Correlation dependences between short-term/long-term static strength characteristics and creep resistance of tungsten at high temperatures
Experimental data on high-temperature mechanical properties under uniaxial tension of commercially pure tungsten obtained by powder metallurgy have been analyzed. It has been found that for powder metallurgy tungsten in the high-temperature region ~ (0.5 — 08)Tmelt, there is a close corr...
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irk-123456789-478292013-08-02T19:38:07Z Correlation dependences between short-term/long-term static strength characteristics and creep resistance of tungsten at high temperatures Borisenko, V.A. Bukhanovskii, V.V. Mamuzic, I. Научно-технический раздел Experimental data on high-temperature mechanical properties under uniaxial tension of commercially pure tungsten obtained by powder metallurgy have been analyzed. It has been found that for powder metallurgy tungsten in the high-temperature region ~ (0.5 — 08)Tmelt, there is a close correlation among the characteristics of short- and long-term static strengths and creep resistance, which are described by a single functional relation. Проаналізовано механічні характеристики технічно чистого вольфраму, що отриманий методами порошкової металургії, за одновісного розтягу в умовах високих температур. Установлено, що для вольфраму в області високих температур ~ (0,5...0,8)Тпл існують кореляційні зв’язки між характеристиками короткочасної та тривалої статичної міцності й опору повзучості, що описуються єдиною функціональною залежністю. Проанализированы механические характеристики технически чистого вольфрама, полученного методами порошковой металлургии, при одноосном растяжении в условиях высоких температур. Установлено, что для вольфрама в высокотемпературной области ~(0,5...0,8)Тпл существуют корреляционные связи между характеристиками кратковременной и длительной статической прочности и сопротивления ползучести, которые описываются единой функциональной зависимостью. 2005 Article Correlation dependences between short-term/long-term static strength characteristics and creep resistance of tungsten at high temperatures / V.A. Borisenko, V.V. Bukhanovskii, I. Mamuzic // Проблемы прочности. — 2005. — № 6. — С. 50-60. — Бібліогр.: 15 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/47829 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 Borisenko, V.A. Bukhanovskii, V.V. Mamuzic, I. Correlation dependences between short-term/long-term static strength characteristics and creep resistance of tungsten at high temperatures Проблемы прочности |
| description |
Experimental data on high-temperature mechanical
properties under uniaxial tension of commercially
pure tungsten obtained by powder
metallurgy have been analyzed. It has been
found that for powder metallurgy tungsten in
the high-temperature region ~ (0.5 — 08)Tmelt,
there is a close correlation among the characteristics
of short- and long-term static strengths
and creep resistance, which are described by a
single functional relation. |
| format |
Article |
| author |
Borisenko, V.A. Bukhanovskii, V.V. Mamuzic, I. |
| author_facet |
Borisenko, V.A. Bukhanovskii, V.V. Mamuzic, I. |
| author_sort |
Borisenko, V.A. |
| title |
Correlation dependences between short-term/long-term static strength characteristics and creep resistance of tungsten at high temperatures |
| title_short |
Correlation dependences between short-term/long-term static strength characteristics and creep resistance of tungsten at high temperatures |
| title_full |
Correlation dependences between short-term/long-term static strength characteristics and creep resistance of tungsten at high temperatures |
| title_fullStr |
Correlation dependences between short-term/long-term static strength characteristics and creep resistance of tungsten at high temperatures |
| title_full_unstemmed |
Correlation dependences between short-term/long-term static strength characteristics and creep resistance of tungsten at high temperatures |
| title_sort |
correlation dependences between short-term/long-term static strength characteristics and creep resistance of tungsten at high temperatures |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2005 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/47829 |
| citation_txt |
Correlation dependences between short-term/long-term static strength characteristics and creep resistance of tungsten at high temperatures / V.A. Borisenko, V.V. Bukhanovskii, I. Mamuzic // Проблемы прочности. — 2005. — № 6. — С. 50-60. — Бібліогр.: 15 назв. — англ. |
| series |
Проблемы прочности |
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| first_indexed |
2025-07-04T07:52:47Z |
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2025-07-04T07:52:47Z |
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1836702046846189568 |
| fulltext |
UDC 539.4
Correlation Dependences between Short-Term/Long-Term Static
Strength Characteristics and Creep Resistance of Tungsten at High
Temperatures
V. A. Borisenko,a V. V. Bukhanovskii,a and I. Mamuzicb
a Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine,
Kiev, Ukraine
b Faculty of Metallurgy, University of Zagreb, Sisak, Croatia
УДК 539.4
Взаимосвязь между характеристиками кратковременной и
длительной статической прочности и сопротивления ползучести
вольфрама при высоких температурах
В. А. Борисенкоа, В. В. Бухановскийа, И. Мамузич6
а Институт проблем прочности им. Г. С. Писаренко НАН Украины, Киев, Украина
6 Загребский университет, Шишак, Хорватия
Проанализированы механические характеристики технически чистого вольфрама, полученно
го методами порошковой металлургии, при одноосном растяжении в условиях высоких темпе
ратур. Установлено, что для вольфрама в высокотемпературной области ~(0,5...0,8)Тпл
существуют корреляционные связи между характеристиками кратковременной и длитель
ной статической прочности и сопротивления ползучести, которые описываются единой
функциональной зависимостью.
