External Stress Effect on Microstructure and Transformation Plasticity of Hot Work Tool Steel during Quenching
Исследуется изменение пластичности и микроструктуры жаропрочной инструментальной стали при мартенситном превращении. Образцы подвергались аустенитизации и закалке на воздухе. В процессе охлаждения их нагружали статическим изгибом с номинальным напряжением 100 МПа по трем схемам: статический изгиб об...
Saved in:
| Published in: | Проблемы прочности |
|---|---|
| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут проблем міцності ім. Г.С. Писаренко НАН України
2015
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/173384 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | External Stress Effect on Microstructure and Transformation Plasticity of Hot Work Tool Steel during Quenching / R.K. Janutienë, R.K. Dièkuvienë // Проблемы прочности. — 2015. — № 5. — С. 94-108. — Бібліогр.: 31 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-173384 |
|---|---|
| record_format |
dspace |
| spelling |
Janutienë, R.K. Dièkuvienë, R.K. 2020-12-02T11:50:45Z 2020-12-02T11:50:45Z 2015 External Stress Effect on Microstructure and Transformation Plasticity of Hot Work Tool Steel during Quenching / R.K. Janutienë, R.K. Dièkuvienë // Проблемы прочности. — 2015. — № 5. — С. 94-108. — Бібліогр.: 31 назв. — англ. 0556-171X https://nasplib.isofts.kiev.ua/handle/123456789/173384 539.432 Исследуется изменение пластичности и микроструктуры жаропрочной инструментальной стали при мартенситном превращении. Образцы подвергались аустенитизации и закалке на воздухе. В процессе охлаждения их нагружали статическим изгибом с номинальным напряжением 100 МПа по трем схемам: статический изгиб образцов после их изъятия из печи, при этом отмечались деформация исходного аустенита и формирование мартенсита под нагрузкой; изгиб после начала мартенситного превращения с деформацией мартенсита; разгрузка с момента начала мартенситного превращения с преобладающей деформацией аустенита, при этом измерялась деформация при разгрузке. При охлаждении образцов до комнатной температуры измерялась величина их пластического прогиба. Показано, что мартенситное превращение характеризуется существенным повышением пластичности. Различное влияние на мартенситное превращение растягивающих и сжимающих напряжений оценивалось путем измерения деформации образцов при разгрузке. Микроструктура растянутых и сжатых поверхностей образцов исследовалась методами рентгеновской дифрактометрии, электронной микроскопии и электронно-дисперсионной спектроскопии. Досліджується зміна пластичності та мікроструктури жароміцної інструментальної сталі при мартенситному перетворенні. Зразки піддавали астенітизації та закалюванню на повітрі. У процесі охолодження їх навантажували статичним згином із номінальним напруженням 100 МПа за трьома схемами: статичний згин зразків після їх вилучення з печі, при цьому відмічались деформація початкового аустеніту і формування мартенситу під дією навантаження; згин після початку мартенситного перетворення з деформацією мартенситу; розвантаження з моменту початку мартенситного перетворення з переважаючою деформацією аустеніту, при цьому вимірювалась деформація при розвантаженні. При охолодженні зразків до кімнатної температури вимірювалась величина їх пластичного прогину. Показано, що мартенситне перетворення характеризується суттєвим підвищенням пластичності. Різний вплив на мартенситне перетворення розтяжних і стискальних напружень оцінювали шляхом вимірювання деформації зразків при розвантаженні. Мікроструктура розтягнутих і стиснутих поверхностей зразків досліджувалась методами рентгенівської дифрактометр ії, електронної мікроскопії і електронно-дисперсійної спектроскопії. This work has been performed in collaboration with Lithuanian Institute of Energy. en Інститут проблем міцності ім. Г.С. Писаренко НАН України Проблемы прочности Научно-технический раздел External Stress Effect on Microstructure and Transformation Plasticity of Hot Work Tool Steel during Quenching Влияние напряжений от внешних нагрузок на микроструктуру и пластичность при фазовом превращении жаропрочной инструментальной стали при закалке Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
