Method of Evaluation of Distribution Characteristics of Flaky Inclusions
Для определения максимального размера хлопьевидных включений в литом магниевом сплаве с добавками кремния предложен метод оценки характеристик распределения указанных включений. Применимость метода проверена путем компьютерного моделирования с произвольными распределениями включений. Метод позволяе...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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| Cite this: | Method of Evaluation of Distribution Characteristics of Flaky Inclusions / K. Hayashi, S. Hamada, T. Matsumoto, M. Sakamoto, H. Noguchi // Проблемы прочности. — 2011. — № 4. — С. 66-73. — Бібліогр.: 5 назв. — англ. |
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Hayashi, K. Hamada, S. Matsumoto, T. Sakamoto, M. Noguchi, H. 2017-01-27T10:24:51Z 2017-01-27T10:24:51Z 2011 Method of Evaluation of Distribution Characteristics of Flaky Inclusions / K. Hayashi, S. Hamada, T. Matsumoto, M. Sakamoto, H. Noguchi // Проблемы прочности. — 2011. — № 4. — С. 66-73. — Бібліогр.: 5 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/112782 539.4 Для определения максимального размера хлопьевидных включений в литом магниевом сплаве с добавками кремния предложен метод оценки характеристик распределения указанных включений. Применимость метода проверена путем компьютерного моделирования с произвольными распределениями включений. Метод позволяет прогнозировать максимальный размер хлопьевидных включений в произвольном объеме материала. Для визначення максимального розміру пластівчастих включень у литому магнієвому сплаві з домішками кремнію запропоновано метод оцінки характеристик розподілу вказаних включень. Робота методу перевірена шляхом комп’ютерного моделювання з довільним розподілом включень. Метод дозволяє прогнозувати максимальний розмір пластівчастих включень у довільному об’ємі матеріалу. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел Method of Evaluation of Distribution Characteristics of Flaky Inclusions Метод оценки характеристик распределения хлопьевидных включений Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Method of Evaluation of Distribution Characteristics of Flaky Inclusions |
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Method of Evaluation of Distribution Characteristics of Flaky Inclusions Hayashi, K. Hamada, S. Matsumoto, T. Sakamoto, M. Noguchi, H. Научно-технический раздел |
| title_short |
Method of Evaluation of Distribution Characteristics of Flaky Inclusions |
| title_full |
Method of Evaluation of Distribution Characteristics of Flaky Inclusions |
| title_fullStr |
Method of Evaluation of Distribution Characteristics of Flaky Inclusions |
| title_full_unstemmed |
Method of Evaluation of Distribution Characteristics of Flaky Inclusions |
| title_sort |
method of evaluation of distribution characteristics of flaky inclusions |
| author |
Hayashi, K. Hamada, S. Matsumoto, T. Sakamoto, M. Noguchi, H. |
| author_facet |
Hayashi, K. Hamada, S. Matsumoto, T. Sakamoto, M. Noguchi, H. |
| topic |
Научно-технический раздел |
| topic_facet |
Научно-технический раздел |
| publishDate |
2011 |
| language |
English |
| container_title |
Проблемы прочности |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| format |
Article |
| title_alt |
Метод оценки характеристик распределения хлопьевидных включений |
| description |
Для определения максимального размера хлопьевидных включений в литом магниевом сплаве с
добавками кремния предложен метод оценки характеристик распределения указанных включений. Применимость метода проверена путем компьютерного моделирования с произвольными распределениями включений. Метод позволяет прогнозировать максимальный размер
хлопьевидных включений в произвольном объеме материала.
Для визначення максимального розміру пластівчастих включень у литому
магнієвому сплаві з домішками кремнію запропоновано метод оцінки характеристик розподілу вказаних включень. Робота методу перевірена шляхом
комп’ютерного моделювання з довільним розподілом включень. Метод дозволяє прогнозувати максимальний розмір пластівчастих включень у довільному
об’ємі матеріалу.
