Improved Method of Fatigue Life Assessment for TiAl Alloys
For rapid fatigue life assessment of TiAl alloys, the new method was proposed based on qualitative and quantitative analyses. The qualitative analysis was employed to illustrate the microstructure effect for TiAl alloys on their fatigue life. The new formula is derived for estimation of the in...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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Feng, R.C. Rui, Z.Y. Zhang, G.T. Yan, C.F. Yi, X.B. 2017-01-26T18:03:12Z 2017-01-26T18:03:12Z 2014 Improved Method of Fatigue Life Assessment for TiAl Alloys / R.C. Feng, Z.Y. Rui, G.T. Zhang, C.F. Yan, X.B. Yi // Проблемы прочности. — 2014. — № 2. — С. 37-44. — Бібліогр.: 15 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/112701 539.4 For rapid fatigue life assessment of TiAl alloys, the new method was proposed based on qualitative and quantitative analyses. The qualitative analysis was employed to illustrate the microstructure effect for TiAl alloys on their fatigue life. The new formula is derived for estimation of the interaction forces of dislocations, which yields quite satisfactory results. The results of qualitative and quantitative analyses were used to predict the fatigue life improvement by the addition of trace elements producing grain refinement. Предложен новый метод оценки усталостной долговечности TiAl сплавов по результатам количественного и качественного анализа. С помощью количественного анализа определено влияние микроструктуры TiAl сплавов на их усталостную долговечность. Расчет усилия между дислокациями проведен по стандартной формуле, с помощью которой можно получить точный результат. Количественный и качественный анализ показал, что усталостную долговечность можно повысить путем введения микроэлементов, которые способствуют измельчению зерен. Запропоновано новий метод оцінки довговічності від утомленості ТіАl сплавів за результатами кількісного та якісного аналізу. За допомогою кількісного аналізу визначено вплив мікроструктури TiAl сплавів на їх довговічність від утомленості. Розрахунок зусилля між дислокаціями проведено за стандартною формулою, за допомогою якої можна отримати точний результат. Кількісний та якісний аналіз показав, що довговічність від утомленості можна підвищити шляхом введення мікроелементів, які сприяють подрібненню зерен. This work was supported by the National Natural Science Fund of China (51065014) and the Program for Changjiang Scholars and Innovative Research Team in University of Ministry of Education of China (IRT1140). R. C. Feng would like to thank Engineering Research Center of Nonferrous Metallurgy’s New Equipment, Ministry of Education, Lanzhou University of Technology for providing help. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Improved Method of Fatigue Life Assessment for TiAl Alloys Усовершенствованный метод оценки усталостной долговечности TiAl сплавов Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Improved Method of Fatigue Life Assessment for TiAl Alloys |
| spellingShingle |
Improved Method of Fatigue Life Assessment for TiAl Alloys Feng, R.C. Rui, Z.Y. Zhang, G.T. Yan, C.F. Yi, X.B. Научно-технический раздел |
| title_short |
Improved Method of Fatigue Life Assessment for TiAl Alloys |
| title_full |
Improved Method of Fatigue Life Assessment for TiAl Alloys |
| title_fullStr |
Improved Method of Fatigue Life Assessment for TiAl Alloys |
| title_full_unstemmed |
Improved Method of Fatigue Life Assessment for TiAl Alloys |
| title_sort |
improved method of fatigue life assessment for tial alloys |
| author |
Feng, R.C. Rui, Z.Y. Zhang, G.T. Yan, C.F. Yi, X.B. |
| author_facet |
Feng, R.C. Rui, Z.Y. Zhang, G.T. Yan, C.F. Yi, X.B. |
| topic |
Научно-технический раздел |
| topic_facet |
Научно-технический раздел |
| publishDate |
2014 |
| language |
English |
| container_title |
Проблемы прочности |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| format |
Article |
| title_alt |
Усовершенствованный метод оценки усталостной долговечности TiAl сплавов |
| description |
For rapid fatigue life assessment of TiAl alloys,
the new method was proposed based on qualitative
and quantitative analyses. The qualitative
analysis was employed to illustrate the microstructure
effect for TiAl alloys on their fatigue
life. The new formula is derived for estimation
of the interaction forces of dislocations, which
yields quite satisfactory results. The results of
qualitative and quantitative analyses were used
to predict the fatigue life improvement by the
addition of trace elements producing grain refinement.