External Stress Effect on Microstructure and Transformation Plasticity of Hot Work Tool Steel during Quenching |
| spellingShingle |
External Stress Effect on Microstructure and Transformation Plasticity of Hot Work Tool Steel during Quenching Janutienë, R.K. Dièkuvienë, R.K. Научно-технический раздел |
| title_short |
External Stress Effect on Microstructure and Transformation Plasticity of Hot Work Tool Steel during Quenching |
| title_full |
External Stress Effect on Microstructure and Transformation Plasticity of Hot Work Tool Steel during Quenching |
| title_fullStr |
External Stress Effect on Microstructure and Transformation Plasticity of Hot Work Tool Steel during Quenching |
| title_full_unstemmed |
External Stress Effect on Microstructure and Transformation Plasticity of Hot Work Tool Steel during Quenching |
| title_sort |
external stress effect on microstructure and transformation plasticity of hot work tool steel during quenching |
| author |
Janutienë, R.K. Dièkuvienë, R.K. |
| author_facet |
Janutienë, R.K. Dièkuvienë, R.K. |
| topic |
Научно-технический раздел |
| topic_facet |
Научно-технический раздел |
| publishDate |
2015 |
| language |
English |
| container_title |
Проблемы прочности |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| format |
Article |
| title_alt |
Влияние напряжений от внешних нагрузок на микроструктуру и пластичность при фазовом превращении жаропрочной инструментальной стали при закалке |
| description |
Исследуется изменение пластичности и микроструктуры жаропрочной инструментальной стали при мартенситном превращении. Образцы подвергались аустенитизации и закалке на воздухе. В процессе охлаждения их нагружали статическим изгибом с номинальным напряжением 100 МПа по трем схемам: статический изгиб образцов после их изъятия из печи, при этом отмечались деформация исходного аустенита и формирование мартенсита под нагрузкой; изгиб после начала мартенситного превращения с деформацией мартенсита; разгрузка с момента начала мартенситного превращения с преобладающей деформацией аустенита, при этом измерялась деформация при разгрузке. При охлаждении образцов до комнатной температуры измерялась величина их пластического прогиба. Показано, что мартенситное превращение характеризуется существенным повышением пластичности. Различное влияние на мартенситное превращение растягивающих и сжимающих напряжений оценивалось путем измерения деформации образцов при разгрузке. Микроструктура растянутых и сжатых поверхностей образцов исследовалась методами рентгеновской дифрактометрии, электронной микроскопии и электронно-дисперсионной спектроскопии.
Досліджується зміна пластичності та мікроструктури жароміцної інструментальної сталі при мартенситному перетворенні. Зразки піддавали астенітизації та закалюванню на повітрі. У процесі охолодження їх навантажували статичним згином із номінальним напруженням 100 МПа за трьома схемами: статичний згин зразків після їх вилучення з печі, при цьому відмічались деформація початкового аустеніту і формування мартенситу під дією навантаження; згин після початку мартенситного перетворення з деформацією мартенситу; розвантаження з моменту початку мартенситного перетворення з переважаючою деформацією аустеніту, при цьому вимірювалась деформація при розвантаженні. При охолодженні зразків до кімнатної температури вимірювалась величина їх пластичного прогину. Показано, що мартенситне перетворення характеризується суттєвим підвищенням пластичності. Різний вплив на мартенситне перетворення розтяжних і стискальних напружень оцінювали шляхом вимірювання деформації зразків при розвантаженні. Мікроструктура розтягнутих і стиснутих поверхностей зразків досліджувалась методами рентгенівської дифрактометр ії, електронної мікроскопії і електронно-дисперсійної спектроскопії.
