Real Time Test in situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice Moment Technique
Stress is the direct cause of surface oxide scale exfoliation to ruin the protection for alloy matrix. Therefore, it is the key to study oxide scale mechanical behaviour for discovering the oxidation resistance of alloys. In this paper, a new kind of experimental method ‘Archimedes curve slice momen...
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Інститут металофізики ім. Г.В. Курдюмова НАН України
2016
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| Cite this: | Real Time Test in situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice Moment Technique / Hai-tao Wang, Shao-mei Zheng, Hua-shun Yu // Металлофизика и новейшие технологии. — 2016. — Т. 38, № 12. — С. 1635-1654. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860164902813958144 |
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| author | Hai-tao Wang Shao-mei Zheng Hua-shun Yu |
| author_facet | Hai-tao Wang Shao-mei Zheng Hua-shun Yu |
| citation_txt | Real Time Test in situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice Moment Technique / Hai-tao Wang, Shao-mei Zheng, Hua-shun Yu // Металлофизика и новейшие технологии. — 2016. — Т. 38, № 12. — С. 1635-1654. — Бібліогр.: 14 назв. — англ. |
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| description | Stress is the direct cause of surface oxide scale exfoliation to ruin the protection for alloy matrix. Therefore, it is the key to study oxide scale mechanical behaviour for discovering the oxidation resistance of alloys. In this paper, a new kind of experimental method ‘Archimedes curve slice moment technique’ is studied to test in situ the real time oxide scale stress of ferro-based superalloy K273 during all the high-temperature oxidation. By the derived formula, the oxide scale stress σ can be calculated precisely only by observing Archimedes curve slice real-time polar radius OC′. Having been oxidated for 5 hours at 800°C, the oxide scale stress versus oxidation time is regressed to follow parabola equation strictly. As the oxides grow and the inner new oxides form in scales to press each other, the oxide scale stress is generated. Analysed by SEM, EDS and XRD, the oxide scale is compact composite structure made up of Cr₂O₃ and spinel (Fe, Ni, Mn)Cr₂O₄. The less oxide scale stress increment brings about the lower oxidation weight gain rate and the better oxidation resistance. Improved by the use of vacuum system, the Archimedes curve slice moment technique is going to test the oxide scale growing and thermal stresses qualitatively and quantitatively in situ all the time at high temperature.
Напруження є безпосередньою причиною відшарування приповерхневої циндри, що призводить до руйнування захисту матриці стопу. Отже, вивчення механічної поведінки циндри є ключем до вивчення стійкости стопів до окиснення. В даній роботі розглянуто нову експериментальну методу міряння скручувального моменту для тонкого шару матеріялу, що був вирізаний за Архімедовою кривою, яка слугує для in situ дослідження в режимі реального часу напружень, що виникають через циндру у суперстопі на основі заліза K273 впродовж усього високотемпературного окиснення. Згідно з одержаним виразом, для точного розрахунку у режимі реального часу напружень σ, що виникають завдяки циндрі, достатньо лише спостереження за полярним радіюсом OC′ зразка, вирізаного за Архімедовою кривою. При дослідженні процесу окиснення протягом 5 годин за температури у 800°C залежність напружень через циндру від часу окиснення було зведено до рівняння параболи. По мірі росту оксиду та формування нових внутрішніх його шарів, які тиснуть один на одного, ґенеруються напруження за рахунок циндри. Аналіза, проведена методами СЕМ, ЕРС та РДА, показала, що циндра ущільнюється у композитну структуру, яка складається з Cr₂O₃ та шпінелі (Fe, Ni, Mn)Cr₂O₄. Зменшення напружень, що виникають за рахунок циндри, приводить до більш низької швидкости окиснення та підвищення стійкости до окиснення. Поліпшену використанням вакуумної системи методику in situ міряння скручувального моменту для зразків, вирізаних за Архімедовою кривою, якісно та кількісно перевірено шляхом дослідження зростання циндри та термічних напружень впродовж усього часу високотемпературного окиснення.
Напряжения являются непосредственной причиной отслоения приповерхностной окалины, что приводит к разрушению защиты матрицы сплава. Следовательно, изучение механического поведения окалины является ключом к выяснению стойкости сплавов к окислению. В данной работе рассматривается новая экспериментальная методика измерения скручивающего момента для тонкого слоя материала, вырезанного по кривой Архимеда, служащая для in situ изучения в режиме реального времени напряжений, возникающих за счёт окалины, в суперсплаве на основе железа K273 в течение всего высокотемпературного окисления. Согласно полученному выражению, для точного расчёта в режиме реального времени напряжений σ, возникающих из-за окалины, достаточно лишь наблюдения за полярным радиусом OC′ образца, вырезанного по кривой Архимеда. При исследовании процесса окисления на протяжении 5 часов при температуре 800°C зависимость напряжений из-за окалины от времени окисления была сведена к уравнению параболы. По мере роста оксида и формирования новых внутренних его слоёв, давящих друг на друга, генерируются напряжения за счёт окалины. Анализ, проведённый методами СЭМ, ЭРС и РДА, показал, что окалина уплотняется в композитную структуру, состоящую из Cr₂O₃ и шпинели (Fe, Ni, Mn)Cr₂O₄. Уменьшение напряжений, возникающих за счёт окалины, приводит к более низкой скорости окисления и повышению стойкости к окислению. Улучшенная использованием вакуумной системы методика in situ измерения скручивающего момента для образцов, вырезанных по кривой Архимеда, качественно и количественно проверена путём исследования роста окалины и термических напряжений на протяжении всего времени высокотемпературного окисления.