Ключевые слова : вольфрам, кратковременная и длительная статическая
прочность, сопротивление ползучести, высокие температуры.
Introduction. The progress in a number of branches of modern engineering
is related to the use of refractory metals and alloys, which can ensure strength of
components and structural elements operating under conditions of extremely high
temperatures (up to 2300-3300 K) and mechanical loads. Tungsten and tungsten-
based alloys have the most unique range of physico-mechanical characteristics
including heat resistance [1-3].
In addition to short-term strength, the characteristics of long-term static
strength and creep are the most important factors characterizing serviceability of
metals at high temperatures. Complete experimental evaluation of such
characteristics for refractory materials presents great difficulties and is unrealistic
in many cases.
It is known that temperature dependences of various mechanical
characteristics that determine the resistance of metallic materials to deformation
are qualitatively similar. Under short-term and long-term static loading, there are
© V. A. BORISENKO, V. V. BUKHANOVSKII, I. MAMUZIC, 2005
50 ISSN 0556-171X. Проблемы прочности, 2005, № 6
Correlation Dependences between
correlation dependences between strength characteristics of metals and alloys,
which can be described by certain analytical expressions based on both empirical
and physically justified approaches. They are undoubtedly of scientific and
practical interest, because they make it possible to evaluate heat-resistance
characteristics of advanced structural materials at minimum cost [4, 5].
In the present study, based on the analysis of experimental data obtained
earlier, a generalized correlation dependence has been established between the
characteristics of high-temperature short-term and long-term static strength and
creep resistance of commercially pure tungsten produced by powder metallurgy
(PM) technique.
Theoretical Background. On the basis of numerous experiments it has been
found that temperature dependence of any mechanical characteristics, which
determine the resistance of metallic materials to deformation, is described
quantitatively by the following equation [4]:
which, considering weak influence of preexponential terms as compared to the
exponent, is simplified appreciably and takes the form
where M is the mechanical characteristic of the material, £ is the plastic strain
rate, T is the thermodynamic temperature, G is the shear modulus, U is the
plastic strain activation energy (enthalpy), k is the Boltzmann constant, B is the
material parameters’ function involving the entropy term exp(—S /k ), and c is a
constant, which is a function of the material parameters and strain rate.
From Eq. (2) it follows that in the absence of physicochemical
transformations in the material, the logarithm of the deformation resistance (ln M )
should vary depending on the inverse thermodynamic temperature (1/T) according
to a linear law. In practice, the dependence turns out to be more complex and
generally the ln M — 1/ T curve has the form of a broken line. Low- and
high-temperature kinks in the logarithm of mechanical characteristic vs inverse
thermodynamic temperature curves accompanied by the variation of the slope
take place for metals at ~0.2Tmeit and at about (0.5-0.55)Tmeft, respectively.
Both types of these kinks are generally related to changes in the dominating
mechanism of the material plastic deformation [3, 4].
When a material is deformed by a constant load under the action of high
stresses (exceeding 10—4 of the shear modulus G) in the high-temperature region
(above 0.5Tmeit), the following relations hold true [6]:
(1)
(2)
(3)
ISSN 0556-171X. npodxeMbi npounocmu, 2005, N 6 51
V. A. Borisenko, V. V. Bukhanovskii, and I. Mamuzic
r = B 0To n e x p f ^ I , (4)
where £ is the steady-state creep rate, r is the creep-rupture time, o is the
stress, A0 and B 0 are material constants, and n is a parameter, which
characterizes the slopes of the steady-state creep rate and creep-rupture time vs
stress curves in the logarithmic coordinate system [5].
At constant temperature, expressions (3) and (4) are transformed to the
following equations:
£ = aT o n , (5)
r = B T o ~ n , (6)
T Twhere A0 and B 0 are material constants at a given temperature.
Equations (3) and (4) can be reduced to the Monkman-Grant expression.
