Physical model of W and Ti compound during hot vacuum rolling in the solid phase
The paper considers alternative methods for protecting metal surfaces from corrosion-erosion destruction (CED), based on galvanization or on the use of an oxide film. Their advantages and disadvantages are noted. For the manufacture of CED-resistant tungsten targets, which are used in the subcritica...
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irk-123456789-1961002023-12-10T14:53:45Z Physical model of W and Ti compound during hot vacuum rolling in the solid phase Andrieieva, O.L. Tkachenko, V.I. Physics of radiation and ion-plasma technologies The paper considers alternative methods for protecting metal surfaces from corrosion-erosion destruction (CED), based on galvanization or on the use of an oxide film. Their advantages and disadvantages are noted. For the manufacture of CED-resistant tungsten targets, which are used in the subcritical assembly created at the NSC KIPT, it is proposed to use the method of vacuum rolling of W and Ti. A layer of Ti serves as a protective coating. To describe the process of combining these metals, a model description is proposed, which is based on the use of the Rayleigh-Taylor dissipative instability theory (DRTI). An estimate of the values of the parameters of a binary metal system subjected to DRTI is given. The obtained characteristic bonding time of dissimilar metals corresponds to that observed in experiments. Розглянуті альтернативні методи запобігання металевих поверхонь корозійно-ерозійному руйнуванню (КЕР), засновані на гальванізації або на використанні оксидної плівки. Відзначені їхні переваги та недоліки. Для виготовлення стійких до КЕР вольфрамових мішеней, які використовуються у створеній ННЦ ХФТІ підкритичній збірці, запропоновано використовувати метод вакуумної прокатки W і Ti. Захисним покриттям є шар Ti. Для опису процесу з’єднання цих металів запропоновано модельний опис, який ґрунтується на використанні теорії дисипативної нестійкості Релея-Тейлора (ДНРТ). Наведено оцінку значень параметрів бінарної металевої системи, схильної до ДНРТ. Отриманий характерний час з’єднання різнорідних металів відповідає спостережуваному в експериментах. 2023 Article Physical model of W and Ti compound during hot vacuum rolling in the solid phase / O.L. Andrieieva, V.I. Tkachenko // Problems of Atomic Science and Technology. — 2023. — № 2. — С. 118-121. — Бібліогр.: 18 назв. — англ. 1562-6016 DOI: https://doi.org/10.46813/2023-144-118 http://dspace.nbuv.gov.ua/handle/123456789/196100 621.771+621.791.051.4+669-1 en Problems of Atomic Science and Technology Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Physics of radiation and ion-plasma technologies Physics of radiation and ion-plasma technologies |
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Physics of radiation and ion-plasma technologies Physics of radiation and ion-plasma technologies Andrieieva, O.L. Tkachenko, V.I. Physical model of W and Ti compound during hot vacuum rolling in the solid phase Problems of Atomic Science and Technology |
| description |
The paper considers alternative methods for protecting metal surfaces from corrosion-erosion destruction (CED), based on galvanization or on the use of an oxide film. Their advantages and disadvantages are noted. For the manufacture of CED-resistant tungsten targets, which are used in the subcritical assembly created at the NSC KIPT, it is proposed to use the method of vacuum rolling of W and Ti. A layer of Ti serves as a protective coating. To describe the process of combining these metals, a model description is proposed, which is based on the use of the Rayleigh-Taylor dissipative instability theory (DRTI). An estimate of the values of the parameters of a binary metal system subjected to DRTI is given. The obtained characteristic bonding time of dissimilar metals corresponds to that observed in experiments. |
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Article |
| author |
Andrieieva, O.L. Tkachenko, V.I. |
| author_facet |
Andrieieva, O.L. Tkachenko, V.I. |
| author_sort |
Andrieieva, O.L. |
| title |
Physical model of W and Ti compound during hot vacuum rolling in the solid phase |
| title_short |
Physical model of W and Ti compound during hot vacuum rolling in the solid phase |
| title_full |
Physical model of W and Ti compound during hot vacuum rolling in the solid phase |
| title_fullStr |
Physical model of W and Ti compound during hot vacuum rolling in the solid phase |
| title_full_unstemmed |
Physical model of W and Ti compound during hot vacuum rolling in the solid phase |
| title_sort |
physical model of w and ti compound during hot vacuum rolling in the solid phase |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2023 |
| topic_facet |
Physics of radiation and ion-plasma technologies |
