Power aspects of energy dissipation during plastic deformation in different stressed states. Part
Work of plastic deformation defined as the area under deformation curve plotted on the «load-absolute elongation» coordinates for tension and on the «torque-turning angle» coordinates for torsion has been considered. To obtain adequate results the specific values of work determined by the «stresses-...
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| Опубліковано в: : | Физика и техника высоких давлений |
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| Дата: | 2006 |
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Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України
2006
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| Цитувати: | Power aspects of energy dissipation during plastic deformation in different stressed states. Part 1/ E.G. Pashinskaya // Физика и техника высоких давлений. — 2006. — Т. 16, № 4. — С. 79-83. — Бібліогр.: 10 назв. — англ. |
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Pashinskaya, E.G. 2014-11-01T16:10:20Z 2014-11-01T16:10:20Z 2006 Power aspects of energy dissipation during plastic deformation in different stressed states. Part 1/ E.G. Pashinskaya // Физика и техника высоких давлений. — 2006. — Т. 16, № 4. — С. 79-83. — Бібліогр.: 10 назв. — англ. 0868-5924 PACS: 61.72.Bb https://nasplib.isofts.kiev.ua/handle/123456789/70261 Work of plastic deformation defined as the area under deformation curve plotted on the «load-absolute elongation» coordinates for tension and on the «torque-turning angle» coordinates for torsion has been considered. To obtain adequate results the specific values of work determined by the «stresses-relative deformation» diagram have been compared. It is shown that for torsion the observed changes in values of specific work of the deformation are 3−5 times larger than for tension. This is connected with different activation of sliding systems during the deformation resulting in changes of the character of developing processes of generation, redistribution, accumulation and annihilation of crystalline structure defects of the material. en Донецький фізико-технічний інститут ім. О.О. Галкіна НАН України Физика и техника высоких давлений Power aspects of energy dissipation during plastic deformation in different stressed states. Part Article published earlier |
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Power aspects of energy dissipation during plastic deformation in different stressed states. Part Pashinskaya, E.G. |
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power aspects of energy dissipation during plastic deformation in different stressed states. part |
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Pashinskaya, E.G. |
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Pashinskaya, E.G. |
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2006 |
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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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Work of plastic deformation defined as the area under deformation curve plotted on the «load-absolute elongation» coordinates for tension and on the «torque-turning angle» coordinates for torsion has been considered. To obtain adequate results the specific values of work determined by the «stresses-relative deformation» diagram have been compared. It is shown that for torsion the observed changes in values of specific work of the deformation are 3−5 times larger than for tension. This is connected with different activation of sliding systems during the deformation resulting in changes of the character of developing processes of generation, redistribution, accumulation and annihilation of crystalline structure defects of the material.
|
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0868-5924 |
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https://nasplib.isofts.kiev.ua/handle/123456789/70261 |
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Power aspects of energy dissipation during plastic deformation in different stressed states. Part 1/ E.G. Pashinskaya // Физика и техника высоких давлений. — 2006. — Т. 16, № 4. — С. 79-83. — Бібліогр.: 10 назв. — англ. |
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Физика и техника высоких давлений 2006, том 16, № 4
79
PACS: 61.72.Bb
E.G. Pashinskaya
POWER ASPECTS OF ENERGY DISSIPATION DURING PLASTIC
DEFORMATION IN DIFFERENT STRESSED STATES. PART 1
Donetsk Institute for Physics and Engineering, named after A. Galkin,
the National Academy of Sciences of Ukraine
72 R. Luxemburg Str., Donetsk 83114, Ukraine
Work of plastic deformation defined as the area under deformation curve plotted on the
«load-absolute elongation» coordinates for tension and on the «torque-turning angle»
coordinates for torsion has been considered. To obtain adequate results the specific val-
ues of work determined by the «stresses-relative deformation» diagram have been com-
pared. It is shown that for torsion the observed changes in values of specific work of the
deformation are 3−5 times larger than for tension. This is connected with different acti-
vation of sliding systems during the deformation resulting in changes of the character of
developing processes of generation, redistribution, accumulation and annihilation of
crystalline structure defects of the material.