Предложен новый метод оценки усталостной долговечности TiAl сплавов по результатам
количественного и качественного анализа. С помощью количественного анализа определено
влияние микроструктуры TiAl сплавов на их усталостную долговечность. Расчет усилия
между дислокациями проведен по стандартной формуле, с помощью которой можно получить точный результат. Количественный и качественный анализ показал, что усталостную
долговечность можно повысить путем введения микроэлементов, которые способствуют измельчению зерен.
Запропоновано новий метод оцінки довговічності від утомленості ТіАl сплавів за
результатами кількісного та якісного аналізу. За допомогою кількісного аналізу
визначено вплив мікроструктури TiAl сплавів на їх довговічність від утомленості.
Розрахунок зусилля між дислокаціями проведено за стандартною формулою, за
допомогою якої можна отримати точний результат. Кількісний та якісний аналіз
показав, що довговічність від утомленості можна підвищити шляхом введення мікроелементів, які сприяють подрібненню зерен.
|
| issn |
0556-171X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/112701 |
| citation_txt |
Improved Method of Fatigue Life Assessment for TiAl Alloys / R.C. Feng, Z.Y. Rui, G.T. Zhang, C.F. Yan, X.B. Yi // Проблемы прочности. — 2014. — № 2. — С. 37-44. — Бібліогр.: 15 назв. — англ. |
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| first_indexed |
2025-11-25T15:39:10Z |
| last_indexed |
2025-11-25T15:39:10Z |
| _version_ |
1850517023052791808 |
| fulltext |
UDC 539.4
Improved Method of Fatigue Life Assessment for TiAl Alloys
R. C. Feng,a,b,1 Z. Y. Rui,a,b,2 G. T. Zhang,a,b,3 C. F. Yan,a,b,4 and X. B. Yia,b,5
a Key Laboratory of Digital Manufacturing Technology and Application, Ministry of Education,
Lanzhou University of Technology, Lanzhou, China
b School of Mechanical and Electronical Engineering, Lanzhou University of Technology, Lanzhou,
China
1 frcly@163.com
2 zhiy_rui@163.com
3 zhangguotao_good@126.com
4 changf_yan@163.com
5 yibin2003@126.com
ÓÄÊ 539.4
Óñîâåðøåíñòâîâàííûé ìåòîä îöåíêè óñòàëîñòíîé äîëãîâå÷íîñòè TiAl
ñïëàâîâ
Ð. ×. Ôåíãà,á,1, Æ. É. Ðóèà,á,2, Ï.Ò. Æàíãà,á,3, ×. Ô. ßíà,á,4, Ñ. Á. Éèà,á,5
à Ëàáîðàòîðèÿ ïðîèçâîäñòâà è ïðèìåíåíèÿ öèôðîâûõ òåõíîëîãèé, Ìèíèñòåðñòâî îáðàçîâàíèÿ,
Ëàíü÷æîóñêèé òåõíîëîãè÷åñêèé óíèâåðñèòåò, Ëàíü÷æîó, Êèòàé
á Ôàêóëüòåò ìàøèíîñòðîåíèÿ è ýëåêòðîíèêè, Ëàíü÷æîóñêèé òåõíîëîãè÷åñêèé óíèâåðñèòåò,
Ëàíü÷æîó, Êèòàé
Ïðåäëîæåí íîâûé ìåòîä îöåíêè óñòàëîñòíîé äîëãîâå÷íîñòè TiAl ñïëàâîâ ïî ðåçóëüòàòàì
êîëè÷åñòâåííîãî è êà÷åñòâåííîãî àíàëèçà. Ñ ïîìîùüþ êîëè÷åñòâåííîãî àíàëèçà îïðåäåëåíî
âëèÿíèå ìèêðîñòðóêòóðû TiAl ñïëàâîâ íà èõ óñòàëîñòíóþ äîëãîâå÷íîñòü. Ðàñ÷åò óñèëèÿ
ìåæäó äèñëîêàöèÿìè ïðîâåäåí ïî ñòàíäàðòíîé ôîðìóëå, ñ ïîìîùüþ êîòîðîé ìîæíî ïîëó-
÷èòü òî÷íûé ðåçóëüòàò. Êîëè÷åñòâåííûé è êà÷åñòâåííûé àíàëèç ïîêàçàë, ÷òî óñòàëîñòíóþ
äîëãîâå÷íîñòü ìîæíî ïîâûñèòü ïóòåì ââåäåíèÿ ìèêðîýëåìåíòîâ, êîòîðûå ñïîñîáñòâóþò
èçìåëü÷åíèþ çåðåí.