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http://dspace.nbuv.gov.ua/handle/123456789/196100 |
| citation_txt |
Physical model of W and Ti compound during hot vacuum rolling in the solid phase / O.L. Andrieieva, V.I. Tkachenko // Problems of Atomic Science and Technology. — 2023. — № 2. — С. 118-121. — Бібліогр.: 18 назв. — англ. |
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Problems of Atomic Science and Technology |
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118 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144)
https://doi.org/10.46813/2023-144-118
UDC 621.771+621.791.051.4+669-1
PHYSICAL MODEL OF W AND Ti COMPOUND DURING HOT
VACUUM ROLLING IN THE SOLID PHASE
O.L. Andrieieva
1
, V.I. Tkachenko
1,2
1
National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
2
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: tkachenko.vikiv52@gmail.com; tkachenko@kipt.kharkov.ua
The paper considers alternative methods for protecting metal surfaces from corrosion-erosion destruction (CED),
based on galvanization or on the use of an oxide film. Their advantages and disadvantages are noted. For the
manufacture of CED-resistant tungsten targets, which are used in the subcritical assembly created at the NSC KIPT,
it is proposed to use the method of vacuum rolling of W and Ti. A layer of Ti serves as a protective coating. To
describe the process of combining these metals, a model description is proposed, which is based on the use of the
Rayleigh-Taylor dissipative instability theory (DRTI). An estimate of the values of the parameters of a binary metal
system subjected to DRTI is given. The obtained characteristic bonding time of dissimilar metals corresponds to that
observed in experiments.
INTRODUCTION
In a number of technological processes, it is
necessary to use metal structures that can withstand
such external factors as: aggressive environments; high
temperatures; elevated pressures, corpuscular flows and
electromagnetic radiation, as well as mechanical effects
(abrasion, bending, wear, etc.). Under such conditions,
metal structures are subject to corrosion, accompanied
by degradation under the influence of the external
environment, or, to a lesser extent, erosion,
accompanied by destruction due to mechanical
influences [1].
As a rule, electrochemical corrosion is observed in
aqueous media, since it proceeds in solutions –
electrolytes. Erosive destruction is inherent in metal
structures that come into contact and are washed by
water flows.
For the course of metal corrosion processes, the
following factors are of great importance: type of metal;
homogeneity of its bulk structure; surface cleanliness;
the magnitude of the electrode potential and the ability
of the metal to passivate. The passivation of metals, i.e.,
the slowing down of the corrosion process, is caused by
a change in the metal surface during the formation of
oxide films on it. The possibility of passivation depends
on the nature of the metal [1]. Metals such as aluminum,
titanium, tantalum, tungsten, nickel, chromium and
other metals are very easy to passivate.
From the above list of metals, let us dwell on the
consideration of the corrosion-erosion properties of W
as the most suitable candidate for the manufacture of
targets for the NSC KIPT subcritical assembly [2]. As
follows from [2], subcritical assembly targets are plates
in the form of rectangular prisms made of W, the
thickness of which is much less than equal length and
width.
However, it is known that W has poor corrosion
resistance with respect to aqueous coolants due to the
formation of a WO3 oxide film on the surface with a
continuity of SW = 3.35. It is known that at a continuity
of SMe > 2.5, the protective properties of the film
deteriorate as a result of an increase in internal stresses
and, as a consequence, its swelling and peeling [3].
Thus, the use of an oxide film W does not provide
protection against corrosion-erosion destruction of the
material.
In addition, W is characterized by high susceptibility
to radiation embrittlement [4, 5], which also does not
contribute to maintaining the integrity of the material.
Therefore, to use W as targets in a subcritical
assembly bathed in an aqueous coolant and exposed to
high-energy electron flows, it is necessary to find ways
to ensure their corrosion-erosion resistance.
One of the approaches to impart corrosion and
erosion resistance to W can be the use of galvanic
deposition of cladding coatings from various metals. Ti
and Ta can be chosen as such metals, which are also
corrosion resistant, but less brittle compared to W. Such
coatings are good for providing erosion resistance of
large and small (end) areas of metal plates.
However, the galvanization technology is
characterized by a multi-stage process, special
requirements for cladding metals, thorough surface
preparation, and requires long process times.
