High pressure effects in severe plastic deformation
The analysis is made of effect and physical mechanisms of the influence of pressure on metal materials that are in the state of plastic flow, as well as on characteristics of materials undergone severe plastic deformation under pressure.
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Varyukhin, V.N. Beygelzimer, Y.Y. Efros, B.M. Prokof’eva, O.V. Pilyugin, V.P. 2020-04-21T17:55:08Z 2020-04-21T17:55:08Z 2004 High pressure effects in severe plastic deformation / V.N. Varyukhin, Y.Y. Beygelzimer, B.M. Efros, O.V. Prokof’eva, V.P. Pilyugin // Физика и техника высоких давлений. — 2004. — Т. 14, № 4. — С. 9-18. — Бібліогр.: 7 назв. — англ. 0868-5924 https://nasplib.isofts.kiev.ua/handle/123456789/168093 PACS: 61.72.Qq, 81.40.−z, 81.40.Vw The analysis is made of effect and physical mechanisms of the influence of pressure on metal materials that are in the state of plastic flow, as well as on characteristics of materials undergone severe plastic deformation under pressure. en Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України Физика и техника высоких давлений High pressure effects in severe plastic deformation Article published earlier |
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High pressure effects in severe plastic deformation Varyukhin, V.N. Beygelzimer, Y.Y. Efros, B.M. Prokof’eva, O.V. Pilyugin, V.P. |
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High pressure effects in severe plastic deformation |
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high pressure effects in severe plastic deformation |
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Varyukhin, V.N. Beygelzimer, Y.Y. Efros, B.M. Prokof’eva, O.V. Pilyugin, V.P. |
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Физика и техника высоких давлений |
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Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України |
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The analysis is made of effect and physical mechanisms of the influence of pressure on metal materials that are in the state of plastic flow, as well as on characteristics of materials undergone severe plastic deformation under pressure.
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0868-5924 |
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High pressure effects in severe plastic deformation / V.N. Varyukhin, Y.Y. Beygelzimer, B.M. Efros, O.V. Prokof’eva, V.P. Pilyugin // Физика и техника высоких давлений. — 2004. — Т. 14, № 4. — С. 9-18. — Бібліогр.: 7 назв. — англ. |
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2025-11-24T16:49:12Z |
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Физика и техника высоких давлений 2004, том 14, № 4
9
PACS: 61.72.Qq, 81.40.−z, 81.40.Vw
V.N. Varyukhin1, Y.Y. Beygelzimer1, B.M. Efros1, O.V. Prokof’eva1,
V.P. Pilyugin2
HIGH PRESSURE EFFECTS IN SEVERE PLASTIC DEFORMATION
1Donetsk Physics & Technology Institute of NASU
72 R. Luxemburg Str., Donetsk 83114, Ukraine
2Institute of Metal Physics of the RAN
18 S. Kovalevskaya Str., Ekaterinburg 620219, Russia
The analysis is made of effect and physical mechanisms of the influence of pressure on
metal materials that are in the state of plastic flow, as well as on characteristics of mate-
rials undergone severe plastic deformation under pressure.
Influence of pressure on deformation behavior of materials
Increasing the plasticity of solids under pressure has been the subject of nu-
merous investigations starting from fundamental works [1,2]. It is currently shown
that the effect is due to two interrelating processes: suppression of fracture and
defect structure homogenization (DSH) during active deformation under high
pressure [3,4].
For a wide class of solids there exist two levels of critical pressure: Pc ~ σs ~
~ 10−3K and P0 ~ 10−2K (σs – yield stress, K – compression modulus). When P = Pc
the process of micro-inhomogeneities (pores and cracks) development is retarded
under deformation, i.e. the solid plasticizes and the ultimate strain εp increases (εp −
value of strain prior to fracture). For brittle bodies the value of Pc coincides with
that of pressure of brittle – plastic transition. With further P growth, in the Pc < P <
< P0 range, the process of suppression of nonuniformity origination becomes
more intensive and for P > P0 the solid can be ideally plastic (it deforms as a high-
viscous liquid). Table lists values of P0 calculated for various metals (see [4]).
Let us consider the process of DSH for a solid subjected to active deforma-
tion under high pressure at relatively low deformation velocities. The nucleation
and the mobility of dislocations in solids are limited by thermally activated pro-
cesses. The application of pressure results in decreasing thermal activation and,
thus, in the grows of number of dislocation sources and, finally, in the increase
of DSH.