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| first_indexed | 2025-12-07T17:56:02Z |
| format | Article |
| fulltext |
1635
PACS numbers:68.35.Gy, 68.47.Gh,68.55.J-,68.55.Nq,68.60.Dv,81.65.Kn, 81.65.Mq
Real Time Test in Situ of Superalloy Oxide Scale Stress
by Archimedes Curve Slice Moment Technique
Hai-tao Wang, Shao-mei Zheng, and Hua-shun Yu*
College of Mechanical Engineering, Qingdao University of Technology,
11 Fushun Road,
266033 Qingdao, China
*Key Laboratory for Liquid-Solid Structural Evolution and Processing of Materials,
Ministry of Education, Shandong University,
17923 Jingshi Road,
250061 Jinan, China
Stress is the direct cause of surface oxide scale exfoliation to ruin the protec-
tion for alloy matrix. Therefore, it is the key to study oxide scale mechanical
behaviour for discovering the oxidation resistance of alloys. In this paper, a
new kind of experimental method ‘Archimedes curve slice moment tech-
nique’ is studied to test in situ the real time oxide scale stress of ferro-based
superalloy K273 during all the high-temperature oxidation. By the derived
formula, the oxide scale stress can be calculated precisely only by observing
Archimedes curve slice real-time polar radius OC. Having been oxidated for
5 hours at 800C, the oxide scale stress versus oxidation time is regressed to
follow parabola equation strictly. As the oxides grow and the inner new ox-
ides form in scales to press each other, the oxide scale stress is generated.
Analysed by SEM, EDS and XRD, the oxide scale is compact composite struc-
ture made up of Cr2O3 and spinel (Fe, Ni, Mn)Cr2O4. The less oxide scale stress
increment brings about the lower oxidation weight gain rate and the better
oxidation resistance. Improved by the use of vacuum system, the Archimedes
curve slice moment technique is going to test the oxide scale growing and
thermal stresses qualitatively and quantitatively in situ all the time at high
temperature.
Key words: ferro-based superalloy, oxide scale stress, oxidation resistance,
Corresponding author: Hai-tao Wang
E-mail: htwangsd@126.com
Please cite this article as: Hai-tao Wang, Shao-mei Zheng, and Hua-shun Yu,
Real Time Test in Situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice
Moment Technique, Metallofiz. Noveishie Tekhnol., 38, No. 12: 1635—1654 (2016),
DOI: 10.15407/mfint.38.12.1635.
Металлофиз. новейшие технол. / Metallofiz. Noveishie Tekhnol.
2016, т. 38, № 12, сс. 1635—1654 / DOI: 10.15407/mfint.38.12.1635
Оттиски доступны непосредственно от издателя
Фотокопирование разрешено только
в соответствии с лицензией
2016 ИМФ (Институт металлофизики
им. Г. В. Курдюмова НАН Украины)
Напечатано в Украине.
1636 Hai-tao WANG, Shao-mei ZHENG, and Hua-shun YU
Archimedes curve.
Напруження є безпосередньою причиною відшарування приповерхневої
циндри, що призводить до руйнування захисту матриці стопу. Отже, ви-
вчення механічної поведінки циндри є ключем до вивчення стійкости
стопів до окиснення. В даній роботі розглянуто нову експериментальну
методу міряння скручувального моменту для тонкого шару матеріялу, що
був вирізаний за Архімедовою кривою, яка слугує для in situ дослідження
в режимі реального часу напружень, що виникають через циндру у супер-
стопі на основі заліза K273 впродовж усього високотемпературного окис-
нення. Згідно з одержаним виразом, для точного розрахунку у режимі
реального часу напружень , що виникають завдяки циндрі, достатньо
лише спостереження за полярним радіюсом OC зразка, вирізаного за Ар-
хімедовою кривою. При дослідженні процесу окиснення протягом 5 годин
за температури у 800C залежність напружень через циндру від часу оки-
снення було зведено до рівняння параболи. По мірі росту оксиду та фор-
мування нових внутрішніх його шарів, які тиснуть один на одного, ґене-
руються напруження за рахунок циндри. Аналіза, проведена методами
СЕМ, ЕРС та РДА, показала, що циндра ущільнюється у композитну
структуру, яка складається з Cr2O3 та шпінелі (Fe, Ni, Mn)Cr2O4. Змен-
шення напружень, що виникають за рахунок циндри, приводить до більш
низької швидкости окиснення та підвищення стійкости до окиснення.
Поліпшену використанням вакуумної системи методику in situ міряння
скручувального моменту для зразків, вирізаних за Архімедовою кривою,
якісно та кількісно перевірено шляхом дослідження зростання циндри та
термічних напружень впродовж усього часу високотемпературного окис-
нення.
Ключові слова: суперстоп на основі заліза, напруження, що виникають
через циндру, стійкість до окиснення, Архімедова крива.
Напряжения являются непосредственной причиной отслоения припо-
верхностной окалины, что приводит к разрушению защиты матрицы
сплава. Следовательно, изучение механического поведения окалины яв-
ляется ключом к выяснению стойкости сплавов к окислению. В данной
работе рассматривается новая экспериментальная методика измерения
скручивающего момента для тонкого слоя материала, вырезанного по
кривой Архимеда, служащая для in situ изучения в режиме реального
времени напряжений, возникающих за счёт окалины, в суперсплаве на
основе железа K273 в течение всего высокотемпературного окисления.
Согласно полученному выражению, для точного расчёта в режиме реаль-
ного времени напряжений , возникающих из-за окалины, достаточно
лишь наблюдения за полярным радиусом OC образца, вырезанного по
кривой Архимеда. При исследовании процесса окисления на протяжении
5 часов при температуре 800C зависимость напряжений из-за окалины от
времени окисления была сведена к уравнению параболы. По мере роста
оксида и формирования новых внутренних его слоёв, давящих друг на
друга, генерируются напряжения за счёт окалины. Анализ, проведённый
методами СЭМ, ЭРС и РДА, показал, что окалина уплотняется в компо-
зитную структуру, состоящую из Cr2O3 и шпинели (Fe, Ni, Mn)Cr2O4.
REAL TIME TEST IN SITU OF SUPERALLOY OXIDE SCALE STRESS 1637
Уменьшение напряжений, возникающих за счёт окалины, приводит к
более низкой скорости окисления и повышению стойкости к окислению.
Улучшенная использованием вакуумной системы методика in situ изме-
рения скручивающего момента для образцов, вырезанных по кривой Ар-
химеда, качественно и количественно проверена путём исследования ро-
ста окалины и термических напряжений на протяжении всего времени
высокотемпературного окисления.
Ключевые слова: суперсплав на основе железа, напряжения, возникаю-
щие за счёт окалины, стойкость к окислению, кривая Архимеда.