Electroplated coatings, depending on the operating
conditions of the part [6], have a thickness of
0.1…60 µm are characterized by low adhesive strength
(does not exceed the tensile strength of the least durable
metal), as well as inhomogeneity in thickness (arises
due to the presence of sharp corners and edges parts
closest to the anode).
Thus, galvanization is also of little use for ensuring
the corrosion-erosion resistance W of the plates.
The most suitable method for ensuring the corrosion
and erosion resistance W of plates is the method of
joining dissimilar metals in the solid phase by hot
vacuum rolling (HVR) [2]. This method makes it
possible to eliminate the disadvantages of galvanic
coatings noted above. For example, the adhesion
strength of an electrolytic iron coating with mild steel
(steel 10) is about 280…300 MPa [7].
mailto:tkachenko.vikiv52@gmail.com
mailto:tkachenko@kipt.kharkov.ua
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) 119
On the other hand, in the case of HVR, the strength
of the joint W (ultimate strength 1200 MPa [8]) and, for
example, a thin layer of Ti (ultimate strength 600 MPa
[8]) or Ta (ultimate strength 470 MPa [9]) is determined
by the value that exceeds the ultimate strength of a less
durable metal [10].
For a comparative assessment of the strength of the
connection of dissimilar metals, we consider the
galvanic and HVR methods of connection. It follows
from the conclusions [10] that the value of the strength
of the interface between iron (ultimate strength
250 MPa [8]) and steel 10 (ultimate strength 340 MPa
[11]) is less than 340 MPa. This value exceeds the
ultimate strength of the galvanic connection of such
metals [7].
This paper proposes a physical model for describing
the formation conditions and estimating the parameters
of the target of the NSC KIPT subcritical assembly
created by the W and Ti HVR.
EXPERIMENTAL DATA AND MODEL
DESCRIPTION OF W AND Ti COMPOUND
BY ROLLING IN VACUUM
The model of joining W and Ti by rolling in vacuum
was formulate for the experimental setup and
experimental conditions, which are describe in [2].
In this work, the joining of Ta-Ti-W-Ti-Ta by hot
rolling in vacuum is carried out in two stages. Heating
of the package in the furnace up to 1300
0
C with a
holding time of about 1 h and feeding the package under
the rolls.
At the first stage of rolling, rolls move a strong Nb
alloy mandrel, in which Ta-Ti-W-Ti-Ta layers are
packed rigidly and symmetrically with respect to the
tungsten layer. The movement of the mandrel is carried
out in the forward, reverse and again in the forward
direction. Rolling ends when the rolls are in the middle
of the mandrel. This stage will be called dynamic.
In the second stage of rolling, the rolls remain in a
position in the middle of the mandrel, and this state is
maintained for several hours. This stage of rolling will
be called static.
The experimental conditions indicate the absence of
relative motion of the rolled metals: a strong mandrel
does not allow the metals to move relative to each other.
However, it transmits the force of the rolls in the
direction transverse to the speed of movement of the
metals. Due to the high pressures and rather high
temperature of the samples, small volumes of Ti can
pass into a quasi-liquid state [12], while the Nb alloy,
tantalum, and tungsten remain in the solid phase. This
assertion will be supported by estimates below.
In the microscopic dimension, a schematic
representation of the interface between W and Ti after
the dynamic stage (at the beginning of the static phase)
can be represented as shown in Fig. 1.
From Fig. 1 follows, apparently, at the dynamic
stage of rolling, protrusions W penetrate into the quasi-
liquid Ti, while depressions in W remain unfilled.
Fig. 1. Scheme of the arrangement of rolled metals at
the beginning of the static phase. Vacuum cavities
formed by depressions in the tungsten relief are
shown at the interface between the tungsten sample
and the titanium plate
PHYSICAL MODEL FOR THE
DESCRIPTION OF THE W AND Ti HVR
PROCESS AT THE STATIC STAGE
At the static stage Ti penetrates into
microdepressions in W and the surface of Ti and W
joins along the entire interface. Let us consider in more
detail this process of joining metals.