Физика и техника высоких давлений 2004, том 14, № 4
10
Table
Critical pressure for various metals [4]
Material Lattice type Pc, GPa P0, GPa
Cr 0.07−0.72 7
Mo 0.11−1.13 11
W 0.18−1.69 18
Fe 0.08−0.84 8.5
Steel 1045
BCC
0.09−0.91 9.2
Be 0.17−1.72 17.1
Mg 0.16−1.67 16.2
Zn 0.05−0.54 5.1
Ti
HCP
0.04−0.43 4.2
It is known that during the deformation the formation of concentrators results
in origination of micro – and meso-inhomogeneities favoring fracture. For P > Pc,
in the deformed solid the relaxation processes tend to minimize the probability of
nonuniformity origination, otherwise the work ∆Ap = P∆V (∆V − change in vol-
ume due to nonuniformity origination) should be done, which increases with P.
This results in deconcentration of stresses in volume samples and, thus, in DSH
intensification.
In heterophase and noncubic polycrystalline systems, the process of DSH be-
comes more intense due to relaxation processes taking place at the expense of
pressure – induced shearing stresses at inner interfaces or at elastic nonuniformi-
ties. It should be noted that processes of twinning and martensitic transformations
during the deformation of metastable system under high pressure also favor the DSH.
In such a way, the main physical reasons of DSH and, thus, of plasticization of
crystal solids under high pressure are the decreasing of thermal fluctuations, the
suppression of generation and retardation of micro- and mesomicro-inhomogeneity
development, as well as the intensification of effects of compression anisotropy in
elastically nonuniform and noncubic polycrystals. For P ≥ Pc, activation of the
processes results in the intensification of plasticization effects in solids under
pressure that are observed at different scale levels depending on nature of ob-
jects observed (mono- and polycrystals, metastable and heterophase systems,
noncubic and porous solids) and on value of P realized in the experiment.
When DSH is high, the value of maximal internal stresses decreases and de-
fects of crystal structure tend to distribute more uniformly in the volume of sam-
ples, which, as a rule, results in the improvement of physico-mechanical proper-
ties of different materials.
Experimental results on the influence of pressure on grain refinement
and plasticity of metals
The above assumptions concerning the role of hydrostatic pressure in deforma-
tion process are supported by the following experimental facts.
Физика и техника высоких давлений 2004, том 14, № 4
11
When molybdenum is deformed under pressure, on the structural level the
polyhedral grain structure of the annealed material (d ≈ 22 µm) starts showing a
local instability to the origination of rotational structure of the «vortex» type during
direct extrusion with e > 0.3. With e increase, the growing instabilities result in a
cardinal rearrangement of the initial structure (e ≈ 1.2−1.4) to a rotational struc-
ture of the «vortex» type. With further increase in the extrusion ratio up to e ≈ 1.9,
in sample cross-section the «vortex» character of the structure becomes more pro-
nounced, while in the longitudinal section the fibrous structure is observed.
At the level of substructure, the low-misoriented cellular structure existing with
e ≈ 0.15−0.3 changes for a fragmented one, which is a population of fragments
(subgrains) with a 5−10° (and more) misorientation. For e ≈ 1.2−1.9, the process
of a more uniform grain refinement is genetically related to the process of evolu-
tion and branching of nonuniform banded substructure typical of e ≈ 0.4−1.0 (Fig. 1).
a b
c d
Fig. 1. Substructure of molybdenum as a function of direct extrusion parameters (cross-
section, ×27000): a − e = 0; b − e = 1.2, Pbp ≈ 0.1 MPa; c − e = 1.2, Pbp ≈ 800 MPa; d −
e = 1.4, Pbp ≈ 800 MPa
During the direct extrusion of molybdenum, the increase in pressure level at
the expense of backpressure Pbp results in shifting the range of deformation ratios,
necessary for the origination of rotational structures of the «vortex» type, to lower
values of e.
The quantitative analysis of histograms for distribution of structural elements in
size has shown that during the direct extrusion of molybdenum, with the increase
Физика и техника высоких давлений 2004, том 14, № 4
12
0 200 400 600 800 1000
4
8
12
16
20
24
P
bp
, MPa
d,
µ
m
1.6
1.8
2.0
2.2
2.4
2.6
H
V
, G
Pa
in backpressure and thus in extrusion pressure, the average size of structural ele-
ments of molybdenum is decreasing. At the same time, the hardening increases
with the growth of Pbp (Fig. 2).
Mathematical modeling of the effects resulting from the influence of pressure
on plastic deformation of solids
The development of the SPD technologies should be based on the mathemati-
cal models describing fracture and grain refinement of solids and taking into ac-
count the pressure effect on this process.
We have proposed a continual model of the deformation of solids describing
the fracture of the material under deformation as well as the effect of pressure on
the process [5]. The model [5] did not take into account the interrelation between
the formation of micro-inhomogeneities and the grain refinement in solids under
severe plastic deformation. Another model has been developed to describe the
above – mentioned effects [6].