(Received June 6, 2016)
1. INTRODUCTION
During high temperature oxidation, stresses arise naturally with oxide
scales forming on the surface of superalloys, forcing oxide scales to
wrinkle, break or even exfoliate off the matrix. The existing of stress-
es is the most important reason to ruin oxide scales and lose the oxida-
tion resistance, so it greatly influenced on the life of superalloys in
service. For a long time, researchers all over the world studied a lot for
oxide scale stresses, many creative techniques were developed, among
which pulling test [1—3], X-ray diffraction [4—6], and Raman spectros-
copy [7—9] were the typical ones, making great efforts to study the
generating mechanism of stresses and evaluate the protecting life of
oxide scales for superalloys.
Pulling test was the earliest research technique in exploring oxide
scale mechanical properties, simple, direct, and primitive, mainly en-
gaged in detecting the adhesive forth between oxide scale and matrix,
but poor in probing oxide scale stresses in situ. The pulling force re-
sults presented the comprehension of the adhesion strength with ma-
trix and the binding strength by itself, a kind of static fuzzy data of
multi forces, but not the accumulated dynamic stresses at real time in
scales, so it was hard for real time test in situ of oxide scale stresses.
X-ray diffraction was a kind of experimental method to detect the
oxide scale stress indirectly. Although several decades went by, there
were many uncertain factors and limitations to affect the oxide scale
stress testing. X-ray diffraction could only measure the superficial
stress, being insufficient for the thick oxide scale stress because of
weak penetrability. In addition, the oxide scale stress was calculated by
difference of diffraction peak drifting, which depended on the purity
of materials. The diffraction peak matched with the standard PDF card
without stress or impurity. Then, the exact testing of inner stress
would be affected by impurity or multidisturbing of materials. There-
fore, X-ray diffraction was only suitable for the oxide scale stress test-
ing of pure structure precisely and qualitatively, but not for the multi
1638 Hai-tao WANG, Shao-mei ZHENG, and Hua-shun YU
oxides or composite oxide scales.
Raman spectroscopy also tested oxide scale stress indirectly; the
spectra band choice, spectra peak precise location, laser penetration
and material purity all limited the accurateness of stress testing. For
composite oxide scale stress testing, Raman spectroscopy could only
detect it roughly, such as the stress distribution or direction, while the
stress qualitative or quantitative testing is insufficient.
It is of great significance to study oxide scale stress of superalloys
for its mechanical prediction in all kinds of conditions, theoretical cal-
culation of strength, on-line controlling in use, life evaluation, and
development of new high quality materials. How to test oxide scale
stress scientifically is the key problem in the work, namely, by what
means to measure the stress correctly and precisely. There is no way to
illustrate the mechanism of oxide scale stress generating and scale ex-
foliating without mechanical properties analyses accurately and quali-
tatively. With long term of research work on ferro-based superalloys
[10, 11], this paper studied a new technology called ‘Archimedes curve
slice moment technique’, which is expected to realize the real time ox-
ide scale stress testing of superalloys in situ.
2. EXPERIMENTAL PROCEDURE
2.1. Experiment Principle of Archimedes Curve Slice Moment
Technique
Archimedes curve is the trajectory running from circle centre at even
velocity along radial and circumferential directions at the same time.
As shown in Figure 1, let v be radial rate, circumferential angular
rate, rotating angle at any point K, the angle between tangent line
KL and radial line KO, so the ratio of radial rate to linear rate is tg
according to Archimedes curve characteristics:
tg KO .
v
(1)
Let the time running from circle centre to any point K be t. Then,
KO vt, t, and the formula (1) becomes (2):
tg KO .
vt
t
v v
(2)
When the metal is made to be Archimedes curve slice, being fixed at
the start point O and put horizontally, it will bend and deform by the
oxide scale stress torque during high temperature oxidation. Three
dimensional stresses at any point K on Archimedes slice surface come
into being, as shown in Fig. 2, x is the tangent line longitudinal stress,
REAL TIME TEST IN SITU OF SUPERALLOY OXIDE SCALE STRESS 1639
y the tangent line transversal stress, and z the normal line stress. Ox-
ide scales grow on both front and back sides of Archimedes curve slice
in the same oxidation conditions, so stresses at any point share the
same size but different directions, which should be discussed accord-
ing to different cases.
For the normal line stress z, its direction varies with the first de-
rivative dy/dx tendency of rectangular coordinates (x, y) on Archime-
des curve, namely the positive or negative sign of the second derivative
d2y/dx2. If the front side scale is convex, its dy/dx decreases gradual-
ly, and d
2y/dx2
0; on the contrary, the concave scale on backside leads
to increasing dy/dx, and d
2y/dx2
0. Therefore, at any point on Ar-
chimedes curve slice, the oxide scale normal line stresses on front and
Fig. 1. Track analysis of Archimedes curve.
Fig. 2. Oxide scale stress analysis at any point K on Archimedes curve slice.
1640 Hai-tao WANG, Shao-mei ZHENG, and Hua-shun YU
backsides share the same size and opposite directions, of which one is
centripetal, and the other is centrifugal, as a result, there is no mo-
ment on slice matrix because of normal line stresses counteracting at
any point of Archimedes curve slice.
For the tangent line longitudinal stress x, its direction is related to
the first derivative dR/d of polar coordinate (R, ), namely the posi-
tive or negative sign of the second derivative d
2R/d2. As shown in
Figure 1, the radius R increases gradually along Archimedes curve
slice:
2 2KO tg
KB tg 1 1.
sin sin cos
v v v v
R
(3)
Therefore, the first derivative of radius R at any point K was
2
1
dR v
d
, increasing gradually with angle , nearly to be a con-
stant v/, namely d
2R/d2
0. Therefore, at any point on Archimedes
slice, the scale tangent line longitudinal stresses on front and back-
sides share the same size and direction, that the acting forces on Ar-
chimedes curve slice added each other.
For the tangent line transversal stress y, its direction is always ver-
tical to the longitudinal stress or the normal line stress, also vertical to
the slice placing ground; so, there is no moment on Archimedes curve
slice in the placing horizontal plane.