This testifies that the product of the steady-state creep rate and creep-rupture time
is a constant value independent of the applied stress and temperature:
£ r = C MG = const. (7)
Here C mg is the Monkman-Grant constant that usually has narrow margins
(between 0.03 and 0.3) for all materials [6-9]. For tungsten, the C Mg values
range approximately between 0.02 and 0.17 [6, 10-13].
Results and Discussion. The amount of accumulated experimental data on
the mechanical properties of tungsten produced by PM technique [10-13] makes
it possible to analyze them and establish correlation dependences between the
characteristics of its short-term and long-term static strength and creep resistance.
The experimental results considered refer to a high-temperature region (above
0.5Tmeit) and are obtained for high stresses (higher than 10_4 of the Young
modulus) at short test time (up to 104 s). Therefore, when processing the data, we
used the approaches based on the assumption that in certain regions of
temperatures and stresses, the strength of metals and alloys under the studied
loading conditions is governed by the same mechanisms of plastic deformation
and fracture. We considered that the influence of temperature on the material
softening under conditions of short-term active and long-term static loading is
similar. The results of fractographic examinations, which establish similarity of
the PM tungsten fracture modes under conditions of high-temperature creep and
static tests, confirm the validity of the hypotheses taken as the basis for our
further considerations [10, 11]. The similarity of the mechanisms of plastic
deformation under active tension and deformation at the stage of steady-state
creep for metallic materials was also noted in [4, 14], where it was mentioned that
under conditions of high-temperature uniform tension, the strain rate is equivalent
to the steady-state creep rate.
Figure 1 presents experimental data [10-13] on short-term strength of
commercially pure PM tungsten (99.97 wt.% W) in the temperature range from
52 ISSN 0556-171X. npodxeMbi npounocmu, 2005, N 6
Correlation Dependences between
1770 to 2770 K, which corresponds to ~ (0.5-0.8)Tmeft, in the form of temperature
dependences of the ultimate strength R m and the offset yield stress Rp0 2. The
plots are constructed in the coordinates ln(R m , R p0 2 ) - 1/T. This figure also
shows the dependences of the tungsten long-term ultimate strength for the test
time 10 s, o 3 , and stresses corresponding to the steady-state creep rate
10-3 % -s - 1 , o 3 - x , on the inverse temperature 1/T. The two latter curves10 %*s
were obtained from the results, which characterize the variation of the steady-
state creep rate with the applied stress, and long-term strength diagrams of
tungsten for the temperatures studied (Figs. 2a and 3 a). The ln £ — ln o and
ln o — ln r curves shown in Figs. 2a and 3a are adequately described by Eqs. (5)
and (6). The values of the coefficient n, which characterizes the slope of the
curves for PM tungsten, are about 5.3 [11, 13].
Thermodynamic temperature T 1 -104,K 1
Fig. 1. Temperature dependences of the tensile ultimate strength, Rm, offset yield stress, Rp02,
creep-rupture strength for the test time 103 s, o 3 s, and stresses corresponding to the steady-state
creep rate 10—3 %- s— 1, o^—3 % —i, for PM tungsten in the temperature range from 1770 to 2270 K.
Deagmtion,: (+) Rm; (O) Rp0,2; (O) o103s; (□) o10—3„%.s—1.
The interrelation between the creep-rupture time r and the steady-state
creep rate £ for PM tungsten in the temperature and stress ranges studied, which
was plotted in logarithmic coordinates, is shown in Fig. 4. From this figure it
follows that, in the general form, this relation is adequately described by the
exponential equation proposed in [11]:
£ r d = D , (8)
where d and D are the material constants.
ISSN 0556-171X. Проблемы прочности, 2005, № 6 53
V. A. Borisenko, V. V. Bukhanovskii, and I. Mamuzic
Creep rate, % • s 1
a
Creep rate, % • s 1
b
Fig. 2. Dependences of the steady-state creep rate on the stress o (a) and on the ratio o/ Rm (b) for
PM tungsten at temperatures of 1770 (1), 2020 (2), 2270 (3), and 2770 K (4). (Here and in Figs. 3-5,
the designations are the same.)
Selected values of the coefficients d and D for PM tungsten, as well as the
coefficient of correlation r between ln e and ln x are listed in Table 1. The value
of d approaching unity indicates that the relation between the steady-state creep
rate and creep-rupture time of tungsten can be described by a classical inversely
proportional Monkman-Grant dependence (7).