|
| issn |
0556-171X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/112782 |
| citation_txt |
Method of Evaluation of Distribution Characteristics of Flaky Inclusions / K. Hayashi, S. Hamada, T. Matsumoto, M. Sakamoto, H. Noguchi // Проблемы прочности. — 2011. — № 4. — С. 66-73. — Бібліогр.: 5 назв. — англ. |
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UDC 539.4
Method of Evaluation of Distribution Characteristics of Flaky
Inclusions*
K. Hayashi,
1
S. Hamada,
2
T. Matsumoto, M. Sakamoto, and H. Noguchi
Department of Mechanical Engineering, Kyushu University, Fukuoka, Japan
1 hayashi@mech.kyushu-u.ac.jp
2 hamada@mech.kyushu-u.ac.jp
ÓÄÊ 539.4
Ìåòîä îöåíêè õàðàêòåðèñòèê ðàñïðåäåëåíèÿ õëîïüåâèäíûõ
âêëþ÷åíèé
Ê. Õàÿøè, Ñ. Õàìàäà, Ò. Ìàöóìîòî, Ì. Ñàêàìîòî, Õ. Íîãó÷è
Îòäåëåíèå ìåõàíèêè, Óíèâåðñèòåò Êþøó, Ôóêóîêà, ßïîíèÿ
Äëÿ îïðåäåëåíèÿ ìàêñèìàëüíîãî ðàçìåðà õëîïüåâèäíûõ âêëþ÷åíèé â ëèòîì ìàãíèåâîì ñïëàâå ñ
äîáàâêàìè êðåìíèÿ ïðåäëîæåí ìåòîä îöåíêè õàðàêòåðèñòèê ðàñïðåäåëåíèÿ óêàçàííûõ âêëþ-
÷åíèé. Ïðèìåíèìîñòü ìåòîäà ïðîâåðåíà ïóòåì êîìïüþòåðíîãî ìîäåëèðîâàíèÿ ñ ïðîèçâîëü-
íûìè ðàñïðåäåëåíèÿìè âêëþ÷åíèé. Ìåòîä ïîçâîëÿåò ïðîãíîçèðîâàòü ìàêñèìàëüíûé ðàçìåð
õëîïüåâèäíûõ âêëþ÷åíèé â ïðîèçâîëüíîì îáúåìå ìàòåðèàëà.
Êëþ÷åâûå ñëîâà: âêëþ÷åíèå, äåôåêò ëèòüÿ, êîíöåíòðàöèÿ íàïðÿæåíèé, ìàñ-
øòàáíûé ôàêòîð, ñòàòèñòè÷åñêèé ìåòîä, äåôåêò ìàòåðèàëà, íåãîðþ÷èé ìàã-
íèåâûé ñïëàâ.
Introduction. A Si-added noncombustible Mg casting alloy [1] has flaky
inclusions. The flaky inclusions are larger than the defects in a normal casting
material and the number of the flaky inclusions in this material per unit volume is
much less than the inclusions in a normal casting material. Figure 1 shows an
example of a flaky inclusion (oxidation).
A mechanical structure has many stress concentration areas. However, the
stress concentration volumes of the mechanical structure made by this alloy are
usually small. In order to put this material into practical use, it is necessary to
control the inclusions so as not to include them in a stress concentration volume. In
order to control the inclusions, it is necessary to evaluate the maximum size of the
flaky inclusions. It seems effective to apply statistics of extreme [2, 3] to this
material, although for such a small volume like a stress concentration volume, it is
important that the control volume should be smaller than the stress concentration
volume. However, the control volume cannot be small due to the properties of the
flaky inclusions. Thus, the statistics of extreme are not effective in this case.
© K. HAYASHI, S. HAMADA, T. MATSUMOTO, M. SAKAMOTO, H. NOGUCHI, 2011
66 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 4
* Report on International Colloquium “Mechanical Fatigue of Metals” (13–15 September 2010,
Opole, Poland).
In this study, we propose an evaluation method of the size distribution
characteristics not only of extreme values, but also all the size regions of the flaky
inclusions. The sizes of the inclusions are measured from the fracture surfaces
obtained from the tensile tests. Alternately, the results of fatigue tests can be used
instead of tensile tests, since in both cases the material fracture start from the
inclusion. The validity of this method is verified through simulations with materials
that have arbitrary inclusion distributions. The proposed method enables prediction
of the maximum size of the flaky inclusions in an arbitrary volume.
1. Proposed Evaluation Method.
1.1. Repetitive Tensile Test. When a tensile test is performed using a material,
which obeys the weakest link theory, the fracture sourcen is the maximum size
inclusion in the control volume. The inclusion appears on the fracture surface.
With this phenomenon, the repetitive tensile test is proposed by the authors as the
method to evaluate the size distribution characteristics of the inclusions. Figure 2
shows the schematic diagram of the repetitive tensile test. For the first test, the
fracture source should be the maximum size inclusion in the specimen, and the
inclusion appears on the fracture surface. After the first test, the inclusions, which
are fracture sources emerging on the fracture surfaces, are smaller than the
inclusion which is a fracture source of the first test. In this way, the sizes of the
inclusions are measured from the fracture surfaces. The size distribution of the
inclusions can then be estimated by the repetitive tensile testing.