In order to incorporate the structure of polycrystals into a continual model of
plasticity, two scalar parameters have been introduced [6]: the total volume of mi-
cropores θ per unit volume of the material and the total length of large-angle
boundaries per unit of cross-section area of the material S. Using the assumption of
self-similarity of the structure changes during quasi-monotone loading and the
complementarity of grain refinement and fracture, we obtain a system of kinetic
equations for these parameters. We show that the proposed model not only explains
a number of known effects, but also suggests new ones. In particular, it turned out
that the loading processes that most intensely fragment the metal should be proc-
esses which lead to the highest decrease of plasticity of the given metal (among all
processes with the same level of hydrostatic pressure in the strain center). To obtain
submicro- and nanostructures, these processes need be carried out under high hy-
drostatic pressure in the strain center. In this case, the relaxation of internal strain
will follow the path of crystal grain refinement, not of the emergence of micropores.
To illustrate conclusions following from the model, a study was done of the evo-
lution of metal structure in processes differing in deformation scheme. The deforma-
tion scheme was accounted for by value of materials ductility when the hydrostatic
component of the stress tensor is zero [6]. The characteristics of carbon steel (0.45%
C) were taken for calculation. The results of calculation are represented in Fig. 3.
Fig. 2. Influence of backpressure Pbp
on changes in the average size of
structure elements d and on value of
hardening HV of molybdenum (e = 1.4)
Физика и техника высоких давлений 2004, том 14, № 4
13
The curve of the average grain size d (inverse value of S) is given below for
comparison of the results as this structure parameter is the most frequently met in
literature. Let us analyze the model curves.
Fig. 3I shows a comparison of direct and twist extrusion processes. A gradual
descent of the both curves on the graph of a number of accumulative zones N(e) is
due to the formation of a considerable share of indivisible fragments. The intro-
duction of the mechanism of mutual slippage results in the lowering of the inten-
sity of internal-stress accumulation.
It is follows from the graphs of S(e) and d(e), which illustrate the material
structure grain refinement, that its intensity is practically the same for the proc-
essing methods under consideration. However, in the case of direct extrusion, e ≈ 3
is a really attainable total deformation when sample is still considered to be three-
dimensional. Indeed, as a rule, under direct extrusion, diameter of the billet is not
larger than D0 = 50 mm. While under the logarithmic deformation (e ≈ 3), extrudate
diameter D = 10 mm, and a high degree of deformation already gives extrudates
which can hardly be considered three-dimensional. The graph of relative porosity
θ(e) shows that twist extrusion ensures a higher plasticity of the deformed mate-
rial. As compared to direct extrusion, the twist extrusion is a cyclic (highly non-
monotonic) process of loading, as during one pass, inside the twist channel the
direction of deformation is changed [7]. Thus, there occur favorable conditions for
healing microvoids of the material as shown by peaks on porosity curve.
Cyclic deformation results in a high plasticity of the deformed material, how-
ever the grain refinement is less intensive as compared to monotonic deformation.
One of the ways of increasing the intensity of substructure grain refinement is the
increase of its amplitude [6]. This is shown by twist extrusion.
In Fig. 3II there is a comparison of two schemes of the twist extrusion: a se-
quence of twist dies of the same orientation and a sequence of interchanging dies
oriented clockwise and anti-clockwise. In the case of scheme with different inter-
changing dies the dislocation charges do not discharge, when the one twist die is
changed by another. So a greater quantity of accumulative zones is formed and
curve N(e) goes higher. The excess of those zones relaxes by the formation of ad-
ditional large-angle boundaries and by increase of porosity, as illustrated by
curves S(e) and θ(e). As expected, we have some improvement of grain refine-
ment, but structure failure has still increased. With e increase, the non-
monotonicity of deformation process less adversely influences the porosity and
for e ≥ 7 the both curves θ(e) merge, while there is still «a gain» in the length of
large-angle boundaries S.
As it has been already said, the processing types resulting in a considerable decrease
of plasticity should activate the formation of fine-grained structure under pressure.
Fig. 3III illustrates the results of calculations showing the role of backpressure
in twist extrusion by the scheme of different interchanging dies. S(e) and d(e)
curves illustrate a more intensive grain refinement and, thus, the smallest size of
fragments corresponds to processing with the backpressure. The run of θ(e) curve
Физика и техника высоких давлений 2004, том 14, № 4
14
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Физика и техника высоких давлений 2004, том 14, № 4
15
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Физика и техника высоких давлений 2004, том 14, № 4
16
evidences the positive influence of backpressure on healing the microvoids of the
material that are the basic cause of its fracture. In such a way, the backpressure
makes it possible to increase plasticity of the metal, the preferences from the grain
refinement being preserved. It can be concluded that the last deformation scheme
is optimal according to characteristics of material structure obtained.
Influence of the formed nanocrystalline state in metals on phase stability
under pressure
It is known that the formation of nanocrystalline (NC) structure by SPD tech-
niques can essentially influence the kinetics and completeness of phase transfor-
mations in metastable materials.
