dynamic deformation in real time.
The second kinetic characteristic is the velocity
loss Au. Its value characterizes a quantity of the
kinetic energy transferred from macro- to mesolevel.
When (c} = Au, the energy exchange is realized
under equilibrium conditions. This case corresponds
to maximum dynamic strength of material. The
mechanism of dynamic fracture corresponding to
optimum kinetic characteristics of structure is the
step-like cracking at the mesolevel-2 (100-400//w)
for ductile steel or network of adiabatic shear bands
for brittle steel.
For the material where Au »(c) the structural
mechanism of the dynamic fracture turns out to be
cleavage while the material itself is not in an
optimum state from the viewpoint of dynamic
strength.
200
150
100
300
350
400
450
500
impact velocity, m/s
FIGURE 4. Fullback velocity (1), diffusion velocity (2)
and velocity loss (3) versus impact velocity (30XH4M steel)
this is step-like cracking at the mesolevel-2 (~ 100 400 fjni) , which is known to be the so-called
"horizon" scale of Grady [6].
REFERENCES
28XH3CMBOA steel (HRc 25)
1. Asay, J. R. and Barker, L.M. , J. Appl Phys. 45,
2540-2550 (1974).
2. Mescheryakov, Yu.I. and Divakov, A.K., Dymat J. 1,
271-277(1994).
3. Mescheryakov, Yu.L, "Mesoscopic effects and particle
velocity distribution in shock compressed solids". In:
"Shock Compression of Condenced Matter-1999"Q&.
M.D. Furnish, L.C. Chhabildas, R.S. Nixon. AIP
Proceedings 505, Melville, New York. 1999, pp 10651070.
4. Khantuleva, T.A. - Presented to "Shock Compression
of Condensed Matter", Atlanta GA, June 24-29,
2001.
5. Mescheryakov, Yu.L, Divakov, A.K., and Zhigacheva,
N.I., Material Physics and Mechanics. 3, 63-100,
(2001).
6. Grady, D.E. J. of the Mech. and Phys. of Solids, 36,
353- 384, (1988).
This steel is commonly used in quenched state.
In
this study, to provide a high plasticity we use the
steel in annealed state. It was expected that this
provides the viscous mechanism of fracture. The
velocity loss curve for that material lies much
higher than the diffusion velocity curve (Au »
(c)). Thus, the behavior of kinetic characteristics
for this steel is similar to that for the first set of
40XCHMA steel (see Fig.l). Accordingly, the basic
mechanism of spall fracture for this steel is
cleavage. This result shows that structural
mechanisms of dynamic plasticity and fracture are
determined by the mutual behavior of kinetic
characteristics of mesostructure during the shock
loading but not by the quasistatic plasticity and
strength of material.
270