In a word, among three dimensional direction stresses, only tangent
line longitudinal stress x affects the slice bending in the placing hori-
zontal plane. In the same oxidation conditions, the oxide scale thick-
ness is even and same everywhere, and stresses at any point are iso-
tropic, so the three dimensional stresses are equal in size,
x y z. It is enough to study one dimension stress, and the
Fig. 3. Oxide scale stress distribution of Archimedes curve slice.
REAL TIME TEST IN SITU OF SUPERALLOY OXIDE SCALE STRESS 1641
synthetic stress is
1/2
S 3 .x In order to deduce formula clearly, the
tangent line longitudinal stress at any point is marked , as shown in
Fig. 1, then, the effective stress on bending moment is sin, and the
moment arm is KO:
KO / ( / )tg .vt v v (4)
Therefore, the scale stress moment at any point K is M:
sin KO sin tg .
v
M
(5)
In formula (5), arctg, increases with the curve rotating angle .
The stress and moment distribution along Archimedes curve slice are
shown in Fig. 3 and Fig. 4, respectively.
The stress holds the same value all over the slice, and the moment
varies from the minimum zero at start O to the matrix (v/)
sin(arctg)tg(arctg) at the end D. So, the total moment M caused
by oxide scale stresses on both front and back sides of the whole Ar-
chimedes curve slice can be calculated by integrating in angle [0; ]:
2
0 0 0
2 12 1
0 0
2
2 2
0
2
0
sin tg sin 1 cos
2 2 2
1 (1 )1 (1 tg )
2 2
2 [ 1 log( 1)] .
1
v v v
M d d d
vv
d d
v v
d
(6)
Fig. 4. Oxide scale stress moment distribution of Archimedes curve slice.
1642 Hai-tao WANG, Shao-mei ZHENG, and Hua-shun YU
Arc length is the product of radius and radian in a circle, hence the
Archimedes curve arc differentiation is:
L
KO .
v
d d vtd d
(7)
The Archimedes curve slice length integrated in angle [0; ] is:
2
0
0
( /2) .
v v
L d
(8)
The Archimedes curve slice deformed to bend in the horizontal plane
by oxide scale stress with fixed total length and changing parameters
radial rate v, angular rate and rotating angle range , as shown in
Fig. 5, they turn from v1, 1, 0 to be v2, 2, 0 respectively, in
which is the net angle variation, hence formula (8) is deduced to be:
0
2
2 1 01
1 0
1 1
( /2) ,
2
vv
L
(9)
0
2
2 2 02
2 0
2 2
( )
( /2) ,
2
vv
L
(10)
L1 L2, (11)
2 2
1 0 1 2 0 2
/(2 ) ( ) /(2 ),v v (12)
0 1 1 0 2 2
/ ( ) / ,v v (13)
0 1 1 2 2 2 2 0 1 2 2 1
( / / ) / / ( ( )/( ) 1).v v v v v (14)
Fig. 5. The bending displacement of Archimedes curve slice by oxide scale
stress.
REAL TIME TEST IN SITU OF SUPERALLOY OXIDE SCALE STRESS 1643
When metal bends by force, the torque T and the angle follows
the formula (15):
,
TL
EI
(15)
where E–metal elastic modulus, L–metal length, I–sectional mo-
ment of inertia (I bh
3/12), b–metal width, h–metal thickness.
Archimedes curve slice stops to bend with the total moment balance,
meanwhile, the curve slice torque T is equal to the scale stress accumu-
lated moment M :
.T M (16)
T can be obtained by solving formulas (9), (14) and (15):
3
31 2 1 2
0 1
2 1 2 1
2
0 10 1 1
1 1
12
.
6/(2 )
v vbh
E Ebh
v vEI
T
L vv
(17)
When curve slice rotates angle by scale stress, namely in the area
[0; 0 ], the accumulated oxide scale stress moment M can be
calculated by formula (6):
00 2
2 2 2 2
2
22 00
2 2 2
0 0 0 0
2
2 [ 1 log( 1)]
1
(18)
(OC)
[( ) ( ) 1 log( ( ) 1)].
v v S
M d
b v
For
0 0 0 1 2 2 1 0 1 2 2 1( ( ) / ( ) 1) ( ) / ( )v v v v , (19)
one can solve formula (18):
2 2 2
0 0 0 0
2
2 1 2 1 2 1 2 1 22 2
0 0 0 0
2 2 1 2 1 2 1 2 1
(OC)
[( ) ( ) 1 log( ( ) 1)]
(20)
(OC)
1 log( 1) .
M
b v
b v v v v v
v v v v
1644 Hai-tao WANG, Shao-mei ZHENG, and Hua-shun YU
It is possible to deduce a formula (16) by (17) and (20) as follows:
3
1 1 2 2 1 22 1 2 1 2
0 0
0 1 2 2 1 2 1
21 2 1 2
0 0
2 1 2 1
( ( ) /( ) 1) (OC)
[ 1
6
log( 1)],
Ebh v v b v v v
v v v
v v
v v
(21)
1
23
1 1 2 2 1 0 1
2
1
1 2 1 2 1 2 1 22 2
0 0 0 0
2 1 2 1 2 1 2 1
( ( ) / ( ) 1) 6 (OC)
1 log( 1) .
v
Eh v v v
v v v v
v v v v
(22)
In experiment, with the Archimedes curve slice scrimping, the radi-
us OC at the rotating angle 2 could be observed at real time.
OC v2t v2(2/); so,
2
2
OC
,
2
v
(23)
v1/1 is the ratio of the initial radial velocity to the angular velocity,
and the start length of Archimedes curve slice OC is OC v1t
v1(2/), hence,
1
1
OC
2
v
. (24)
Therefore, formula (22) turns to be:
1
3 2
0
1
2 2
0 0 0 0
2 ( (OC)/(OC ) 1) 3 (OC) (OC )
OC OC OC OC
1 log( 1) .