Êëþ÷åâûå ñëîâà: òèòàíîâûé ñïëàâ àëþìèíèÿ, óñòàëîñòíàÿ òðåùèíà, óñòàëîñòíàÿ
äîëãîâå÷íîñòü, îöåíêà äîëãîâå÷íîñòè, óñîâåðøåíñòâîâàííûé ìåòîä.
Introduction. The aero-gas turbine industry has been instrumental in the development
of conventional titanium alloys and associated processing techniques since their beginning
in the late 1950s [1]. Titanium aluminum alloys are known to be the key raw materials for
manufacturing of the mechanical parts in high-temperature, and they have been widely used
in many key areas, such as jet engine, aerogas turbine shell or structure, etc. Titanium
aluminum alloys are examples of novel materials with great potential and competitiveness
[2–4]. The reason why titanium aluminum alloys have been widely used is that they have
several excellent characteristics such as low density, high stiffness, high resistance to
burning, high strength at high temperatures, low coefficient of linear dilatation and high
heat conductivity.
© R. C. FENG, Z. Y. RUI, G. T. ZHANG, C. F. YAN, X. B. YI, 2014
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 37
Some trace elements (microelements) such as vanadium and yttrium are ususlly added
to such allays, in order to improve their mechanical properties. Previous studies revealed
that the high-oxidation resistance and mechanical properties of TiAl alloys can be
effectively improved by the addition of trace alloying element [5, 6], while the ductility of
TiAl alloys can be increased by the addition of vanadium [7, 8]. Most of the available
articles are focused only on the performance improvement of TiAl alloys. However, the
mechanical properties/performance and service life are inseparable. Taking this into
account, an improved method of fatigue life assessment based on crack initiation for TiAl
alloys is proposed in this study.
Fracture of metals starts from the crystal defects, such as dislocations and vacancies.
These defects will develop into microcracks, and may gradually turn into macrocracks or
cavities. Therefore, the fatigue crack evolution is conventionaslly subdivided into two
segments: crack initiation and crack propagation. Respectively, the total fatigue life (N f )
also includes two parts: crack initiation life (N i ) and crack propagation life (N p ). The
relationship between N i and N p can be expressed as follows:
N N Nf i p� � , (1)
where crack initiation life (N i ) includes crack nucleation life and microcrack propagation
life. The process of fatigue life ranges from crack initiation to crack propagation and it
could also be called the evolution of life in metallic materials.
The fatigue life is affected by numerous factors, such as stress, temperature, humidity,
microstructure, et al. Authors [9] proved that dislocations and debris have great influence
on the properties of TiAl alloys and the crack formation mechanism in these. Nevertheless,
there is scarce information on the assessment of the crack initiation life of TiAl alloys. Yet
there are fewer articles illustrating the relationship between the interaction forces of
dislocations and fatigue life. Therefore, in this work, the emphpasis is made on the fatigue
life assessment method which is based on the analysis of the relations linking between the
interaction force of dislocations and fatigue life of materials at the room temperature.
Study [10] has provided modeling of fatigue and revealed some limits for the fatigue
life. However, this work failed to yield the relationship between fatigue life and the factors
which have influence on fatigue life of materials. In this paper, a detailed illustration will be
carried out from the standpoint of mechanics.
1. Fatigue Crack and Assessment of Crack Initiation Life. The microcrack
nucleation and propagation are important stages in the evolution of life in metallic
materials, and they account for a significant portion in the total life of materials (the portion
can be up to 90% in the high-cycle fatigue). Because of the difficulty of detecting defects at
the microstructural level and the lack of quantitative information on crack nucleation and
propagation for microcracks, the proposed method of crack initiation life assessment will
be described using some available empirical formulas.
