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
THREE-SCALE MODEL FOR NUMERICAL SIMULATION OF
MECHANO-CHEMICAL PROCESSES IN SHOCK-COMPRESSED
POWDER BODIES
Vladimir N. Leitsin, Vladimir A. Skripnyak, and Maria A. Dmitrieva
Department of Mechanics of Solids, Tomsk State University, Lenin ave., 36, Tomsk 634050, Russia
Abstract. The shock-assisted and shock-induced chemical reactions in powder systems are investigated.
Three-scale model of a reacting powder mixture representing physicochemical processes of shock synthesis of materials at micro-, meso-, and macroscopic levels is used. The element of macroscopic structure of
concentration inhomogeneity of powder mixture is considered as a representative volume of heterogeneous medium. The model takes into account the modification of the structure of a powder material and
changing the reactivity of powder mixture under shock compression. The model is used for computer
simulation of the synthesis process in Ni-Al powder mixtures.
The simulation of mechanochemical processes of
shock synthesis includes the simulation of processes
of shock modification of powder mixture, mass and
heat transfer in the reacting layer, and chemical
reaction.
INTRODUCTION
The shock synthesis of materials is a perspective
direction hi the development of techniques of powder metallurgy. This method combines the technological stages of the activation of components, the
compaction of a powder mixture, and initialization
of chemical reactions. The experimental investigations show different regimes of mechanochemical
conversions in powder mixtures under shock loading [1, 2]. It was shown that the solid-phase chemical reactions in shock compressed powder mixtures
with given duration and amplitudes of shock pulse
can be observed in the narrow range of the powder
grain sizes, and porosity [3].
The creation of a computer model taking into
consideration the structure of powder material is
necessary for prediction of mechanical behavior and
chemical processes in the reacting powder mixtures
under shock loading.
The objective of this article is the development
of the three-scale model defining principal parameters controlling the regimes of processes of structural and chemical conversions in powder mixtures
under shock loading.
PHYSICAL MODEL OF A POWDER BODY
The model of a reacting powder mixture takes
into account the macroscopic structure of concentration inhomogeneity. The initial macroscopic
structure is formed in the stage of preparation of the
powder materials due to creation of the particle
conglomerates, and forming a porous structure under compaction [4]. These processes are connected
with self-organizing in discrete powder system and
produce the formation of a macroscopic interior
structure of a powder body.
The reacting powder mixture can be represented
by a set of elements with determined macroscopic
structure of the concentration inhomogeneity.
For example, the Ni-Al powder mixtures consist
of the reacting components, voids, and inert nickel
aluminides.
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An element of the Ni-Al powder material with
macroscopic structure of concentration inhomogeneity is shown in Fig. 1. The characteristic size b
depends on the powder grain size.
u.^ -
1 - Ni, 2 - NiAl, 3 - Al, 4 - porosity
I 0.43
o on. ^^
o
inertial effect is negligible. Then the mechanical
behavior of powder mixture at the front of the shock
pulse substantially depends on the process of pore
collapse.
The modified model [7] of the mechanical behavior of porous medium was used in the present
work. The modification of the model consists of
taking into account the exothermic effect of chemical conversion in a reacting mixture. In this case
heat source Qz appears in the equations of energy
balance. Here z is the rate of chemical transformation of mixture components, and Q is the heat of
chemical reaction.
-
——Ii
iI——
,2 [r
3
4
"o
8.0.1 -
CO
n-
b
2b
FIGURE 1. The reacting layer of powder mixture consists of
two elements of the macrostructure of concentration inhomogeneity. Here b is the characteristic size of the element.
HEAT AND MASS TRANSFER IN POWDER
BODY
Usually reactions run in a wide range of temperatures that may result in phase changes in the
components of the powder mixture. In this case the
fusible component and product of chemical transformation can be transformed into liquid phase.