OC OC OC OC
Eh
(25)
The synthetic stress is
1/2
3 times of the tangent line longitudinal
stress of Archimedes curve slice. Thus,
1
3 2
0
1
2 2
0 0 0 0
2 3 ( (OC)/(OC ) 1) 3 (OC) (OC )
OC OC OC OC
1 log( 1) ,
OC OC OC OC
Eh
(26)
in which, is oxide scale stress, E–slice metal elastic modulus, h–
Archimedes curve slice thickness, OC–Archimedes curve slice initial
polar radius, OC–Archimedes curve slice real time polar radius, 0–
REAL TIME TEST IN SITU OF SUPERALLOY OXIDE SCALE STRESS 1645
Archimedes curve slice initial rotating angle.
From above all, the scale stress at any point of Archimedes curve
slice could be calculated by equation (26) precisely only by observing
OC length at real time in situ with that the other factors are given.
2.2. Scheme Implementation
(1) Making of Archimedes curve slice samples. The standard superal-
loy K273 with the composition Fe80Cr20Ni5Mn5 was selected to be the
test alloys. At first, the purchased 30 mm superalloy round bar was
melted and cast to be 10010 mm roughcasts by high frequency in-
duction furnace TX-25, then the roughcasts were machined to be
1005 mm thick plates by X52K milling machine, and the plates were
wire cut by DK7740F to be Archimedes curve slice at last, as shown in
Fig. 6, of which the thickness was h 0.4 mm, width b 5 mm, initial
radius velocity v1 2.5 mm/s, initial rotating angle velocity 1 0.314
s
1, 0 2, surface roughness no less than Ra 0.8 m.
Before being milling machined, the roughcasts were heated to 950C
for 5 hours, then cooled in furnace, eliminating the cast or structure
stresses by complete annealing, after that rough machining and finish
machining went on. Before wire cutting with no inner stress by elec-
tric-chemical machining, samples were annealed again at lower tem-
perature 200C to 300C to remove mechanical machining stress. Such
process guaranteed that there was no stress concentration in Archime-
des curve slice to prevent the influence on the oxide scale mechanical
properties detecting.
Before high temperature oxidation, slice samples surface were
washed clean by alcohol, no milling or polishing by emery paper in case
of stress concentration on sample surface.
(2) Oxide scale stress testing. Ferro-based superalloy scale stress was
Fig. 6. Specimen of Archimedes curve slice.
1646 Hai-tao WANG, Shao-mei ZHENG, and Hua-shun YU
tested using oxide scale stress testing apparatus of Archimedes curve
slice sample. As shown in Figure 7, the apparatus was made up of heat-
ing system SX2-8-13, temperature control system KYT, reading mi-
croscope JC-10, platinum rhodium thermocouple and so on. At first,
the slice sample placed in resistance furnace were heated quickly to
testing temperature, recording its beginning displacement OC, then, it
was oxidated at the constant temperature, and the oxide scale growing
stress came into being, resulting in sample slice deforming to bend,
meanwhile, the scale stress was calculated by equation (26) with re-
cording the displacement OC of slice directly at any oxidation real
time.
(3) Oxide scale characterizations. After high-temperature oxidation,
the oxidation weight gain was weighed to evaluate the oxidation re-
sistance of superalloys by automatic photoelectric analysis level
TG3288 10
4
g according to Chinese Standard HB5258-2000. The mor-
phology and structure of oxide scales were analysed by JSM-5800 type
scan electrical microscope (SEM).
The elements existing in oxide scales were detected by Oxford INCA
sight X energy disperse spectroscope (EDS). The oxide scales composi-
tion was tested by Rigaku Horizontal X-ray diffractometer (XRD) with
use of radiation CuK, 40 kV accelerating voltage, and 100 mA cur-
rent.
Fig. 7. Oxide scale stress testing apparatus of Archimedes curve slice sample:
1–KYT Temperature controller, 2–SX2-8-13 Resistance furnace, 3–JC-10
Reading microscope, 4–high temperature glass watching window, 5–
Archimedes curve slice sample, 6–sample fixing station, 7–platinum rhodi-
um thermocouple.
REAL TIME TEST IN SITU OF SUPERALLOY OXIDE SCALE STRESS 1647
3. RESULTS AND DISCUSSION
Having been oxidated at 800C for 5 hours, the scale stresses of differ-
ent oxidation time were calculated and the curve versus time was plot-
ted in Fig. 8. Scale stresses increased gradually with time at high tem-
perature, but the increment in each oxidation time decreased step by
step, as shown, the slop of the curve was steeper at the beginning but
trailed off later.
Regressing the stress data by the least square method and curve fit-
ting, the equations were listed in Table 1, the curve of scale stress ver-
sus time followed the parabolic law ( a)2
bt.
The significance of regression equations and parameters in Table 1
were evaluated.
Given the significant level 0.05 for the curve of scale stress ver-
sus time at 800C, F test for regression equation was calculated:
2 2
2 2
0.9611
( 2) (5 2) 36.3.
1 1 0.9611
R
F n
R
F distribution critical value was consulted in mathematical statistics:
F(1, n 2) 10.13.
For F F(1, n 2), hypothesis H0 was refused, and H1 was obtained.
The regression equation of test alloy ( 3.1015)2
38.8391t was sig-
nificant, and the curve confidence level arrived at 95%.
The regression equation coefficient t was calculated:
2 22/ 1 0.9611 5 2/ 1 0.9611 6.0269.T R n R
Fig. 8. Curves of oxide scale stress versus time of superalloy K273.
1648 Hai-tao WANG, Shao-mei ZHENG, and Hua-shun YU
t distribution critical value was consulted in mathematical statistics:
t0.5(n 2) 3.182.
For T t0.5(n 2), hypothesis H0 was refused, and H1 was obtained.
The regression coefficients 3.1015 and 38.8391 of oxide stress equa-
tion were significant, and the confidence level reached 95%.
In conclusion, the curve of oxide scale stress versus time of test alloy
at 800C followed the parabolic law strictly.
Early in the nineteen twenties and thirties, the relationship between
oxide scale thickness and oxidation time had been studied a lot deeply
by Tammann, Wagner et al. In oxidation atmosphere, the oxide scale
thickness of metals increased with oxidation time, that for alloys with
oxidation resistance, it rigorously followed the parabolic law
y2
Kt C, in which y was oxidation scale thickness, t oxidation time,
K and C constants [12—14]. Such typical theory had deeply influenced
the oxidation kinetics researches of alloys until now. The parabolic
functional relationship of oxide scale stress versus time regressed
above shared the same in nature with that of the oxide scale thickness.