From Fig. 1 one can see that within the temperature range studied the
characteristics of short-term and long-term static strengths and creep resistance of
54 ISSN 0556-171X. npoOneMbi npounocmu, 2005, № 6
Correlation Dependences between
tungsten vary monotonically with increasing temperature. The temperature
dependences of the aforementioned mechanical characteristics in the coordinates
ln M — 1/ T are linear and satisfy Eq. (2). On the basis of experimental data on
strength and creep resistance of tungsten in the temperature range ~ (0.5-0.8)Tmeft,
the authors determined the values of the plastic strain activation energy listed in
Table 2. This table also presents the values of the plastic strain activation energy
for PM tungsten obtained in [4] for H V hardness.
Time to rupture, s
a
Time to rupture, s
b
Fig. 3. Long-term strength diagrams of PM tungsten in the coordinates ln a — ln r (a) and
ln(a/RTT) — lnr (b) at temperatures of 1770 (1), 2020 (2), 2270 (3), and 2770 K (4).
Analysis and comparison of the experimental values of the plastic strain
activation energy of tungsten calculated using different strength characteristics
and the results of theoretical and experimental works at studying the processes of
deformation, internal friction, creep, and self-diffusion of tungsten generalized in
[4], allowed us to make the following conclusions.
ISSN 0556-171X. npodxeMbi npounocmu, 2005, N 6 55
V. A. Borisenko, V. V. Bukhanovskii, and I. Mamuzic
T a b l e 1
Results of Joint Statistical Treatment of the Heat-Resistance Characteristics of Tungsten
at High Temperatures
T , K N r d D rl a A r2 P B
1770-2770 41 -0.92 1.14 15.1 0.917 5.75 0.099 —0.86 4.98 419.6
Note. N is sampling volume, r is coefficient of correlation between ln e and ln r, r is coefficient
of correlation between ln e and ln(a/ Rn ), and r2 is coefficient of correlation between ln r and
ln(ff/RTm ).
T a b l e 2
Plastic Strain Activation Energy of PM Tungsten Calculated Based
on Different Characteristics of Strength
Strength characteristics U (eV) in the temperature range
from 1770 to 2770 K
DRm 2.41
Rp0.2 2.48
V s 2.42
°10-3%-s-1 2.43
HV [4] 2.5± 0.1
10 100 l io3 i-io4 i ios
Time to rupture, s
Fig. 4. Creep-rupture time vs steady-state creep rate of PM tungsten in the temperature range from
1770 to 2770 K.
The pattern of the temperature dependences of the tungsten strength,
hardness, and creep resistance under conditions of short-term and long-term static
loading in the range ~ (0.5-0.8)rmê is similar. They obey the general law of
variation of their values with increasing temperature.
56 ISSN 0556-171X. npoôëeMbi npounocmu, 2005, N 6
Correlation Dependences between
Rather close values of activation energy calculated from various strength
characteristics are indicative of the identity of major mechanisms of plastic
deformation governing the short-term and long-term static strength, hardness, and
creep resistance of tungsten within the temperature and stress ranges under
investigation.
If we represent the results obtained for the long-term strength and creep of
tungsten (Figs. 2a, 3a, and 4) in a three-dimensional spatial coordinate system
XYZ, along the axes of which ln e, ln r, and ln o are plotted, all experimental
data turn out to belong to a single common surface (Fig. 5a and 5b). Figure 5b
shows this surface plotted by the experimental points with a Mathcad 2000
software package. It is seen that this surface is in close proximity to the plane
perpendicular to the coordinate plane XOY. In the adopted spatial coordinate
system, the generalized dependences of the steady-state creep rate and
creep-rupture time on the value of the applied stress F (e , r ) = f (o ) represent a
set of curves that are parallel to each other and are equally sloped to the plane
X O Y (Fig. 5a). Each of these curves corresponds to a certain test temperature. The
generalized dependences can be analytically described by a set of equations
proposed in [15]:
A f ln e + B f ln r + C f ln o + D f = 0, (9)
A f ln e + B f ln r + C f ln o + D f = 0, (10)
where A f , B f , C f , D f , A f , B f , C f , and D f are constants for the given
material and temperature.
Projections of the generalized spatial curves on the planes ZO X and ZOY
represent the dependencies of the steady-state creep rate on the stresses and the
diagram of long-term strength of the PM tungsten shown in Figs. 2a and 3a,
respectively. The projection of the generalized curves on the plane X O Y is nothing
but the Monkman-Grant dependence (Fig. 4) described by Eq. (7).