|
| issn |
0556-171X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/173384 |
| citation_txt |
External Stress Effect on Microstructure and Transformation Plasticity of Hot Work Tool Steel during Quenching / R.K. Janutienë, R.K. Dièkuvienë // Проблемы прочности. — 2015. — № 5. — С. 94-108. — Бібліогр.: 31 назв. — англ. |
| work_keys_str_mv |
AT janutienerk externalstresseffectonmicrostructureandtransformationplasticityofhotworktoolsteelduringquenching AT diekuvienerk externalstresseffectonmicrostructureandtransformationplasticityofhotworktoolsteelduringquenching AT janutienerk vliânienaprâženiiotvnešnihnagruzoknamikrostrukturuiplastičnostʹprifazovomprevraŝeniižaropročnoiinstrumentalʹnoistaliprizakalke AT diekuvienerk vliânienaprâženiiotvnešnihnagruzoknamikrostrukturuiplastičnostʹprifazovomprevraŝeniižaropročnoiinstrumentalʹnoistaliprizakalke |
| first_indexed |
2025-11-25T20:56:30Z |
| last_indexed |
2025-11-25T20:56:30Z |
| _version_ |
1850543750276710400 |
| fulltext |
UDC 539.432
External Stress Effect on Microstructure and Transformation Plasticity of
Hot Work Tool Steel during Quenching
R. K. Janutienëa,1 and R. K. Dièkuvienëb,2
a Kaunas University of Technology, Kaunas, Lithuania
b Lithuanian Energy Institute, Kaunas, Lithuania
1 raskand@ktu.lt
2 regina@isag.lei.lt
ÓÄÊ 539.432
Âëèÿíèå íàïðÿæåíèé îò âíåøíèõ íàãðóçîê íà ìèêðîñòðóêòóðó è ïëàñ-
òè÷íîñòü ïðè ôàçîâîì ïðåâðàùåíèè æàðîïðî÷íîé èíñòðóìåíòàëüíîé
ñòàëè ïðè çàêàëêå
Ð. Ê. Æàíóòèåíåà, Ð. Ê. Äèöêóâèåíåá
à Êàóíàññêèé òåõíîëîãè÷åñêèé óíèâåðñèòåò, Êàóíàñ, Ëèòâà
á Ëèòîâñêèé ýíåðãåòè÷åñêèé èíñòèòóò, Êàóíàñ, Ëèòâà
Èññëåäóåòñÿ èçìåíåíèå ïëàñòè÷íîñòè è ìèêðîñòðóêòóðû æàðîïðî÷íîé èíñòðóìåíòàëüíîé
ñòàëè ïðè ìàðòåíñèòíîì ïðåâðàùåíèè. Îáðàçöû ïîäâåðãàëèñü àóñòåíèòèçàöèè è çàêàëêå íà
âîçäóõå.  ïðîöåññå îõëàæäåíèÿ èõ íàãðóæàëè ñòàòè÷åñêèì èçãèáîì ñ íîìèíàëüíûì íàïðÿ-
æåíèåì 100 ÌÏà ïî òðåì ñõåìàì: ñòàòè÷åñêèé èçãèá îáðàçöîâ ïîñëå èõ èçúÿòèÿ èç ïå÷è, ïðè
ýòîì îòìå÷àëèñü äåôîðìàöèÿ èñõîäíîãî àóñòåíèòà è ôîðìèðîâàíèå ìàðòåíñèòà ïîä íàãðóç-
êîé; èçãèá ïîñëå íà÷àëà ìàðòåíñèòíîãî ïðåâðàùåíèÿ ñ äåôîðìàöèåé ìàðòåíñèòà; ðàçãðóçêà ñ
ìîìåíòà íà÷àëà ìàðòåíñèòíîãî ïðåâðàùåíèÿ ñ ïðåîáëàäàþùåé äåôîðìàöèåé àóñòåíèòà, ïðè
ýòîì èçìåðÿëàñü äåôîðìàöèÿ ïðè ðàçãðóçêå. Ïðè îõëàæäåíèè îáðàçöîâ äî êîìíàòíîé òåì-
ïåðàòóðû èçìåðÿëàñü âåëè÷èíà èõ ïëàñòè÷åñêîãî ïðîãèáà. Ïîêàçàíî, ÷òî ìàðòåíñèòíîå
ïðåâðàùåíèå õàðàêòåðèçóåòñÿ ñóùåñòâåííûì ïîâûøåíèåì ïëàñòè÷íîñòè. Ðàçëè÷íîå âëèÿíèå
íà ìàðòåíñèòíîå ïðåâðàùåíèå ðàñòÿãèâàþùèõ è ñæèìàþùèõ íàïðÿæåíèé îöåíèâàëîñü ïóòåì
èçìåðåíèÿ äåôîðìàöèè îáðàçöîâ ïðè ðàçãðóçêå. Ìèêðîñòðóêòóðà ðàñòÿíóòûõ è ñæàòûõ
ïîâåðõíîñòåé îáðàçöîâ èññëåäîâàëàñü ìåòîäàìè ðåíòãåíîâñêîé äèôðàêòîìåòðèè, ýëåêòðîí-
íîé ìèêðîñêîïèè è ýëåêòðîííî-äèñïåðñèîííîé ñïåêòðîñêîïèè.