We will assume that, in view of the quasi-liquid
state of Ti, the process of joining metals occurs as a
result of the penetration of Ti into the irregularities of
the tungsten boundary. Since the irregularities of
tungsten are filled with rarefied air (vacuum), the
joining process will be associated with the penetration
of a heavier substance (quasi-liquid Ti) into a lighter
substance (vacuum). The whole system is placed in a
force field, the effective acceleration of which g* is
determined by the force of volumetric compression Ti
with the Ta + Nb alloy on the one hand, and W – on the
other, due to different coefficients of their thermal
expansion.
Thus, generalizing the above scheme of joining
metals, we arrive at the Rayleigh-Taylor instability
problem, which describes the motion of the interface
between contacting media located in a gravitational [13]
or other force field. In media with dissipation, which is
the viscosity of media, such instabilities are called
dissipative Rayleigh-Taylor instabilities (DRTI) [14].
To describe the connection of Ti with tungsten, we
will consider the process to be completed when Ti fills
the irregularities of tungsten. Therefore, to describe
such a connection process, we will assume that a
heavier, incompressible quasi-liquid – Ti with a density
ρ1 and dynamic viscosity μ1 borders on a less heavy
incompressible liquid – rarefied air, density ρ2 and
dynamic viscosity μ2. The unperturbed interface
coincides with the plane z=0. The heavier liquid is
indicated by index 1 and is located in the region z>0.
On Fig. 2 shows a schematic representation of the
location of the contacting media, the boundary between
which is subject to DRTI.
Under the compressive stress of the rolls, the
boundary of Ti, which is in the liquid state, is subjected
to the action of surface tension forces and effective
acceleration. Under certain conditions, it can be
unstable as a result of the development of DRTI [14].
Ta
Ti
W
120 ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144)
Fig. 2. Schematic representation of the location
of the contacting media, the boundary between
which is subject to DRTI
Let us estimate the characteristic parameters of the
media and determine the conditions for the development
of such instability.
The dependence of the boundary deviation
amplitude Ti from the equilibrium position on time t has
the form [14]: ( (
)), where – small
deviation of the boundary from the equilibrium position;
– dimensionless instability increment; – charac-
teristic time of the considered system.
The DRTI increment is determined from the
equation [14]:
( ) (1)
where , ,
( )
( )
, √
| |
,
√
( )
| |
.
– wave number; – perturba-
tion wavelength; – surface tension coefficient Ti in
the quasi-liquid state.
If we put ρ1>ρ2 in (1), then the DRTI increment is
determined by the expression
( ) √ , from which it
follows that perturbations of the interface, just as in the
absence of viscosity, occur for wavelengths in the
interval .
On Fig. 3 shows the dependence of the increment of
instability of the interface between media Λ(q) on the
dimensionless wave number q for different values of the
dimensionless viscosity μ*.
From Fig. 3 it follows that with an increase in the
dimensionless viscosity μ*, the maximum value of the
growth rate decreases and shifts to the long-wavelength
part of the perturbation spectrum.
From expression (1), we estimate the time of joining
the boundary Ti + W.
To do this, we use the layout of the metals to be
joined and indicate their characteristic thickness Ta –
250 µm; Ti – 30…50 µm; W – (2.5…9.5)·10
-3
m.
During rolling the compression force of the samples
was created by the pressure of the rolls up to 40 Ts on
the area of contact with the mandrel made of Nb alloy
(the outer area of the upper and lower mandrels is
100×100 mm, the thickness is 20 mm), between which
there was a layer of metals Ta+Ti+W+Ti+Ta (see
Fig. 1).
At an average pressure of the rolls of 4 Ts, the
compression force Ti during rolling can be estimated by the
value
MPa.
Fig. 3. Dependence of the dimensionless increment of
the DRTI of the boundary Ti – Λ(q) on the dimensionless
wave number q for different values of the dimensionless
viscosity: *=0; 1; 10; 100; 1000
It can be seen from the above estimate that, under
experimental conditions, the stress created by the rolls
exceeds the yield strength of Ti ~ 5 MPa, but is less than
the yield strength of the Nb alloy (~18 MPa) [15–17].
At such a pressure and temperature, a thin layer of
Ti can pass into a quasi-liquid state [12] and can form a
boundary with tungsten, a simplified view of which is
shown in Fig. 1.