1.1. Fatigue Crack Nucleation Mechanism. In terms of crystal materials, the concept
that is widely accepted is that crack nucleation is the result of partially obstructed plastic
deformation. The local plastic deformation is a pre-requisite for crack formation, and the
alternating stress is the key factor in the formation of fatigue cracks [12]. To illustrate the
above viewpoint, several kinds of mechanisms have been put forward, such as the
dislocation pile-up mechanism and the dislocation reaction mechanism. The process of
microcrack shaped from dislocation pile-up can be seen in Fig. 1 [13]. Generally speaking,
crack originates from the surface of the components or the stress concentration area which
includes mechanical gaps. Stress concentration plays a vital role in the process of crack
initiation. And in this stage, the crack is inclined and its order is 10 4� – 10 6� m [14]. After
that, the crack will change into microcrack propagation stage.
R. C. Feng, Z. Y. Rui, G. T. Zhang, et al.
38 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
1.2. Assessment of Crack Initiation Life (N i).
1.2.1. Assessment of Crack Initiation Life from the Qualitative Aspect. As it was
mentioned above, crack starts from the stress concentration area or the component surface.
This is occurs due to presence of many inclusions, mechanical gaps or other defects in the
material, which strongly contribute to deterioration of the material fatigue life. The effects
of dislocations and debris existing in the material are discussed in a number of publications.
A rough scheme for the calculation of stable configuration of super-lattice dislocation
dipoles (superdipoles) is depicted in Fig. 2.
In accordance with the model shown in Fig. 2, the interaction force f x yx ( , ) for x
component can be written as [9]:
f x y
b x x y
x y
x ( , )
( )
( )( )
,�
�
� �
�
� �
2 2 2
2 2 22 12
(2)
where � is the shear modulus, � is Poisson’s ratio, and b is magnitude of the Burgers
vector (
~
b).
The total interaction forces which are acting at dislocations I and II from the domain
antiphase boundary (APB) and three other dislocations are given by [9]:
F f w f d h f d w hx x x APBI �� � � � �( , ) ( , ) ( , ) ,0 � (3)
An Improved Method of Fatigue Life Assessment ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 39
Fig. 1. Model of dislocation pile-up edge [12].
Fig. 2. Schematic representation of superlattice dislocation dipoles and its dimensions in a lattice.
F f w f d h f w d hx x x APBII � � � � �( , ) ( , ) ( , ) ,0 � (4)
where � APB is the APB energy, d and w are dimensions shown in Fig. 2, which can be
derived from formulas (2)–(4) under the premise of h being fixed at some constant value.
A new deformation formula can also be derived from Eqs. (2) and (3):
F
b
w
b d d h
d h
b d
I ��
�
�
�
� �
�
�
� �
�
� �
�2 2 2 2
2 2
2 2
2 12 2 12( )
( )
( )( )
( � � �
� � �
�
w d w h
d w h
APB
)[( ) ]
( )[( ) ]
.
2 2
2 2 22 12� �
� (5)
In the last equation, � and � are constant values for the certain material, while w, d ,
and h are variables. Thus, the proposed assessment method for N i can be described as
follows:
(1) Assume that w and h are invariable. When variable d is increasing, the value of
FI will decrease, in accordance with formula (5).
The increase in d implies a smaller number of dislocations contained in the material,
while the decrease in FI implies that the possibility of dislocation slip will dwindle at the
same external condition. The ability to resist deformation can be increased. Therefore, the
fewer dislocations are included in the material, the longer is the fatigue life of TiAl alloys.
(2) Assuming that w and d are constant, the same result as shown above can be
obtained by rising h.
(3) Assuming that h and d are constant, there will be an uncertain result for FI .
However, there is no doubt that fewer defects can contribute to its life.
Similarly, another deformation formula can be derived from Eqs. (2) and (4):
F
b
w
b d d h
d h
b w
II �
�
�
�
� �
�
�
� �
�
� �
�2 2 2 2
2 2 2
2
2 12 2 12( )
( )
( )( )
( � � �
� � �
�
d w d h
w d h
APB
)[( ) ]
( )[( ) ]
.
2 2
2 2 22 12� �
� (6)
The analysis of FII can be conducted similar to the method earlier applied to FI , providing
similar trends as those earlier discussed for FI .
The conclusion that fatigue life of TiAl alloys will be improved with fewer defects, to
a large extent, can be made from the above analysi. To provide such improvement, trace
elements of vanadium and yttrium are added to alloys. Previous works have revealed that
the addition of vanadium and yttrium can make grains refined so that mechanical properties
and fatigue life (just from the qualitative level) of TiAl alloys will be strongly improved.