Êëþ÷åâûå ñëîâà: ìàðòåíñèòíîå ïðåâðàùåíèå, æàðîïðî÷íàÿ ñòàëü, ìèêðîñòðóêòóðà,
ïëàñòè÷íîñòü, òåðìîîáðàáîòêà.
Introduction. The accuracy in size of hot-work tools is a very important question in
manufacturing of forgings [1, 2]. The hot-work tools can be affected by various stresses
originating during the long-term exploitation of tool and the precise measurement of a part
can be lost. Long-term exploitation is related with spontaneous tempering which occurs
during contact between tool and hot material, causing diffusion of carbon and alloying
elements [1]. The stresses occurring in the steel and therefore coming plastic deformations
of parts are related with the following processes [3–5]:
(i) residual stresses remained after machining;
(ii) microstructural stresses caused by constituents volume mismatch in microstructure
after austenite–martensite transformations;
© R. K. JANUTIENË, R. K. DIÈKUVIENË, 2015
94 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5
(iii) stress relaxation under the heat effect, especially when transformation plasticity
proceeds;
(iv) thermal stresses related with different ratios of thermal expansion of martensite,
austenite, and other constituents.
The regimes of quenching and tempering used for tools, simple or complex geometry
of parts also could be mentioned, e.g., tools with high length-to-diameter ratio have a
tendency to quenching distortion. Such distorted parts could be easily straightened out by
tension, bending or other methods performing during transformation plasticity effect.
Therefore the research of properties of each steel grade during thermal operations is very
important.
The variation in plasticity of different sorts of steel during martensitic transformation
and following tempering can be multiform [6–8].
The transformation plasticity of steel can be qualitatively assessed by comparing the
plastic deflection of equal-sized specimens tested at certain transformations. Computing of
the elastic modulus Etp of transformation plasticity can provide a quantitative analysis of
this effect [9]. Steel has the highest plasticity when it undergoes martensitic transformation,
i.e., plasticity of the quenched specimen is greater from several to dozen times comparing
to the one obtained after tempering. The value of transformation plasticity of quenched
steel is directly related with carbon content [10]. Also, the transformation plasticity of steel
is under the influence of the temperature of quenching and tempering, the content of
alloying elements, etc. [9, 10].
In some cases, steel products and hot-work tools as well, are heat treated under the
transformation plasticity effect for ensuring their dimensional accuracy, e.g., by fixing the
shape, but unfortunately the results are often not satisfactory. The most common errors are
too high temperatures for the start of air quenching that cause slight thermal stress,
especially when cooling is asymmetrical. Also, the load force used for correction of
geometric shape can be applied too early or too late considering on the start of martensitic
transformation. Loss of transformation plasticity or self-deformation occurs because of
varying of the intensity of ongoing martensitic transformation. The specimens may bend
themselves even as they are not externally loaded or affected by thermal stresses [6, 11]. In
order to make efficient use of the effect of transformation plasticity of precise steel
production technology it is necessary to know the kinetics of transformation plasticity of
each steel grade and its heat treatment peculiarities.