In the static stage, the mandrel and hard metals are
cooled and reduced in size. Under such conditions, after
the redistribution and balancing of the stresses created
by the rolls, the quasi-liquid Ti will be under an
equilibrium pressure, which can be estimated by the
value
. At this pressure, let us estimate the value
of the instability growth rate (1). To do this, we use
tabular data characterizing the physical properties of Ti:
– density Ti at melting point – 4110 kg/m
3
;
– coefficient of surface tension Ti at the melting
point N/m [18];
– kinematic viscosity of molten Ti
=1.01 m
2
/s [16].
The effective acceleration resulting from the
compression of the samples by the rolls can be
estimated by the value
, where – the
thickness of the mandrel with the tungsten layer, which
in the experiment was on the order of H(3…5)∙10
–5
m.
Therefore | |
m
m
m
m/s
2
.
Because the , expressions for
and are simplified and are determined by the
quantities: √
( )
√
( )
m and
√
√
s. For these parameters, the
dimensionless kinematic viscosity Ti is determined by a
quantity on the order of
1.33∙10
2
.
ISSN 1562-6016. Problems of Atomic Science and Technology. 2023. №2(144) 121
Let us estimate the time of development of the
instability of perturbations with the wave number ,
corresponding to the maximum growth rate for
dimensionless kinematic viscosity .
Calculations show that . For
these parameters, the characteristic time of joining Ti
and W is about ⁄ s. It should be noted that
the experimentally selected holding time of the joined
metals corresponds in order of magnitude to the above
theoretical estimate.
Thus, the physical basis for the connection of Ti and
W is the development of the DRTI [14].
CONCLUSIONS
The article considers the process of joining Ti and W
by hot rolling in a vacuum (HRV). Based on the
analysis of the experimental data obtained and the
characteristic parameters of metals, it is proposed to
consider the process of their joining within the
framework of the problem of the development of the
DRTI. This instability describes the motion of the
interface between the contacting media as a result of the
impact of the compressive force of the rolls. An
estimate is obtained for the values of the characteristic
time of instability development and the characteristic
size of the perturbation of a binary metallic system
subject to DRTI. It is shown that the characteristic time
of joining Ti and W by the HRV method corresponds in
order of magnitude to that observed in experiments.
ACKNOWLEDGEMENTS
This work was carried out at the expense of the
target program of scientific research of the National
Academy of Sciences of Ukraine “Nuclear and radiation
technologies for the energy sector and public needs” for
2022 (КПКВК 6541030).
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Article received 11.02.2023
ФІЗИЧНА МОДЕЛЬ З'ЄДНАННЯ W И Ti ПРИ ВАКУУМНІЙ ПРОКАТЦІ У ТВЕРДІЙ ФАЗІ
О.Л. Андрєєва, В.І. Ткаченко
Розглянуті альтернативні методи запобігання металевих поверхонь корозійно-ерозійному руйнуванню
(КЕР), засновані на гальванізації або на використанні оксидної плівки. Відзначені їхні переваги та недоліки.
Для виготовлення стійких до КЕР вольфрамових мішеней, які використовуються у створеній ННЦ ХФТІ
підкритичній збірці, запропоновано використовувати метод вакуумної прокатки W і Ti. Захисним покриттям
є шар Ti. Для опису процесу з'єднання цих металів запропоновано модельний опис, який ґрунтується на
використанні теорії дисипативної нестійкості Релея-Тейлора (ДНРТ). Наведено оцінку значень параметрів
бінарної металевої системи, схильної до ДНРТ. Отриманий характерний час з'єднання різнорідних металів
відповідає спостережуваному в експериментах.
https://www.nature.com/articles/185455a0#auth-P__J_-BURDON
https://www.nature.com/articles/185455a0#auth-G__L_-DAVIS
https://www.nature.com/
https://link.springer.com/article/10.1007/s42864-021-00075-9#auth-Hang-Xu
https://link.springer.com/article/10.1007/s42864-021-00075-9#auth-Lan_Li-He
https://link.springer.com/article/10.1007/s42864-021-00075-9#auth-Yong_Feng-Pei
https://link.springer.com/article/10.1007/s42864-021-00075-9#auth-Chang_Zhong-Jiang
https://link.springer.com/article/10.1007/s42864-021-00075-9#auth-Wen_Qing-Li
https://link.springer.com/article/10.1007/s42864-021-00075-9#auth-Xiang_Heng-Xiao
https://link.springer.com/journal/42864
https://www.center-pss.ru/st/st166.htm
https://helpiks.org/4-8280.html
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