Based on the hypothesis that the characteristics of short-term and long-term
static strength and creep resistance of tungsten in the temperature-load range
studied are governed by the same system of obstacles in the path of dislocation
motion, we have made an attempt to find a general dependence relating all the
experimental data obtained. Figures 2b and 3b show the plots characterizing the
variation of the steady-state creep rate and life of PM tungsten under conditions
of long-term static loading in the temperature range from 1770 to 2770 K with the
magnitude of the generalized load, i.e., the ratio of the acting stress o to thef
ultimate strength of the material at a corresponding temperature R m [15].
The analysis of the given curves testifies that in the high-temperature range
~ (0.5-0.8)fmeit , all the experimental data obtained on the tungsten heat resistance
are described quite satisfactorily by the unified equations of the form:
e = A (o /R Tm )a , (11)
r = B(o I R Tm )~P , (12)
ISSN 0556-171X. npodxeMbi npounocmu, 2005, N 6 57
V. A. Borisenko, V. V. Bukhanovskii, and I. Mamuzic
Fig. 5. Generalized dependence of the steady-state creep rate and creep-rupture time of PM tungsten
on the stress o (a, b) and the value of the ratio o/R^ (c).
where a , 3, A , and B are constants for the material in the temperature and stress
ranges under investigation.
The values of the constants in Eqs. (11) and (12) obtained as a result of
statistical treatment and regression analysis of experimental data are listed in
Table 1. The values of the coefficients of correlation r1 between ln £ and
ln (o /R m ) and r2 between ln r and ln (o /R m ), which are close to unity, indicate
58 ISSN 0556-171X. npo6neMbi npounocmu, 2005, N 6
Correlation Dependences between
that in the high-temperature region, there are general functional relations between
the characteristics of creep resistance, long-term static and short-term strengths of
tungsten.
Figure 5c presents the dependences between the investigated mechanical
characteristics of PM tungsten in the temperature range ~ (0.5-0.8)Tmeit in the
most general form. It relates three characteristics: the generalized load o / R ^ ,
steady-state creep rate Є, and creep-rupture time r corresponding to the indicated
temperature and stress level under conditions of long-term static loading. This
function has been plotted by the experimental points in the XYZ coordinate
system, with logarithms of є, r, and o / R ^ plotted respectively on its axes, and
has the form of a straight line in a 3D space.
To analytically describe the proposed generalized relationship, which
characterizes the mechanical behavior of PM tungsten in the temperature and
stress ranges studied, we propose a system of Eqs. (9) and (10) in the following
form:
A 1 ln є + B 1 ln r + C 1 ln(o/ R m̂) + D 1 = 0, (13)
A 2 ln є + B 2 ln r + C 2 ln(o/ R ^ ) + D 2 = 0, (14)
where A1, B1, C 1, D 1, A2, B 2, C 2, and D 2 are constants for the investigated
material in a certain temperature and stress range within which the resistance of
the material to plastic deformation and fracture is mainly governed by the same
dominating physical processes and mechanisms.
C o n c l u s i o n s
1. As a result of the joint analysis of experimental data on the strength of PM
tungsten under conditions of short-term active and long-term static loading in the
temperature range ~ (0.5-0.8)Tmeit , the authors established the existence of close
correlation dependences between the characteristics of its short-term and long
term static strengths and creep resistance.
2. To analytically describe the obtained correlation dependences, a generalized
empirical relation has been proposed, which represents the mechanical behavior
of tungsten in the temperature and stress ranges studied.
Р е з ю м е
Проаналізовано механічні характеристики технічно чистого вольфраму, що
отриманий методами порошкової металургії, за одновісного розтягу в умо
вах високих температур. Установлено, що для вольфраму в області високих
температур ~ (0,5...0,8)Тпл існують кореляційні зв’язки між характеристи
ками короткочасної та тривалої статичної міцності й опору повзучості, що
описуються єдиною функціональною залежністю.
1. G. S. Burkhanov and Yu. V. Efimov, Refractory Metals and Alloys [in
Russian], Metalurgiya, Moscow (1986).
ISSN 0556-171X. Проблемы прочности, 2005, № 6 59
V. A. Borisenko, V. V. Bukhanovskii, and I. Mamuzic
2. S. M. Gurevich (Ed.), Metallurgy and Technology o f Welding o f Refractory
Metals and Alloys Based on Refractory Metals [in Russian], Naukova
Dumka, Kiev (1982).
3. G. S. Pisarenko, V. A. Borisenko, S. S. Gorodetskii, et al., Strength o f
Refractory Metals [in Russian], Metalurgiya, Moscow (1970).
4. V. A. Borisenko, Hardness and Strength o f Refractory Materials at High
Temperatures [in Russian], Naukova Dumka, Kiev (1984).
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Received 17. 01. 2005
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