The coefficient a and b in parabolic law ( a)2
bt were determined
synthetically by oxide scale composition, structure and density, oxida-
tion temperature, oxygen partial pressure and so on. The function of
oxide scale stress played an active role to guide detecting on line for
superalloys. The prediction of oxide scale stress by time was beneficial
for the monitoring of the exfoliation or ruining of oxide scale and oxi-
dation resistance of alloys.
At high temperature, oxidation reaction took place on the surface of
test alloys. On the basis of the principle of the lowest oxides forming
Gibbs free energy, consulting Ellingham figures, the matrix elements
Fe, Cr, Mn, Ni were oxidated to be FeO, Cr2O3, MnO and NiO, respec-
tively, such were the compositions of the first oxide scale at the begin-
ning. On the one hand, with the oxidation reaction going on, the exist-
ed oxides grew bigger and bigger, during which the bigger oxides
touched and pressed each other, as a result, the oxide scale stress
arouse. On the other hand, new oxides came into being constantly at-
taching on the former existed oxides, if they grew on the outer surface
of the oxide scales, with no concentration and naturally releasing of
TABLE 1. Regressing equations of oxide scale stress with time of superalloy
K273.
Temperature, C Regressing equation
Correlation
coefficient (R)
Regressing
time area, h
800 ( 3.1015)2 38.8391t 0.9611 1—5
REAL TIME TEST IN SITU OF SUPERALLOY OXIDE SCALE STRESS 1649
growing force, there was no stress accumulated in oxide scales; but if
the new oxides grew in the oxide scales, the growing brought squeezing
on the matrix or oxide scales, such inner oxides growing was another
main source of the oxide scale stress. To sum up, the oxides growing
and the inner new oxides forming created stress in oxide scales. When
such stress went up over the strength limitation of the oxide scale,
meanwhile, the alloy matrix was rigid without any deformation, the
scale would bear the full stress to break even exfoliate, speeding up the
oxidation reaction, losing the oxidation resistance and matrix protec-
tion, which was as far as possible to be avoided for superalloys in use.
In this experiment, the test alloys was made to be Archimedes thin
slice, which was elastic to be easily bent by stress. Whereupon, being
transformed to the deformation of the slice, the oxide scale stress was
calculated by the bending displacement.
After being oxidated for 5 hours at 800C, the oxide scale morpholo-
gy was analysed by SEM. In Figure 9, it was found that the scale struc-
ture was complete, compact and continuous, fully covering the matrix.
The coarse oxides were the former generated ones as a result of contin-
uous growing, during which the oxide scale stress accumulated. Oth-
erwise, plenty of small oxide grains attaching on the coarse ones
formed later, scattering all over the scales at random, of which the in-
ner born ones also made lots of oxide scale stress. Analysed by EDS pat-
terns and X-ray Diffraction, as shown in Figs. 10 and 11, the oxide
scale composition of test alloys were made up of Cr2O3 and spinel, a
kind of composite structure, in which FeO, NiO and MnO did not exist-
ed alone, but were polymerized together in spinel (Fe, Ni, Mn)Cr2O4.
Such compact highly composited structure endowed the oxide scale
high oxidation resistance for superalloys.
It was found that the oxide weight gain rate in every oxidation time
matched the oxide scale stress increment well. As shown in Figure 12,
Fig. 9. SEM morphology of oxide scale of superalloy K273 after 5 hours oxida-
tion at 800C.
1650 Hai-tao WANG, Shao-mei ZHENG, and Hua-shun YU
less oxide scale stress increment corresponded to lower oxide weight
gain rate and better oxidation resistance. Lower oxide weight gain rate
meant less or slower oxidation reaction, and fewer new oxide produc-
ing. Therefore, there were fewer new oxides to draw or press each other
in scales, resulting in smaller oxide scale stress increment.
According to formula (26), the oxide scale stress was calculated only
by observing the Archimedes curve slice free terminal OC, without de-
tecting oxide scale thickness or weighing oxidation weight gain, with-
out deriving the relationship of oxide scale thickness or oxidation
weight gain versus time. Especially, it was after the oxidation to detect
oxide scale thickness or oxidation weight gain of alloys, both of which
the real time testing in situ could not be carried out anyway. There-
fore, such Archimedes curve slice moment technique formula (26) was
terse, clear and convenient, realizing the real time detecting and calcu-
lating of oxide scale stress in situ.
4. EXPECTATION
The oxide scale stress tested above is a synthetic value, including grow-
ing stress in oxides forming and thermal stress during heating or cool-
ing. How to distinguish the growing stress and thermal stress is the
key problem in the next research work.
(1). Testing of oxide scale growing stress. Based on oxide scale stress
testing apparatus in Fig. 7, the vacuum system was introduced to test
oxide scale growing stress. As shown in Figure 13, the new experiment
device were made up of heating system, temperature controlling sys-
Fig. 10. EDS patterns of oxide scale of superalloy K273 after 5 hours oxida-
tion at 800C.
REAL TIME TEST IN SITU OF SUPERALLOY OXIDE SCALE STRESS 1651
tem, vacuum system, reading microscope, vacuum gage, valves, and so
on. At first, the slice sample was heated to the given temperature in
vacuum condition, then broke vacuum by opening air valve, and let the
slice sample be oxidated in air for a certain time, during which the dis-
placement of the slice were recorded every moment, and the oxide scale
stress was worked out by formula (26). There was no temperature
change, oxides formed at the same temperature with no thermal stress,
so the stress measured was the pure oxide scale growing stress at given
temperature.
The bending slice displacement could be read in situ at real time by
long focus microscope directly through watching window fixed on the
furnace.
(2). Testing of oxide scale thermal stress. Oxide scale thermal stress
was tested after that for the growing stress. Having been observed the
bending displacement for a certain time oxidation at given tempera-
ture, the slice sample cooled down to room temperature, during which
the slice real time bending displacement was recorded and the scale
stress at different temperature was calculated by formula (26). Such
stress was the vector sum of the oxide scale growing and thermal
stress, subtracting the growing stress calculated above, the leave was
the pure thermal stress only by temperature changing. During the pe-
Fig. 11. X-ray diffraction of oxide scale of superalloy K273 after 5 hours oxi-
dation at 800C.