The objects of investigation were Fe−Mn alloys with manganese concentration
CMn = 0−55 wt% and of different phase composition in the initial state.
For Fe, the NC state was reached by high-pressure torsion (HPT). It has been shown
that the formation of NC state in Fe (d ≈ 80 nm) in the process of preliminary HPT with
e = 6−7 and P = 10 GPa increases critical points Pα←ε of direct transformation and de-
creases Pα←ε of reverse transformation by ~ 4 GPa as compared to coarse-grained (CG)
state (d3 ~ 400 µm), as determined by in situ investigations in high-pressure chamber
(see Fig. 4,а). This fact is explained by the stabilizing action of the NC state in Fe,
which is the restraining force for the basic γ → ε transformation (the ratio of the volume
fraction of the microcrystallite boundaries to the «defect-free» portion in NC Fe is 2−3
orders of magnitude larger than the same ratio in CG Fe). HPT with parameters e ≈ 6.4
and P = 10 GPa does not result in α-Fe−Mn alloys (CMn < 10%).
Under SPD by HPT of (γ + ε)- and γ-alloys based on Fe–Mn solid solution a
banded-type structure originates consisting of twins and stacking-fault twins. When
degree of deformation increases (e ≥ 4), the NC state is formed with the average size
of microcrystallites ~80 nm (e ~ 7–8) (it should be stated that NC state is character-
ized by 3–4 fold hardening as compared to the initial one).
0 5 10 15 20
0
20
40
60
80
100
4 2 31
C
ε ,
%
P, GPa
0 5 10 15 20
0
20
40
60
80
100
4
32 1
C
ε ,
%
P, GPa
a b
Fig. 4. Pressure dependence of HCP high-pressure ε-phase concentration Cε in α-Fe (a)
and γ-Fe55Mn45 alloys (b) in CG and NC states: 1, 2 − CG structure (d ≈ 400 µm); 3, 4 –
NC structure (d ≈ 80 nm); 1, 3 – loading; 2, 4 − unloading
Физика и техника высоких давлений 2004, том 14, № 4
17
HPT of (γ + ε)-Fe−Mn alloys results
in the increase of high-pressure HCP ε-
phase as compared to other types of
pressure treatment (direct extrusion,
shock waves). This is confirmed by
investigation of changes in phase com-
position of Fe80Mn20 alloy, placed into
high-pressure chamber, depending on
value of stressed-state indices.
HPT with parameters e = 6.4 and
P = 10 GPa induces γ → ε transforma-
tion in γ-Fe−Mn alloys. In this case,
from 70 (Fe60Mn40 alloy) to 10%
(Fe55Mn45 alloy) of high-pressure HCP ε-phase has been conserved after treat-
ment (the quantity of ε-phase decreases with the increase of stacking-fault energy
in γ-phase) HPT with parameters e ≈ 4−5 and P = 19−20 GPa has induced γ → ε
transformation. After the treatment the high-pressure HCP ε-phase has been con-
served completely (the in situ investigation in Fe−Mn alloys, CMn = 40−55%, is
reversible). Analysis of the results has shown that the increase in hysteresis of the
reverse ε → γ transformation due to stabilization of high-pressure phase in NC
state of γ-Fe−Mn alloys subjected to preliminary HPT is the mechanism of HCP
high-pressure ε-phase stabilization under the decompression (Fig. 4,b).
Investigation of the temperature stability of HCP high-pressure ε-phase in
NC γ-Fe−Mn alloys has shown that the heating to T ≥ 250°C initiates the re-
verse ε → γ-transformation (single-phase γ-state needs a 5 min holding at T ≈
≈ 340−390°C), Fig. 5.
Conclusions
The experiments show that in metals the intensity of grain refinement under
severe plastic deformation increases with pressure. As a result, the hardening of
metals becomes higher than the hardening under atmospheric pressure.
The results of modeling have shown the twist extrusion to be an effective
scheme of deformation accumulation, which gives the improved characteris-
tics of material structure. In the case of the scheme with different inter-
changing twist dies and application of backpressure to the process of defor-
mation make it possible to produce fine-grained low-damage materials pos-
sessing a high plasticity.
The obtained results of complex investigation of alloys based on Fe−Mn solid
solution have shown that their structural-phase state depends on parameters of
SPD under pressure as well as on the initial phase and concentration composition
which, in the end, determines the level of mechanical and service properties of
this class of materials.
100 200 300 400 500
0
20
40
60
80
100
C
ε ,
%
d,
n
m
T, o C
100
200
300
400
500
Fig. 5. Tempering temperature dependence
of the Cε and average size of crystallites
(grains) d for γ-Fe55Mn45 alloy
Физика и техника высоких давлений 2004, том 14, № 4
18
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