Method of Evaluation of Distribution Characteristics ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 4 67
Fig. 1. Oxide inclusion appeared on fracture surface [1].
Fig. 2. Schematic diagram of the repetitive tensile test.
A tensile specimen usually has grip sections. The diameter of the specimen
grip section is greater than that of the control volume. However, since the total
volume of the specimen for the repetitive tensile test must be treated as the control
volume, specimens with no grip section should be used for the tests. The cross
section of the specimen has a uniform shape. In order to apply a tensile load to the
specimen, its edge must be gripped. However, the inclusions in the grip sections
will not be the fracture origin because no load is applied to the grip sections. The
true size distribution of inclusions may not correspond to the distribution obtained
from the repetitive tensile tests. Therefore, in order to estimate the size distribution
of inclusions from the result with the specimen with grip sections, the repetitive
test results need to be refined.
1.2. Correction Method of the Test Results. In this paper, area is used as
the size of the flaky inclusions similar to the Murakami method [4]. Figure 3 shows
the definitions of area.
Figure 4 shows the correction method of the repetitive tensile test considering
the grip sections. The expected value of the inclusion whose size is area1 in the
control volume V1 is estimated as follows. A tensile test is carried out using the
specimen whose volume is V1 in Test 1. The fracture origin size is area1 . When
the total grip section volume is Vg , the tested volume is (V Vg1 � ). The Test 1
result is that the maximum inclusion size in the volume (V Vg1 � ) is area2 .
Considering the ratio of volume V1 to volume (V Vg1 � ), the expected value of the
inclusions whose size is area1 in the volume V1 is 1 1 1� �V V Vg( ).
The expected value of the inclusion whose size is area2 in the control
volume V2 is considered as follows. The tensile test is carried out using the
specimen whose volume is V2 in Test 2. The fracture origin size is area2 . The
Test 2 result is that the maximum inclusion size in the volume (V Vg2 � ) is area2 .
The expected value of the inclusions whose size is area2 in the volume V2 is
1 1 1� �V V Vg( ). The number of inclusions whose sizes are over area is defined
as F areaV ( ). The expected value of the inclusions whose size is area2 in the
K. Hayashi, S. Hamada, T. Matsumoto, et al.
68 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 4
Fig. 3. Definitions of area.
volume V1 is F area V V V V V VV g g1 2 1 1 2 21 1( ) ( ) ( )� � � � � � when
considering the Test 1 result because area area1 2� .
Test n is carried out using the specimen whose volume is Vn . The expected
value of the inclusions whose size is arean in the volume Vn is
F area
V
V VV n
k
k gk
n
n
( ) .� �
�
�
�
�
�
�
�
1
1
(1)
Based on the correction to the test result by considering the grip sections
volume, the size distribution of the inclusions can be predicted. The specimen
becomes shorter after every tensile test. When the specimen cannot be gripped, the
repetitive tensile test ends.
2. Validation by Simulation.
2.1. Validation Method. Real materials have an unknown inclusion distribution.
Therefore, corrected distributions and real distributions cannot be compared by
repetitive tensile tests using real materials, and.the validity of the proposed
repetitive tensile test cannot be verified. In this paper, numerical simulations of
repetitive tensile tests are performed on a computer with an assumed inclusion
distribution. The following expression based on the expression proposed by
Hashimoto et al. [5] is used as the assumed inclusion distribution.
F area M
area
V V( ) exp ,� �
�
�
�
�
�
�
�
�
�
�
�
�
��
�
(2)
where M V is average number of all inclusions in the specimen, and � and � are
constant number depending on particle characteristic.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 4 69
Method of Evaluation of Distribution Characteristics ...
Fig. 4. Correction method.
At the start, � and � are assumed. In order to confirm that the proposed
method does not depend on a distribution characteristic, simulations are performed
for three materials that have different � and � values. Table 1 shows the assumed
� and � values.
The length of the specimen is assumed to be a unit length. Random numbers
are allocated to the inclusions. The random numbers are the position coordinates of
the inclusions in a specimen. The coordinate uses one axis parallel to the loading
direction. With this specimen, operations to break the specimen from the maximum
size inclusions are repeated. However, some constant length from the edge of the
specimen is the grip section. When the maximum size inclusion is in the grip
section, the specimen is broken from the maximum size inclusion in the volume
without grip sections.