This work presents the investigation of transformation plasticity during martensitic
transformation of the Swedish company Uddeholm hot-work tool steel Hotvar alloyed with
chromium, molybdenum, and vanadium, used in hot-deformation dies, mould fabrication,
etc.
1. Experimental. The chemical composition of the investigated steel is listed in
Table 1.
The steel rods were used for manufacturing of the specimens of rectangular cross
section and measurement of 100 8 6� � mm3. The specimens were austenized at 1050, 1070,
and 1090�C temperatures in the environment of protective gas of N2 + CO + CO2 and then
air quenched. For the investigation of transformation plasticity effect, the austenized
specimen was placed in the special bending device [10] and air quenched at the same time.
T a b l e 1
Chemical Composition of Uddeholm Hotvar Steel (%)
C Si Mn Cr Mo V Fe
0.55 1.00 0.80 2.60 2.30 0.90 Bal.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5 95
External Stress Effect on Microstructure ...
At the set temperature the specimen was loaded by bending load generated bending stress
of 100 MPa and not exceeded yield strength R p0 2. of steel at the certain temperature (yield
strength of Hotvar is R p0 2. � 1110 MPa at T � �550 C [12]), then the plastic deflection of
specimen was measured with accuracy of 0.01 mm until room temperature of specimen was
reached. The ranges of bending test temperatures were:
(i) from 550�C to room temperature (RT). The temperature 550�C is an approximate
temperature at which the specimen is placed in testing device and bending starts. This
temperature was indicated by chromel-alumel thermocouple. At the start of bending, the
deformation affects the initial structure (austenite). Then, under the effect of stresses the
martensite transformation starts;
(ii) from 160–180�C to RT. According the data of manufacture of the steel, the
martensite start temperature M s is in the range of 210–220�C [12], so, at the moment of the
beginning of deformation, the martensite transformation is already started;
(iii) from 550�C to 160–180�C temperature followed by free-load cooling to RT. This
regime was chosen mainly to observe the self-deformation of specimen, when the initial
structure (austenite) was deformed.
The bending load was chosen for the purpose of producing different types of stresses
in the specimen. During bending, one part of the specimen was stretched, while the other
was compressed. Effect of tension and compression on transformations of steel was
observed. According to available literary data, transformations in steel can be influenced
differently by the variant stress state [13, 14].
The temperature of specimen during heat treatment was measured by welded
chromel-alumel thermocouple of 0.3 mm diameter, and the data were plotted together with
the deflection curves.
After quenching the specimens were tested for heat treatment quality. Universal
hardness meter VERZUS 750CCD for Rockwell hardness measurement was used.
The microstructural analysis was carried out on ZEISS EVO MA10 scanning electron
microscope (SEM) in back scattering mode and operated at 20 kV. Heat or thermo-
mechanically treated specimens were machine ground, polished using 1 �m diamond
suspension, and etched in 3% Nital solution.
he XRD analysis was performed using a D8 Advance diffractometer (Bruker AXS,
Karlsruhe, Germany) operating at the tube voltage of 40 kV and tube current of 40 mA.
The X-ray beam was filtered with Ni 0.02 mm filter to select the CuK� CuK wavelength
(� � 1.5406 Å). Diffraction patterns were recorded in a Bragg–Brentano geometry using a
fast counting detector Bruker LynxEye based on the silicon strip technology. The
specimens of metal and electrochemically extracted carbides were scanned over the range
2�� 25–90� and 2�� 3–100�, respectively, at a scanning speed of 6 deg/min using a
coupled two theta/theta scan type.
The crystal lattice parameters of martensite phase were calculated using PowderCell
program and Le Bail structureless whole pattern fitting algorithm [15].
Carbide phases were identified using search match program Bruker EVA and PDF-4
database [16].
The XRD analysis allowed identify the type of phases, content of retained austenite,
and the parameters of lattice of martensite at the compressed and stretched surfaces of
specimen.