1652 Hai-tao WANG, Shao-mei ZHENG, and Hua-shun YU
riod of cooling, no oxidation reaction occurred without heating, and no
oxides formed. Therefore, no new oxide scale growing stress came into
being, and the growing stress could be looked as a constant at every
temperature, the same as that at the temperature from cooling. Even-
tually, the thermal stresses in oxide scale of slice samples in various
temperature ranges could be obtained exactly.
Such Archimedes curve slice moment technique could observe the
slice bending displacement in situ all the time in oxidation. Conse-
quently, the oxide scale growing and thermal stresses would be both
tested accurately at any temperature for a certain time, which was
hard in the former research technologies.
5. CONCLUSIONS
1. A new method of Archimedes curve slice moment was studied to test
superalloy oxide scale stress at real time in situ, in which the stress
calculating formula was deduced to be:
3
2 2 2
0 0 0 0 0
2 3 ( (OC)/(OC ) 1)
,
OC OC OC OC
3 (OC) (OC ) 1 log( 1)
OC OC OC OC
Eh
in which, is oxide scale stress, E–slice metal elastic modulus, h–
Archimedes curve slice thickness, OC–Archimedes curve slice initial
Fig. 12. Oxide scale stress increment and oxidation weight gain rate of super-
alloy K273 at 800C in different time.
REAL TIME TEST IN SITU OF SUPERALLOY OXIDE SCALE STRESS 1653
polar radius, OC–Archimedes curve slice real time polar radius, 0–
Archimedes curve slice initial rotating angle.
2. The curve of oxide scale stress versus time of superalloy K273 fol-
lowed the parabolic law ( 3.1015)2
38.8391t, strictly oxidated at
800C in 5 hours.
3. The oxides growing and the inner new oxides forming created stress
in oxide scales.
4. Having been oxidated for 5 hours at 800C, the oxide scale composi-
tion of superalloy K273 was composed by Cr2O3 and spinel (Fe, Ni,
Mn)Cr2O4.
5. The oxide scale stress increment matched with the oxide weight gain
rate, the less stress increment, the lower oxidation weight gain rate,
and the stronger oxidation resistance.
This research was financially supported by the Scientific Research
Program of Shandong Higher Education of China (No. J14LA09) and
the National Natural Science Foundation of China (No. 51307091).
REFERENCES
1. H. J. Engell und F. K. Peter, Archiv für das Eisenhüttenwesen, 28: 567 (1957)
Fig. 13. Oxide scale stress testing apparatus with vacuum system of Archime-
des curve slice sample: 1–reading microscope, 2–watching windows, 3–
vacuum furnace, 4–high temperature quartz cover, 5–insulating layer, 6–
carbon tube heater, 7–Archimedes curve slice sample, 8–sample fixing sta-
tion, 9–cooling water box, 10–cooling water pump, 11–electric motor,
12–vacuum pump, 13–electric motor, 14–convex cavity diffusion pump,
15–high vacuum butterfly bumpers, 16–vacuum pressure gage, 17–
platinum rhodium thermocouple, 18–air valve, 19–electrical control cabi-
net, 20–transformer.
1654 Hai-tao WANG, Shao-mei ZHENG, and Hua-shun YU
(in German).
2. K. Kendall, J. Phys. D: Appl. Phys., 4: 1186 (1971).
3. M. Schutze, Mater. Sci. Technol., 4: 407 (1988).
4. A. M. Huntz, J. L. Lebru, and A. Boumaza, Oxid. Metals, 33: 321 (1990).
5. C. Juricic, H. Pinto, D.Cardinali, M. Klaus, Ch. Genzel, and A. R. Pyzalla,
Oxid. Metals, 73: 115 (2010).
6. J. L. Ruan, Y. M. Pei, and D. N. Fang, Acta Mechanica, 223: 2597 (2012).
7. J. Birnie, C. Craggs, D. J. Gardiner, and P. R. Graves, Corrosion Sci., 33: 1
(1992).
8. P. Y. Hou, J. Ager, J. Mougin, and A. Galerie, Oxid. Metals, 75: 229 (2011).
9. F. Yang, X. F. Zhao, and P. Xiao, Oxid. Metals, 81: 331 (2014).
10. Hai-tao Wang, Hua-shun Yu, Yu-qing Wang, Jing Zhang, Zhen-ya Zhang, and
Zhi-fu Wang, Metallofiz. Noveishie Tekhnol., 31, No. 5: 701 (2009).
11. Hai-tao Wang, Ji-wen Tan, Chang-song Liu, and Hua-shun Yu, Metallofiz. No-
veishie Tekhnol., 33, No. 6: 757 (2011).
12. G. Tammann, Z. Anorg. Chem., 111: 78 (1920).
13. C. Wagner, Z. Physik. Chem., B21: 25 (1933).
14. C. Wagner, Z. Physik. Chem., B32: 447 (1936).
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/HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 5.0 i kasnijim verzijama.)