Test results may vary according to the proportion of grip section volume to
specimen volume. The grip section volume is prepared of 2 proportions, and the
differences in both are compared. The prepared proportion of the grip sections to
the specimen volume are 10 and 20%.
2.2. Simulation Results and Discussion. Figures 5 and 6 show the repetitive
tensile test simulation results and the refined results in which the grip sections are
assumed to be 10 and 20% of the specimen volume, respectively.
All figures show ten simulation results with the changing positions of the
inclusions. The reason why more than one simulation result is shown is that
F areaV ( ) is the mean distribution of the inclusion sizes and the number in a
certain volume material. The simulation results for the same material differ because
inclusions are randomly placed in a specimen. The simulation results and refined
results are case studies. It is expedient to compare the assumed distributions and
corrected results by more than one simulation result. The test results are lower than
assumed distributions in Figs. 5 and 6 because the inclusions in the grip sections do
not originate from a fracture. However, the refined results are distributed around
the assumed distributions. The refined results agree with the assumed distributions.
The scatter of the refined results in Fig. 5 is wider than that in Fig. 6 because the
grip section volume of the specimen in Fig. 5 is larger than that in Fig. 6. However,
the refined results in Fig. 5 and Fig. 6 agree with the assumed distributions.
Consequently, the proposed correction method for the repetitive tensile test result is
considered to be adequate and invariant to the grip section length.
Conclusions. The repetitive tensile test and the correction method are proposed
as the method to evaluate the inclusion distribution for the all size ranges. The
70 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 4
K. Hayashi, S. Hamada, T. Matsumoto, et al.
T a b l e 1
Assumed Constants for Simulation
Material MV � �
Material I 10 93 0.3
Material II 10 651 1.0
Material III 10 1136 3.0
validity of the proposed correction method is verified by the simulation using the
proposed evaluation method.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 4 71
Fig. 5. Simulation results. (The grip volume is 10% of the specimen volume.)
Method of Evaluation of Distribution Characteristics ...
72 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 4
Method of Evaluation of Distribution Characteristics ...
Fig. 6. Simulation results. (The grip volume is 20% of the specimen volume.)
Ð å ç þ ì å
Äëÿ âèçíà÷åííÿ ìàêñèìàëüíîãî ðîçì³ðó ïëàñò³â÷àñòèõ âêëþ÷åíü ó ëèòîìó
ìàãí³ºâîìó ñïëàâ³ ç äîì³øêàìè êðåìí³þ çàïðîïîíîâàíî ìåòîä îö³íêè õàðàê-
òåðèñòèê ðîçïîä³ëó âêàçàíèõ âêëþ÷åíü. Ðîáîòà ìåòîäó ïåðåâ³ðåíà øëÿõîì
êîìï’þòåðíîãî ìîäåëþâàííÿ ç äîâ³ëüíèì ðîçïîä³ëîì âêëþ÷åíü. Ìåòîä äîçâî-
ëÿº ïðîãíîçóâàòè ìàêñèìàëüíèé ðîçì³ð ïëàñò³â÷àñòèõ âêëþ÷åíü ó äîâ³ëüíîìó
îá’ºì³ ìàòåð³àëó.
1. S. Hamada, K. Hayashi, T. Matsumoto, et al., “Proposal of strength evaluation
method in casting material with defect: using Si-added noncombustible Mg
alloy,” Trans. Jpn. Soc. Mech. Eng. [in Japanese], 75, No. 758A, 1326–1333
(2009).
2. E. J. Gumbel, Statistics of Extremes, Columbia University Press (1958).
3. Y. Murakami and T. Toriyama, “Critical review of the inclusion rating by
JIS-G-0555 method and new inclusion rating based on statistics of extreme
and its applications,” Tetsu-to-Hagane, 79, No. 12A, 1380–1385 (1993).
4. Y. Murakami, Metal Fatigue: Effects of Small Defects and Nonmetallic
Inclusions, Elsevier Science Ltd (2002).
5. A. Hashimoto, T. Miyazaki, H. Kang, et al., “Estimation of particle size
distribution in materials in case of spheroidal particles with quantitative
microscopy,” J. Test. Eval., 28, No. 9, 367–377 (2000).
Received 10. 02. 2011
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2011, ¹ 4 73
Method of Evaluation of Distribution Characteristics ...
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/ENU (Use these settings to create Adobe PDF documents for quality printing on desktop printers and proofers. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
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/OtherNamespaces [
<<
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/OmitPlacedBitmaps false
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>>
<<
/AddBleedMarks false
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/PresetSelector /MediumResolution
>>
/FormElements false
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>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|