2. Results and Discussion.
2.1. Microstructural Analysis of Quenched Steel. The steel containing vanadium has
a very fine microstructure: grains are several micrometers in size, i.e., about the size of
ASTM9 [17].
The analysis of quenched cross-cuts’ microstructure has shown that after heat
treatment the structure was formed mainly of lath martensite and retained austenite (in a
very low content, as it will be discussed later) mixed with dispersive carbides (Fig. 1). The
96 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5
R. K. Janutienë and R. K. Dièkuvienë
martensite can be identified as grey brindle zones (some of them are marked with arrows)
located in the austenite matrix with the primary grain boundaries.
The carbides are very small, less than 1 �m in diameter, highlighted with circles in
Fig. 1. Elemental mapping by SEM with energy dispersive X-ray spectrometry (EDS) was
used to reveal the carbides’ type. It was found that the carbides mainly consisted of
vanadium (Figs. 2 and. 3). Molybdenum could also be found in carbides, as SEM line
scanning showed a slight increase of its amount in carbides, which was confirmed by the
XRD analysis. The dominant presence of vanadium in carbides is clearly revealed by SEM
elemental scanning of the area (Fig. 3).
Fig. 1. SEM micrograph of air quenched Hotvar steel austenized at 1090�C.
Fig. 2. Carbide SEM line scanning of air quenched Hotvar steel specimen austenized at 1050�C.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5 97
External Stress Effect on Microstructure ...
No significant differences between the microstructure of the cross-cuts from different
quenching temperatures were observed.
The presence of vanadium in carbides was confirmed by the XRD analysis. The list
of detected carbides depending on the austenizing temperature is presented in Table 2. The
peaks were matched with the standard materials of PDF-4 database [16]. The list is given
by the declining order of confidence.
T a b l e 2
List of Carbides Detected in Hotvar Steel after Air Quenching from Different Temperatures
Air quenching temperature (�C)
1050 1070 1090
Matched materials
Formula
PDF number
VC0.88
77-2003
Formula
PDF number
VC
73-476
Formula
PDF number
VC0.88
77-2003
Formula
PDF number
VC
73-476
Formula
PDF number
V8C7
73-394
Formula
PDF number
V8C7
73-394
Formula
PDF number
V8C7
73-394
Formula
PDF number
VC0.88
77-2003
Formula
PDF number
VC
73-476
– – Formula
PDF number
MoOC
17-104
Formula
PDF number
MoOC
17-104
– – Formula
PDF number
Mo2C
15-457
Formula
PDF number
Mo2C
15-457
Fig. 3. Elemental mapping of air quenched Hotvar steel specimen austenized at 1050�C.
98 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5
R. K. Janutienë and R. K. Dièkuvienë
However, detection of molybdenum in carbides was quite problematic, due to the lack
of material for precise XRF quantitative analysis. XRD of carbides showed a possible peak
of molybdenum carbide (Fig. 4). It looks like being stuck to clearly expressed peak of
vanadium carbide. The peak of possible molybdenum carbide in XRD curves was marked
by arrows (Fig. 4). Also, it was observed that the intensity of carbides peaks increased by
lowering the heating temperature. This may attributed to the changes of solubility of
elements in the matrix.
The cross-cuts of quenched specimens showed high hardness: 63–66 HRC irrespective
of the austenizing temperature. Large hardness values are also related with the presence of
dispersive carbides.
2.2. Investigation of Bending Stress Effect on Martensitic Transformation. At the
moment of starting bending of air quenching specimen, the one is able to resist bending
force as its yield strength is rather greater than bending stress that was just 100 MPa. The
manufacture deals with the data concerning mechanical properties of Hotvar steel at high
temperatures; however these are just tentative data as represent strength in quenched
tempered steel (Table 3). The temperature during loading of specimen was measured to be
600�C (Fig. 5). The yield strength of quenched and tempered steels at 600�C is declared to
be 830 MPa.