Introduction
The current methods used to describe the stressed and strained states by the
continuum mechanics methods [1,2] are based on material presentation as a uni-
form elastic medium. The resulting was a strict classification of the stress-strain
relationship for the elastic region and it has become possible to describe the like
relationship in the plastic region. The description of real polycrystalline materials
as uniform (isotropic) bodies is undoubtedly correct on a macrolevel (deformation
of a body as a whole), but there occur difficulties when this approach is used to
describe elementary processes of plastic deformation on a microlevel (the defor-
mation as a consequence of motion of crystalline structure defects). The problem
is that at this level the medium is no longer considered as the isotropic one and
elementary acts of plastic deformation are just determined by the anisotropy of
crystal lattice structure. The anisotropy present at the microlevel results in varying
behavior of quasi-isotropic bodies under the plastic deformation at the macrolevel.
A descriptive example of macroanisotropy developed under the deformation of
polycrystals is the formation of regions of localized plastic deformation (the Lud-
ers−Chernov lines) during the uniaxial tension of the specimen. It is evident that
the model of uniform medium does not imply that deformation is localized in
Физика и техника высоких давлений 2006, том 16, № 4
80
certain regions and it is expected that the elementary traces of sliding will be
equiprobably distributed in the bulk of material. But in practice we have the proc-
esses of quasi-isotropic medium self-organization and self-organization and
structuring under the influence of power applied from outside.
On the other hand, the dependence of strength and plasticity characteristics of
solids on the stressed-state type has been determined experimentally. It is evident
that parameters of defect (dislocation) structure evolution in single crystallites de-
pend on macrostressed state, however, model representations about the influence
of stressed (and deformed) state of body as a whole on processes of dislocation
motion and nucleation of failure have been insufficiently developed. In such a
way, it becomes necessary to develop theoretical approaches to describe the inter-
action and mutual influence of the processes of deformation and failure nucleation
at different structure (scale) levels.
Formulation of the problem
In the development of such approach one of the problems is the necessity of
physically grounded distinction of structure levels in the structure of real deform-
able alloys. It has been shown [3−5] that processes of power accumulation and
dissipation in the system result in structural and phase transformations followed
by the formation of hierarchy structures in the originally uniform isotropic me-
dium. In what follows we make use of the synergetic approach [3−5] considering
the evolution of material structure under the action of power as a process of non-
equilibrium phase transitions in open systems interchanging with fluxes of power
and substance with the environment.
Relying upon the mentioned representations, let us specify the basic processes
characterizing the accumulation, redistribution and reduction of the accumulated
power in polycrystalline material during plastic deformation under the influence
of external forces and power fluxes (Fig.).
Due to this scheme it can be assumed that a change in parameters of the A-type
processes (including those resulting from changes in the stressed and strained
state of the material) induces changes in the flow of the B-type processes, thus in-
fluencing the run of processes of type C and D. In this way, for subsequent analy-
sis we propose to use the approach based on the estimation of balance between
power fluxes in the material. Furthermore, according to the principles formulated,
in particular, in papers [6−9], the system evolution is towards the attaining of a
relative minimum of the accumulated power.
Discussion. Work of plastic deformation
Let us demonstrate the essence of the approach by means of simplest example.
We evaluate power consumption for the uniaxial tension and torsion during the
plastic deformation.
The work of plastic deformation can be estimated as the area under the defor-
mation curve plotted on the «load-absolute elongation» coordinates for the case of
Физика и техника высоких давлений 2006, том 16, № 4
81
Fig. Scheme of relationship between the processes of power redistribution and transfor-
mation of structure under the plastic deformation.
specimen tension and on the «torque-turning angle» coordinates for the case of
torsion. To obtain the comparable results we must take specific values deter-
mined by the «stress-relative deformation» diagram. It has been shown [10] that
for different tests the primary diagrams can be transformed to generalized curve
of the flow. The physical sense of quantitative value obtained by the integration
of the flow curve can be interpreted as the work of deformation of materials unit
volume.
Apart from physical arguments, this is confirmed by the analysis of dimen-
sions of quantities: J/m3 = H·m/m3 = H/m2.
The processing of the flow curves [10] for copper (the fcc lattice) and iron (the
bcc lattice) in the annealed state and subjected to cold prestraining gave the results
listed in Table.
А. External power sources:
1. Operation of elastic defor-
mation.
2. Operation of plastic defor-
mation.
3. External heat fluxes.
B. Processes of power dissi-
pation and redistribution:
1. Generation of crystal-struc-
ture defects.
2. Motion of crystal-structure
defects.
3. Interaction of crystal-struc-
ture defects.
4. Increase of heat content in
deformed material.
C. Processes of structural
transformations in deformed
material as a consequence of an
increase in internal energy of the
material:
1. Accumulation of defects.
2. Formation of deformational
dislocation structures.
