Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals at High-Rate Deformation
The results of calculations of the theoretical limiting shear stress for fcc metals Cu, Ni, Ag, Au, Pd, and Pt performed using “universal” empirical potentials of interatomic interactions of the embedded-atom type are presented. The effects of lattice relaxation are shown to play an important role i...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2002
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| Zitieren: | Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals at High-Rate Deformation / V.V. Kamyshenko, V.V. Kartuzov, V.I. Shevchenko, W.A. Gooch // Проблемы прочности. — 2002. — № 3. — С. 73-76. — Бібліогр.: 5 назв. — англ. |
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irk-123456789-467652013-07-06T19:19:25Z Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals at High-Rate Deformation Kamyshenko, V.V. Kartuzov, V.V. Shevchenko, V.I. Gooch, W.A. Научно-технический раздел The results of calculations of the theoretical limiting shear stress for fcc metals Cu, Ni, Ag, Au, Pd, and Pt performed using “universal” empirical potentials of interatomic interactions of the embedded-atom type are presented. The effects of lattice relaxation are shown to play an important role in the formation of intermediate defect structures and lead to a considerable decrease in the theoretical yield point. Qualitative effects of the “anti-adiabatic” influence on the material ultimate strength under conditions of high-velocity loading are discussed. Наведено результати розрахунків теоретичної границі напруження зсуву для ГЦК-металів Cu, Ni, Ag, Au, Pd, Pt з використанням “універсальних” емпіричних потенціалів міжатомної взаємодії типу зануреного атома. Показано, що ефекти граткової релаксації відіграють важливу роль у формуванні проміжних дефектних структур і приводять до значного зменшення відповідних значень теоретичної границі текучості. Обговорюються ефекти “антиадіабатичного” впливу на граничну міцність матеріалу в умовах високошвидкісного навантаження. Представлены результаты расчетов теоретического предела сдвига для ГЦК-металлов Сu, Ni, Ag, Au, Pd, Pt с применением "универсальных” эмпирических потенциалов межатомного взаимодействия типа погруженного атома. Показано, что эффекты релаксации решетки играют важную роль в формировании промежуточних дефектных структур и приводят к значительному уменьшению соответствующих значений теоретического предела текучести. Обсуждаются эффекты “антиадиабатического” влияния на предельную прочность материала в условиях высокоскоростного нагружения. 2002 Article Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals at High-Rate Deformation / V.V. Kamyshenko, V.V. Kartuzov, V.I. Shevchenko, W.A. Gooch // Проблемы прочности. — 2002. — № 3. — С. 73-76. — Бібліогр.: 5 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/46765 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел |
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Научно-технический раздел Научно-технический раздел Kamyshenko, V.V. Kartuzov, V.V. Shevchenko, V.I. Gooch, W.A. Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals at High-Rate Deformation Проблемы прочности |
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The results of calculations of the theoretical limiting shear stress for fcc metals Cu, Ni, Ag, Au, Pd, and Pt performed using “universal” empirical potentials of interatomic interactions of the embedded-atom type are presented. The effects of lattice relaxation are shown to play an important role in the formation of intermediate defect structures and lead to a considerable decrease in the theoretical yield point. Qualitative effects of the “anti-adiabatic” influence on the material ultimate strength under conditions of high-velocity loading are discussed. |
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Article |
| author |
Kamyshenko, V.V. Kartuzov, V.V. Shevchenko, V.I. Gooch, W.A. |
| author_facet |
Kamyshenko, V.V. Kartuzov, V.V. Shevchenko, V.I. Gooch, W.A. |
| author_sort |
Kamyshenko, V.V. |
| title |
Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals at High-Rate Deformation |
| title_short |
Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals at High-Rate Deformation |
| title_full |
Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals at High-Rate Deformation |
| title_fullStr |
Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals at High-Rate Deformation |
| title_full_unstemmed |
Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals at High-Rate Deformation |
| title_sort |
effects of lattice relaxation and limiting shear stress of fcc metals at high-rate deformation |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2002 |