Trace elements should also be added according toa certain proportion. Only in this way the
best performance, meaning fewer defects, can be achieved for TiAl alloys: a higher fatigue
life can be attained with fewer defects.
1.2.2. Assessment of Crack Initiation Life from the Quantitative Aspect. The analysis
for any problem should include two components: qualitative and quantitative. These two
components should be unified and complement each other. The qualitative analysis is the
basic premise of quantitative analysis, while the quantitative one will be aimless and
useless with no qualitative analysis. Since qualitative analysis will be more scientific and
accurate due to quantitative analysis, the latter is also included in this study.
In view of the lack of data for the microstructural dimensions of TiAl alloys, some
data on particular alloys are quoted from work [9], since the main goal of this section is to
verify the correctness of the qualitative analysis performed in the previous section. Some
necessary parameters are tabulated in Table 1. The parameters w and d are also necessary.
However, due to the lack of microstructural dimensions, these two parameters will be
referred to as unknowns in the following formulas, in order to make the following analysis
universal for various TiAl alloys. Note that although values or w and d are, in the general
40 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
R. C. Feng, Z. Y. Rui, G. T. Zhang, et al.
case, unknown, these values are available for certain materials under certain conditions.
Authors [9] observed that values of w and d can be derived from Eqs. (3) and (4) if
parameter h is fixed at a constant value. However, the values derived from Eqs. (3) and (4)
are suitable for the case where each dislocation takes a stable position. For the case of
cyclic loading, the values of w and d will vary in accordance with the load, thus the
analysis of F FI II ration can be carried out for a varying range of w and d .
Using the parameters given in Table 1 and formula (5), the result can be reduced to
the following:
F
d d
d w
I MPa nm�
�
�
�
�
�
� �50 326
1
1
1
2
2 2
.
( )
( )
( )
�
� � �
� �
�2204 288
1
1
64 6
2
2 2
.
( )[( ) ]
[( ) ]
( ) .
d w d w
d w
MPa nm mJ m2. (7)
Case 1. The value w is fixed at a constant value and w d� can be obtained from the
schematic drawing in Fig. 2. A coefficient m will be adopted to illustrate the relationship
between w and d. This relationship can be expressed as follows: w md� (m�1). When
m� 2 is substituted into Eq. (7), the equation can be transformed into the following one:
F
d d
d d
d d
I MPa nm�
� �
�
�
�
25 163
4 1
1
6612 864
9 14 2
2 2
2
.
( )
( ) .
( )
(9 12 2d �
�
)
( )MPa nm
� � �64 6 64 62 2. ( ) . .mJ m MPa nm mJ mFa (8)
Thus, when the value of d is increased, FI is descreased as the result.
Case 2. The value d is fixed at a constant value, and a different deformation equation
will be applied for FI [d nw� (0 1� �n ), and the value n� 0 5. is used]
F
w w
w
w
I MPa nm�
�
�
�6 29075
4
1 4 1
3306 432
9 42
2 2
.
( )
[( ) ]
( ) .
[( )w
w
2
2 2
1
9 4 1
�
�
�
]
[( ) ]
( )MPa nm
� � �64 6 64 62 2. ( ) . .mJ m MPa nm mJ mFb (9)
The result is that FI will decrease with the increase in w.
A more accurate result has been obtained from the above analysis. The uncertainty
shown in in Section 1.2.1 has been modified. The quantitative analysis of problems can
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 41
T a b l e 1
Parameters Used in Calculation (Selected from [9])
Shear modulus �, GPa 43.8
Poisson’s ratio � 0.447
Magnitude of the Burgers vector | |,b nm 0.2888
APB energy � APB , mJ/m2 64.6
Height of dipole h, nm 1.0
An Improved Method of Fatigue Life Assessment ...
contribute to making more extensive and in-depth conclusion in combination with the
qualitative analysis.
The relations between Fa and d , as well as between Fb and w, are depicted in
Fig. 3.
From the above-mentioned relations, the tendency of the curve can be easily traced. In
Fig. 3a, Fa attains the maximum value when d is in the vicinity of 1. Then the curve will
asymptotically approach zero. The equality Fa � 0 means that the material has no defects,
namely, the material is composed of complete grains, and therefore its fracture toughness
will be higher and the fatigue life will be longer than those of material with some defects.