3. Crystallite shape change.
4. Formation of regions of
localized deformation.
5. Processes of intergrain ac-
comodation of deformation.
D. Processes of physical and
structural transformations in de-
formed material relating with a
decrease in the internal power of
the material:
1. Annihilation of defects.
2. Polygonization.
3. Recrystallization.
4. Heat transfer to the envi-
ronment.
Физика и техника высоких давлений 2006, том 16, № 4
82
Table
Specific work of deformation prior to materials failure
Material State Specific work upon
tension, J/mm3
Specific work upon
torsion, J/mm3
Cold-work 0.01−0.02 0.30−0.35Copper Annealing 0.08−0.10 0.35−0.40
Cold-work 0.02−0.03 0.50−0.55Iron Annealing 0.10−0.12 0.80−0.90
The analyzed results show that values of power absorbed under realization of
the B-type processes (see Fig.) much (1−2 orders of magnitude) differ for one and
the same material depending on the initial state and loading type. At the same
time, for identical states and loading types the differences (2−2.5 times) in the first
approximation correspond to differences in moduli of elasticity and in values of
materials strength.
We can qualitatively explain the influence of the original state by a high level
of power preaccumulated by specimens subjected to cold drawing and, as a result,
the material is less capable of dissipating power applied later on. At the same
time, the changes in specific work of the deformation observed at the tension-
torsion stage have no trivial explanation and should be analyzed in detail. Of spe-
cial importance is the fact that upon twisting the work of deformation is less re-
spondent to the cold-work in the case of cold predrawing as compared to that
during tension, especially in the material with fcc lattice. Within the above-
formulated approach it can be postulated that such a significant difference in
power parameters of the deformation process should be associated with different
character of developed processes of generation, redistribution, accumulation and
annihilation of crystal structure defects.
First we assume that the main mechanism of power accumulation is the in-
crease of the dislocation density under disordered (chaotic) distribution thereof in
the bulk of material. Basing on values of the specific work of deformation that are
listed in the Table we can evaluate the increase in density of crystal structure de-
fects. Power of chaotically arranged dislocations can be estimated from the relation
Аdis = 2ραGb2,
where ρ � dislocation density, α � structural factor, G � shear modulus, b � Bur-
gers vector.
Let us specify values of parameters: α = 1; Burgers vector � of 2.5·10−10 m,
shear modulus � of the order of 40 GPa for copper and 2·10−10 m, 80 GPa for iron,
respectively.
It follows from the equation that for the absorption of deformation work of the
order of 0.01-1 J/mm3 the dislocation density should be increased by 1011−1013 m−2.
Taking into account that in highly annealed metal the original dislocation density
is at a level of 107−108 m−2, the total density (1018−1021 m−2) is much larger than
Физика и техника высоких давлений 2006, том 16, № 4
83
the experimentally observed values for metals before failure (1014−1015 m−2). In
the case of metal after the cold-work the discrepancy is even more prominent.
Thus, it can be concluded that during the cold plastic deformation, in the metal
there are active processes of motion, redistribution and annihilation of generated
defects of the crystal structure, to provide the dissipation of mechanical energy
applied from outside. This topic will be discussed in the second part of the paper.
It should be noted that the process of dislocation motion is the definitive one as a
possibility of dislocation redistribution and annihilation depends on it.
Conclusion
In plastic materials the macroscopic plastic deformation is the sum of multiple
acts of shear, which, in turn, results from the sliding of dislocations in sliding systems
activated with the stressed state. Therefore, the following statement can be formu-
lated: during the deformation the stressed state effect on plasticity reserve is through
different activation of sliding systems. Upon torsion, the deformation scheme is evi-
dently of simple shear type when the direction of action of the maximum tangential
stresses is constant and the state of direction of the largest elongation with respect to
the line of stress action is continuously changed. Therefore, during the torsion more
and more new sliding systems are involved. In the case of tension, the angle between
the direction of action of the maximum tangential stresses remains constant, which
does not favour the activation of new sliding systems. Upon torsion of the predrawn
specimens the dislocation motion develops in systems that were not activated before
because of changes in direction of action of the maximum tangential stresses and in
direction of the maximum elongation, so the influence of pretreatment in the case of
torsion is weaker than in the case of tension. Upon the tension of drawn specimens,
position of the both directions is preserved, thus leading to exhaustion of plasticity
reserve in the limited number of sliding systems activated before.
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