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Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/46765 |
| citation_txt |
Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals
at High-Rate Deformation / V.V. Kamyshenko, V.V. Kartuzov, V.I. Shevchenko, W.A. Gooch // Проблемы прочности. — 2002. — № 3. — С. 73-76. — Бібліогр.: 5 назв. — англ. |
| series |
Проблемы прочности |
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2025-07-04T06:13:25Z |
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2025-07-04T06:13:25Z |
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1836695795613564928 |
| fulltext |
UDC 539.4
Effects of Lattice Relaxation and Limiting Shear Stress of fcc Metals
at High-Rate Deformation
V. V. Kamyshenko,a V. V. Kartuzov,a V. I. Shevchenko,a and W. A. Goochb
a Institute of Problems in Material Science, National Academy of Sciences of Ukraine,
Kiev, Ukraine
b U.S. Army Research Laboratory, USA
УДК 539.4
Влияние релаксации решетки и предельного напряжения сдвига
ГЦК-металлов при высокоскоростном деформировании
В. В. Камышенкоа, В. В. Картузова, В. И. Шевченкоа, В. А. Гуч6
а Институт проблем материаловедения НАН Украины, Киев, Украина
6 Исследовательская лаборатория армии США, США
Представлены результаты расчетов теоретического предела сдвига для ГЦК-металлов Си,
Ni, Ag, Au, Pd, Pt с применением "универсальных” эмпирических потенциалов межатомного
взаимодействия типа погруженного атома. Показано, что эффекты релаксации решетки
играют важную роль в формировании промежуточних дефектных структур и приводят к
значительному уменьшению соответствующих значений теоретического предела текучес
ти. Обсуждаются эффекты “антиадиабатического” влияния на предельную прочность
материала в условиях высокоскоростного нагружения.
Introduction. The existence of the limiting shear stress plays an important
role in the processes of formation and propagation of shock waves in solids.
Therefore, for each quantitative theory of impact, it is necessary to take into
account impingement or other high-rate deformation processes, where a solid
material is present. An important feature of the limiting shear stress in the process
of high-rate deformation is its dependence on the strain rate. Under conditions of
impact, this dependence may be quite strong (note, for example, that in [1] the
concept of “the ultimate velocity of deformation” has been proposed), but its
physical nature is not yet clear. To address this problem, we consider the simplest
model for r max similar to the classical Frenkel model [2]. The difference is that
we take specific crystallographic structure (fcc structure), use true model of interatomic interactions (“universal” embedded atom potentials [3, 4] from [5]),
and allow for full atomic relaxation during the shear process. The purpose is to
investigate quantitatively the influence of the effects of lattice relaxation on the
magnitude of r max. With the assumption that r max is limited by its “theoretical
limit” (in the sense that neither cracks nor plastic deformation are present), one
can distinguish the “low-rate” and “high-rate” regions by the ability of atoms to
follow the most preferable (energetically) path of the deformation process. In the
limiting cases of infinitely slow and infinitely fast deformation, this corresponds
© V. V. KAMYSHENKO, V. V. KARTUZOV, V. I. SHEVCHENKO, W. A. GOOCH, 2002
ISSN 0556-171X. Проблемы прочности, 2002, N 3 73
V. V. Kamyshenko, V. V. Kartuzov, V. I. Shevchenko, and W. A. Gooch
to the “adiabatic” (for a given macroscopic deformation, the atomic configuration
corresponds to the global minimum of potential energy) and “anti-adiabatic”
(atomic positions are fixed by external conditions and no local relaxation is
allowed) limits. The actual relation r(£) must lie somewhere between those
limits.
Results of Modeling. Six materials with fcc lattices were investigated. Two
shear planes were considered with two directions of shear in each plane: [100] and
[110] for the (001) plane, and [1 1 0] and [211] for the (111) plane.
In Fig. 1, the energies of non-relaxed sheared configurations are presented.
In order to omit obvious dependence of U on the lattice parameter and shear
modulus G, the units G ■ b and b were used for U and x, respectively; b is the
atomic lattice parameter in the shear direction.
As it could be expected, the peaks of the curves in Fig. 1 are in agreement
with Frenkel’s estimation (according to the latter, the maximum of the curves in
Fig. 1 would be at the level of 1/2n2). The lattice relaxation, if it takes place
during the process of deformation, changes significantly the values of the limiting
shear stress. This is illustrated in Fig. 2.