When the structure of porosity exist in powder
mixture, the liquid phase will move into the porous
skeleton, and provide the convective heat and mass
transfer. The model of processes of heat and mass
transfer in a reacting powder body was suggested in
[8]. The energy conservation law is considered for
the reacting layer. When convective heat and mass
transfer takes place, the laws of conservation of
energy are described by the two-temperature equations of heat transfer with variable coefficients, and
heat sources. All thermal parameters of the powder
medium are defined as effective functions of concentration of components, porosity, and temperature
for microvolumes of the reacting layer of a powder
body. These functions are defined using the approach of the mechanics of the reacting granular
layer [9].
The exothermic effects of chemical conversions
determine heat sources in heat conduction equations, and the endothermic effects of the phase transitions determine heat losses. In the model, the
heating is considered only in temperature region
lying between T0 and TI. Here, T0 is initial temperature of the mixture, and TI is the temperature of
the mixture, at which the porous powder skeleton
loses its strength.
The maximum of aluminum concentration is at
the left side of each element of the macrostructure
of the concentration inhomogeneity. The maximum
of nickel concentration is at the right side of each
element. In the reacting layer the distribution of
porosity (curve 4) and concentration of a product of
chemical reaction (curve 2) changes during the process of mechanochemical transformations.
MODEL OF A COMPRESSED POWDER
MIXTURE
The simulation mechanical behavior of a powder
mixture during shock compression is based on the
mechanical models of porous elastic-plastic medium [5-7]. The conservation laws of mass, momentum, and energy during loading were considered in [6] at the macroscopic level neglecting the
formal value of average density of a porous medium. At the mesoscopic level in compressed powder mixtures the concentration inhomogeneity
causes the high local temperatures, convection heat
and mass transfer.
The dissipation of the kinetic energy activates
the components of mixture and forms the hot spots.
These heat sources are taken into account in the
equation of energy balance.
Shock compression of powder mixture at the microscopic level was described in [5]. It was shown
that when the size of pores is less than 10 jiim the
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in powders mixture reactivity caused by different
mechanisms.
The critical values of pressure Pi* and portions of
dissipated works Aj are defined by the method [7]
in a points of a porous medium. The possibility of
plastic deformation and destruction of surface layers of powder grains is considered for each component separately.
SIMULATION OF PROCESSES OF SHOCK
MODIFICATION OF A MIXTURE
At shock loading of powder mixtures plastic
strain of powder grains, destruction of oxide and
adsorbed layers on the surface of grains are observed. These processes influence on the reactivity
of the powder mixture [2].
In the presented model the velocity of chemical
conversion (z ) is defined by the kinetic equation
z = k0cp(z)exp(-Ea/RT),
NUMERICAL REALIZATION OF THE
MODEL
(1)
Shock compression of volume of the powder
body consisting of the several reacting layers is
numerically simulated.
The problems of shock compression, heat transfer, and macrokinetics of chemical conversions are
solved for the set of reacting layers.
In the case of shock-assisted chemical processes,
the nonlinear boundary problem of thermal conductivity is additionally solved by the finite-difference
method using the implicit central-difference scheme
[11, 12].
where k0 is a constant, q>(z) is a function, which
depends on the nature of conversion [10], Ea is the
activation energy of chemical reaction, and R is the
absolute gas constant.
The parameters k 0 , cp(z), and Ea are the characteristics of the kinetics of chemical conversion at
the mesoscopic level.
Coefficient ko depends on the size of considered
microvolumes of powder mixture. Therefore, the
kinetics of chemical conversions will be different
for same mixtures with various grains size.
When the parabolic law approximates the width
of the reacting layer, ko can be defined by formula
k0=k/b2,
RESULTS AND DISCUSSION
(2)
The computer experiment was carried out for NiAl powder mixtures, in which mechanochemical
conversions were initiated by shock pulse loading
with different duration, amplitudes, and initial temperatures of the powder sample. Various structures
of powder samples were investigated. The thermal,
mechanical and macrokinetic parameters of the
model were borrowed from the literature. The parameters of mechanical activation of powder mixtures were estimated using the experimental data on
the mechanically activated synthesis of nickel aluminides. The computational experiment has shown
the possibility of realization of different processes
of synthesis depending on the inhomogeneity, porosity, and intensity of shock loading.