The manufacturer indicates [12] that martensitic transformation start temperature of
Hotvar hot-work tool steel is about 220�C. The theoretical martensite start temperature was
calculated according Capdevila et al. model [18] and it was obtained 267.42�C:
M K w w w w ws ( ) . . . . . .�
764 2 3026 306 166 89 24C Mn Ni Cr Mo 113. wCu
858 74 14 5. . . .w w wCo W Si (1)
a b
c d
Fig. 4. XRD analysis of carbides of air quenched Hotvar steel showing the possible presence of
molybdenum carbide (its peak is marked by arrows).
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5 99
External Stress Effect on Microstructure ...
Figure 5 shows that in our test the martensite transformation started when temperature
of specimen dropped to 298�C, which is higher than that declared by manufacturer, as well
as the calculated one. The reason of higher M s can be the effect of stresses as it was found
that tension and compression stimulate martensite transformation [19].
The intense bending of specimens began when temperature of the specimen had
reached M s (Fig. 5). At stress level � � 100 MPa, the specimens’ deflection amounted to
1.30, 1.39, and 1.52 mm, respectively, to austenizing temperature, during loading through
air quenching. The higher temperatures were applied to specimens the greater deformations
were obtained: when austenizing temperatures were 1070 and 1090�C, the plastic
deflections exceeded the one obtained after quenching from 1050�C by 8 and 15%,
respectively (Fig. 5).
Deformation magnitude depends directly on the temperature of austenizing because at
higher temperatures austenite has more dissolved carbides, and solid solution gets more
T a b l e 3
Mechanical Properties of Hotvar Steel at Elevated Temperatures [12]
Test
temperature (�C)
Rm ,
MPa
Rp0 2. ,
MPa
Test
temperature (�C)
Rm ,
MPa
Rp0 2. ,
MPa
50 2300 1860 450 1760 1430
100 2200 1810 500 1650 1300
150 2130 1790 550 1450 1110
200 2060 1750 600 1180 830
250 2010 1710 650 800 520
300 1970 1690 700 350 210
350 1910 1600 750 200 100
400 1850 1510
Fig. 5. Plastic deformation of specimens’ air quenched from different austenizing temperatures.
100 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5
R. K. Janutienë and R. K. Dièkuvienë
saturated with carbon and alloying elements. The principle role plays carbon dissolved in
the austenite lattice.
Martensitic transformation is a non-diffusional process, so when it proceeds, all
carbon dissolved in face-centred cubic (fcc) austenite lattice remains in the new phase –
martensitic lattice saturated with carbon. It is known, that at room temperature �-iron may
contain just up to 0.006% carbon, as austenite may reach even 2.14% [20]. During � �
,
the fcc lattice of austenite transforms to body-centred cubic (bcc) martensite lattice. Carbon
atoms may occupy the sites of austenite lattice parallel to [100], [010], and [001]
crystallographic directions. The transformation � �
is non-diffusional, therefore, during
changes of fcc austenite lattice to bcc martensite lattice, carbon atoms remain inserted in
martensite lattice only in [001] direction (and at the centers of planes parallel to (001))
thereby stretching the parameter c of tetragonal lattice [20].
So with increasing temperature of austenizing, more and more carbides are dissolved
in austenite. As austenite becomes more rich in carbon atoms, the more of them intervene in
[001] crystallographic directions.The carbon atoms create substantial strains or displacements
of the neighboring iron atoms [21] and, therefore the specimens reach higher plastic
deflections during bending. In this case, the stress effect on transformation plasticity of
steel is just an instrumental way to show the transformation plasticity phenomenon as its
conditioning was always a constant value.
The described theory requires the additional experiments as there is no undivided
opinion about the relationship between parameters ratio c a of tetragonal martensite lattice
and carbon content in austenite and following martensite. Some researchers present the
results of studies when the ratio c a becomes larger than one only when the carbon content
in austenite exceeds 0.6% [22, 23]. The Hotvar steel contains total amount of carbon of just
0.55%, moreover, the part of carbon is combined in carbides, so the carbon content
remained in austenite is rather lower than the mentioned 0.6% limit. Hence, no matter how
high austenizing temperature is, we could not reach the required carbon content for c a�1.