Fig. 1. D ependence o f the strain-energy density U on the value o f the relative shear x fo r six fcc
m etals (no atom ic relaxation). H ere and in Fig. 2: G is the shear m odulus and d is the atom ic lattice
param eter in shear direction; (a) shear plane (111), shear d irection [1 1 0 ] (b) shear p lane (111),
shear d irection [211]; (c) shear plane (001), shear direction [100]; (d) shear p lane (001), shear
direction [110].
74 ISSN 0556-171X. npoôëeuu npouHocmu, 2002, № 3
Effects o f Lattice Relaxation and Limiting Shear Stress
Fig. 2. D ependence o f the strain-energy density U on the value o f the relative shear x fo r six fcc
m etals (full atom ic relaxation).
As can be seen from these Figures, the effect of lattice relaxation decreases
the “theoretical” value of the limiting shear stress by a factor of 30 and brings it to_3the order of 10 G, which is only 100 times higher than the experimental value
typical of metals. This difference can be even smaller. The local minimum
between the peaks corresponds to the formation of the stacking fault, and the
height of the left minimum corresponds to the minimum energy spent for its
formation. If the direction of deformation changes at the point of the minimum
energy, one can get resulting deformation in [110] or [ 110] directions and, as a
combination of the latter, in an arbitrary direction in the (111) plane. The energy
needed for such processes is now completely determined by the height of the first
peak in Figs. 1b and 2b and is, for the relaxed case, of the order of 10_4 G ■ b.
Discussion and Conclusions. Let us discuss now possible applications of
these results. There are situations where the “ideal” mechanism of inelastic deformation may play an important role. This is the case of high-rate deformation,
where the rate of deformation exceeds the velocity of cracks (of course, other
defects intrinsically present in a real material such as grain boundaries,
dislocations, and point defects are still to be taken into account). It follows from
our considerations that the deformation rate is higher than the rate of lattice
relaxation and the limiting shear stress generally increases by a factor of 30-50.
ISSN 0556-171X. npo6n.eubi npounocmu, 2002, N 3 75
V. V. Kamyshenko, V. V. Kartuzov, V. I. Shevchenko, and W. A. Gooch
v/(k c j
Fig. 3. Possible dependence o f the lim iting shear stress r max on the strain rate.
Simple estimations of the lattice-relaxation rate give the value, which is about the
speed of sound. Thus, one can expect that the dependence r max( v) will be
similar to the dependence shown in Fig. 3 (where k is of the order of unity and
c± is the speed of sound).
In all probability, the results obtained here for six fcc metals can be directly
generalized for other metallic systems due to the similarity of the chemical bonds
these materials possess. Systems with covalent bonding need special
investigation, and such investigations are now in progress.
Резюме
Наведено результати розрахунків теоретичної границі напруження зсуву для
ГЦК-металів Cu, Ni, Ag, Au, Pd, Pt з використанням “універсальних” емпі
ричних потенціалів міжатомної взаємодії типу зануреного атома. Показано,
що ефекти граткової релаксації відіграють важливу роль у формуванні
проміжних дефектних структур і приводять до значного зменшення відповід
них значень теоретичної границі текучості. Обговорюються ефекти “анти-
адіабатичного” впливу на граничну міцність матеріалу в умовах високо-
швидкісного навантаження.
1. V. P. Alekseevskii, “Penetration of a rod into a plate at high velocity,” Fiz.
goren. vzryva, No. 2, 99 - 106 (1966).
2. J. Frenkel, Z. Fiz., 37, 572-609 (1926).
3. M. S. Daw and M. I. Baskes, “Embedded-atom method: Derivation and
application to impurities, surfaces, and other defects in metals,” Phys. Rev. B,
29, No. 12, 6443 - 6453 (1984).
4. M. W. Finnis and J. E. Sinclair, “A simple empirical n-body potential for
transition metals,” Phil. Mag. A, 50, 45 (1984).
5. S. M. Foiles, M. J. Baskes, and M. S. Daw, “Embedded-atom-method
functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys,” Phys.
Rev. B, 33, No. 12, 7983 - 7991 (1986).
R eceived 14. 11. 2001
76 ISSN 0556-171X. Проблеми прочности, 2002, № 3
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