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/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
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| id | nasplib_isofts_kiev_ua-123456789-112644 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1024-1809 |
| language | English |
| last_indexed | 2025-12-07T17:56:02Z |
| publishDate | 2016 |
| publisher | Інститут металофізики ім. Г.В. Курдюмова НАН України |
| record_format | dspace |
| spelling | Hai-tao Wang Shao-mei Zheng Hua-shun Yu 2017-01-24T21:05:27Z 2017-01-24T21:05:27Z 2016 Real Time Test in situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice Moment Technique / Hai-tao Wang, Shao-mei Zheng, Hua-shun Yu // Металлофизика и новейшие технологии. — 2016. — Т. 38, № 12. — С. 1635-1654. — Бібліогр.: 14 назв. — англ. 1024-1809 DOI: 10.15407/mfint.38.12.1635 PACS: 68.35.Gy, 68.47.Gh, 68.55.J-, 68.55.Nq, 68.60.Dv, 81.65.Kn, 81.65.Mq https://nasplib.isofts.kiev.ua/handle/123456789/112644 Stress is the direct cause of surface oxide scale exfoliation to ruin the protection for alloy matrix. Therefore, it is the key to study oxide scale mechanical behaviour for discovering the oxidation resistance of alloys. In this paper, a new kind of experimental method ‘Archimedes curve slice moment technique’ is studied to test in situ the real time oxide scale stress of ferro-based superalloy K273 during all the high-temperature oxidation. By the derived formula, the oxide scale stress σ can be calculated precisely only by observing Archimedes curve slice real-time polar radius OC′. Having been oxidated for 5 hours at 800°C, the oxide scale stress versus oxidation time is regressed to follow parabola equation strictly. As the oxides grow and the inner new oxides form in scales to press each other, the oxide scale stress is generated. Analysed by SEM, EDS and XRD, the oxide scale is compact composite structure made up of Cr₂O₃ and spinel (Fe, Ni, Mn)Cr₂O₄. The less oxide scale stress increment brings about the lower oxidation weight gain rate and the better oxidation resistance. Improved by the use of vacuum system, the Archimedes curve slice moment technique is going to test the oxide scale growing and thermal stresses qualitatively and quantitatively in situ all the time at high temperature. Напруження є безпосередньою причиною відшарування приповерхневої циндри, що призводить до руйнування захисту матриці стопу. Отже, вивчення механічної поведінки циндри є ключем до вивчення стійкости стопів до окиснення. В даній роботі розглянуто нову експериментальну методу міряння скручувального моменту для тонкого шару матеріялу, що був вирізаний за Архімедовою кривою, яка слугує для in situ дослідження в режимі реального часу напружень, що виникають через циндру у суперстопі на основі заліза K273 впродовж усього високотемпературного окиснення. Згідно з одержаним виразом, для точного розрахунку у режимі реального часу напружень σ, що виникають завдяки циндрі, достатньо лише спостереження за полярним радіюсом OC′ зразка, вирізаного за Архімедовою кривою. При дослідженні процесу окиснення протягом 5 годин за температури у 800°C залежність напружень через циндру від часу окиснення було зведено до рівняння параболи. По мірі росту оксиду та формування нових внутрішніх його шарів, які тиснуть один на одного, ґенеруються напруження за рахунок циндри. Аналіза, проведена методами СЕМ, ЕРС та РДА, показала, що циндра ущільнюється у композитну структуру, яка складається з Cr₂O₃ та шпінелі (Fe, Ni, Mn)Cr₂O₄. Зменшення напружень, що виникають за рахунок циндри, приводить до більш низької швидкости окиснення та підвищення стійкости до окиснення. Поліпшену використанням вакуумної системи методику in situ міряння скручувального моменту для зразків, вирізаних за Архімедовою кривою, якісно та кількісно перевірено шляхом дослідження зростання циндри та термічних напружень впродовж усього часу високотемпературного окиснення. Напряжения являются непосредственной причиной отслоения приповерхностной окалины, что приводит к разрушению защиты матрицы сплава. Следовательно, изучение механического поведения окалины является ключом к выяснению стойкости сплавов к окислению. В данной работе рассматривается новая экспериментальная методика измерения скручивающего момента для тонкого слоя материала, вырезанного по кривой Архимеда, служащая для in situ изучения в режиме реального времени напряжений, возникающих за счёт окалины, в суперсплаве на основе железа K273 в течение всего высокотемпературного окисления. Согласно полученному выражению, для точного расчёта в режиме реального времени напряжений σ, возникающих из-за окалины, достаточно лишь наблюдения за полярным радиусом OC′ образца, вырезанного по кривой Архимеда. При исследовании процесса окисления на протяжении 5 часов при температуре 800°C зависимость напряжений из-за окалины от времени окисления была сведена к уравнению параболы. По мере роста оксида и формирования новых внутренних его слоёв, давящих друг на друга, генерируются напряжения за счёт окалины. Анализ, проведённый методами СЭМ, ЭРС и РДА, показал, что окалина уплотняется в композитную структуру, состоящую из Cr₂O₃ и шпинели (Fe, Ni, Mn)Cr₂O₄. Уменьшение напряжений, возникающих за счёт окалины, приводит к более низкой скорости окисления и повышению стойкости к окислению. Улучшенная использованием вакуумной системы методика in situ измерения скручивающего момента для образцов, вырезанных по кривой Архимеда, качественно и количественно проверена путём исследования роста окалины и термических напряжений на протяжении всего времени высокотемпературного окисления. This research was financially supported by the Scientific Research Program of Shandong Higher Education of China (No. J14LA09) and the National Natural Science Foundation of China (No. 51307091). en Інститут металофізики ім. Г.В. Курдюмова НАН України Металлофизика и новейшие технологии Металлические поверхности и плёнки Real Time Test in situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice Moment Technique Натурні випробування в реальному часі напружень через циндру у суперстопі методою скручувального моменту для зразка, вирізаного за Архімедовою кривою Натурные испытания в режиме реального времени напряжений из-за окалины в суперсплаве методом скручивающего момента для образца, вырезанного по кривой Архимеда Article published earlier |
| spellingShingle | Real Time Test in situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice Moment Technique Hai-tao Wang Shao-mei Zheng Hua-shun Yu Металлические поверхности и плёнки |
| title | Real Time Test in situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice Moment Technique |
| title_alt | Натурні випробування в реальному часі напружень через циндру у суперстопі методою скручувального моменту для зразка, вирізаного за Архімедовою кривою Натурные испытания в режиме реального времени напряжений из-за окалины в суперсплаве методом скручивающего момента для образца, вырезанного по кривой Архимеда |
| title_full | Real Time Test in situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice Moment Technique |
| title_fullStr | Real Time Test in situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice Moment Technique |
| title_full_unstemmed | Real Time Test in situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice Moment Technique |
| title_short | Real Time Test in situ of Superalloy Oxide Scale Stress by Archimedes Curve Slice Moment Technique |
| title_sort | real time test in situ of superalloy oxide scale stress by archimedes curve slice moment technique |
| topic | Металлические поверхности и плёнки |
| topic_facet | Металлические поверхности и плёнки |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112644 |
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