The possibility of transformation of chemical
transition similar to the combustion into volumetric
thermal explosion was detected.
The presence of solid inert fillers in compressed
powder mixture allows to increase degree of its
mechanical activation and to decrease the maximum
where k corresponds to the element of unit width.
Shock compression decreases the actual size of
the element of concentration inhomogeneity of the
porous powder mixture. In this case, the parameter
k0 also changes.
In the model the changes of the reactivity of the
powder mixture under shock compression are described by the parameter of activation energy
Ea=Eo-H(P-Pi*)oiAi,
(3)
where E0 is the energy of thermal activation of the
chemical transformations in the reacting mixture, H
is the Heaviside function, Pi* are the critical values
of shock pressure specifying the mechanisms of the
activation of chemical reaction, A; are the parameters specifying the contributions of activation energy for the different mechanisms caused by the
work of shock compression, and o^ are the changes
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3.
Aizawa, T., Kamenosono, S., Tanaka, K., Kihara, J.
"Shock Reactive Mechanisms for Direct Synthesis
of Titanium Aluminides from Element Powder
Mixture" in Metallurgical and Materials Application
of Shock Waves and High -Strain-Rate Phenomena
editted by L.E. Murr, K.P. Staudhammer and M.A.
Meyers, Elsevier Science B.V. 1995,pp. 645-652.
4. Balshin, M. Yu., Kiparisov, S. S., Fundamentals of
Powder Metallurgy, Metallurgy, Moscow, 1978.
5. Buzyurkin, A. E., Kiselev, S. P., J. Appl Mech. and
Tech. Physics 41, 192-197 (2000).
6. Schetinin, V. G., "Shock Compression and Heating
of Porous Media" in Shock Waves in Condensed
Matter, Int. Conf. Proc., Saint Petersburg, 1998,
pp. 186-187.
7. Nesterenko, V. F., Pulse Loading of Heterogeneous
Materials, Nauka. Sib. Branch, Novosibirsk, 1992.
8. Dmitrieva, M. A., Leitsin, V. N, Izvestia VUZov.
Fizika (Rus. Phys. J.) 3, 57-62 (1999).
9. Goldshtik, M. A., Transfer Processes in Granular
Layer, Institute of Thermophysics SB AS USSR,
Novosibirsk, 1984.
10. Merzhanov, A. G., Phys. Chemistry 3, 6-45 (1983).
11. Leitsin, V. N., Dmitrieva, M. A., Kobral, I. V., Phys.
Mesomechanics 4, 43-49 (2001).
12. Leitsin, V. N., Skripnyak, V. A., Dmitrieva, M. A.,
"Simulation of Processes of Shock Synthesis of
Aluminides" in Shock Waves in Condensed Matter,
Int. Conf. Proc., Saint-Petersburg, 2000, pp. 107-110.
temperature of the initiation of chemical conversions.
The results of estimation of characteristic times
of mechanochemical processes at chemical conversions are shown in Fig. 2.
5
1 - start of conversion,
2- end of conversion
FIGURE 2. Characteristic times of mechanochemical processes
in the reacting layer.
Regime of chemical conversion in the Ni-Al
powder mixture similar to the "layer-by-layer combustion" is transformed to volumetric thermal explosion at the region I in Fig.2. The ultrafast chemical reactions were obtained in the region II where
there was the maximum gradient of the concentration inhomogeneity of components. The calculations show that ultrafast solid phase reactions can
take place in fine-grained mixtures under intensive
shock loading.
CONCLUSION
A new approach to the investigation of behavior
of a reacting powder mixture under compression
has been suggested.
The obtained results demonstrate that the macrostructure of concentration inhomogeneity in powder
mixture play important role in the initiation of
mechanochemical conversions. The presented
model taking into consideration the macrostructure
of concentration inhomogeneity can predict different regimes of mechanochemical conversions in
shock-compressed powder mixtures.
REFERENCES
1.
2.
Thadhani, N. N., J. Appl. Phys. 76, 2129-2138
(1994).
Batsanov, S. S., Effects of Explosions on Materials,
New York: Springer-Verlag, 1994.
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