That is to say, the interaction force of dislocations will be decreased with increasing d
(after Fa has reached the maximum value). So the conclusion that fatigue life of TiAl
alloys can be improved by the addition of trace elements to make grains more refined can
be easily made.
In Fig. 3b, Fb is maximized when w attains the value of 2.5. Then Fb will always
fall near zero, and Fb � 0 also means that the material has no defects, namely, the material
is an ideal one made up of whole grains. The fatigue life for the ideal material must be
longer than that of the material with defects. Thus, trace elements should be added to make
R. C. Feng, Z. Y. Rui, G. T. Zhang, et al.
42 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
a
b
Fig. 3. Relation between F and variables d (a) or w (b).
w, nm
d , nm
F
a
,
M
P
a
n
m
F
b
,
M
P
a
n
m
grains more refined, in order to improve the fatigue life. The fatigue life of TiAl alloys and
other materials can usually be improved by making grains more refined with the addition of
trace elements.
2. Discussion. It is known that there are many other factors which have strong
influence on mechanical properties and fatigue life of materials, in addition to dislocations
and debris, as it has been shown above. Examples of these are temperature, loading
frequency and stress ratio. However, in this section, the focus is put on the influence of
stress ratio. The stress ratio R K K� min max has a significant effect on fatigue life of
material, so the discussion of the stress ratio effect is expedient. In double logarithmic
coordinates with da dN K� � , data about da dN K� � with banner loading will stratify
due to the different values of stress ratio. The influence will be more sensitive for low
values of �K [15]. That is to say, the fatigue life of material will be strongly affected by
stress ratio. In order to take the stress ratio effect into consideration in the quantitative
analysis, a modifying factor f is recommended to be applied in the process of calculation,
so that a more accurate result could be reached by modifying the above formula. In this
paper, several factors that have an effect on fatigue life have been ignored, so there is a
long way to go before an accurate result can be reached.
Conclusions. TiAl alloys play a vital role in modern industies. Dislocations, debris
and other defects in TiAl alloys and other materials have a strong effect on the fatigue life.
It is important to study new methods for assessing fatigue life, especially for prediction of
the fatigue crack initiation life. The following conclusions are made.
1. A new method yielding more accurate results has been obtained via the quantitative
rather than qualitative analysis.
2. The fatigue life of TiAl alloys and other materials can be improved by addition of
trace alloying elements.
3. The method shown above can also be used for other materials, besides the
investigated TiAl alloys.
Acknowledgements. This work was supported by the National Natural Science
Fund of China (51065014) and the Program for Changjiang Scholars and Innovative
Research Team in University of Ministry of Education of China (IRT1140). R. C. Feng
would like to thank Engineering Research Center of Nonferrous Metallurgy’s New
Equipment, Ministry of Education, Lanzhou University of Technology for providing
help.
Ð å ç þ ì å
Çàïðîïîíîâàíî íîâèé ìåòîä îö³íêè äîâãîâ³÷íîñò³ â³ä óòîìëåíîñò³ Ò³Àl ñïëàâ³â çà
ðåçóëüòàòàìè ê³ëüê³ñíîãî òà ÿê³ñíîãî àíàë³çó. Çà äîïîìîãîþ ê³ëüê³ñíîãî àíàë³çó
âèçíà÷åíî âïëèâ ì³êðîñòðóêòóðè TiAl ñïëàâ³â íà ¿õ äîâãîâ³÷í³ñòü â³ä óòîìëåíîñò³.
Ðîçðàõóíîê çóñèëëÿ ì³æ äèñëîêàö³ÿìè ïðîâåäåíî çà ñòàíäàðòíîþ ôîðìóëîþ, çà
äîïîìîãîþ ÿêî¿ ìîæíà îòðèìàòè òî÷íèé ðåçóëüòàò. ʳëüê³ñíèé òà ÿê³ñíèé àíàë³ç
ïîêàçàâ, ùî äîâãîâ³÷í³ñòü â³ä óòîìëåíîñò³ ìîæíà ï³äâèùèòè øëÿõîì ââåäåííÿ ì³êðî-
åëåìåíò³â, ÿê³ ñïðèÿþòü ïîäð³áíåííþ çåðåí.
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Received 22. 11. 2013
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