As a result,the distance between adjacent iron atoms in martensite lattice in [001]
crystallographic direction should not increase with rising austenizing temperature, so the
same binds between atoms should occur. Hence, the plasticity should not increase, as well.
One can find other scientific works, where the opposite results were obtained. For
example, Kremnev [24] indicated that quenching from various temperatures of high speed
steel that contains 0.30, 0.42, and 0.43% of carbon in martensite, the ratio c a of
martensite lattice parameters was obtained greater than one, namely, 1.014–1.019 [24]. In
this case, the interpretation of the increasing of steel plastic deflection dependent on
austenizing temperature would be appropriate. Of course, influence of alloying elements on
transformation plasticity needs to be checked, as it was also mentioned in [24].
For the purpose of developing the ideas of the carbon content influence on c a ratio,
the X-ray analysis was performed separately for the stretched and compressed surfaces of
the specimen, also, a and c parameters were determined. The results are presented in
Table 4. X-ray analysis showed that, in all cases, the ratio c a was greater than 1.
Furthermore, the differences of lattice parameters in stretched and compressed surfaces
were revealed (see the last column of Table 4).
The main purpose of this research was to reveal the differences in phase
transformations that occur during air quenching under tension and compression. We had a
possibility to discover an effect of tension and compression on martensitic transformation.
X-ray showed that intensities of martensite of compressed surfaces were of greater
magnitude comparing to the ones of stretched layers (Fig. 6). This allows assumption that
compression stimulates the martensitic transformation more than tension; moreover, this is
in a good agreement with the results obtained by Fischlschweiger et al. [19].
Different influence of compression and tension was also determined by calculating the
quantity of retained austenite in stretched and compressed layers by the XRD patterns of
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5 101
External Stress Effect on Microstructure ...
steel. The calculation was made according to the ASTM E975 standard [25], where the
following equation was used:
V I R I R I R� � � � � � ��
( ) [( ) ( )], (2)
where V� and V� are the volume fraction of �- and �-phase, respectively (here �-phase
means the volume of ferrite and martensite as the martensite peaks cannot be resolved from
the ferrite peaks [26]), I � and I � are the integrated intensity per angular diffraction peak
(hkl) in the �- and �-phase, respectively (they were calculated by taking the production of
the maximum peak height and the peak width at half maximum height [27]), R� and R�
are the parameters depending on interplanar spacing (hkl), the Bragg angle, lattice
parameters of the phases, R is defined as ( )( *)( )1 2 2� i
MFF LPF pe ; the details of the
calculation of R are described in [25–30].
According to the ASTM E975 [25], several methods of the calculation can be used
such as choosing two peaks (�200, �200), three peaks (�200, �200, �220) and four peaks
(�200, �211, �200, �220). The peaks (110) of martensite and the (111) of austenite cannot
be chosen because of overlapping [28]. The peaks (�200, �200) were chosen for calculation
of retained austenite of steel.
All parameters required for calculation of volume of retained austenite is listed in
Tables 5–7. The quantity of retained austenite in stretched and compressed layers is
presented in Table 8. The calculation showed less quantity of austenite in compressed
layers at all austenizing temperatures and confirms that compression stimulates martensitic
T a b l e 4
Determination of Lattice Parameters for Stretched and Compressed Surfaces of Martensite
after Air Quenching from Different Austenizing Temperatures
Austenizing
temperature (�C)
Specimen
surface
a, Å c, Å c a Difference between
stretched and compressed
1050 Stretched 2.8504 2.8784 1.0098
Compressed 2.8506 2.8829 1.0113 More by 0.15%
1070 Stretched 2.8495 2.8808 1.0110 More by 0.08%
Compressed 2.8509 2.8800 1.0102
1090 Stretched 2.8537 2.8839 1.0106 More by 0.25%
Compressed 2.8577 2.8809 1.0081
a b
Fig. 6. X-ray diffraction from stretched and compressed surfaces of specimen austenized at 1070 (a)
and 1090�C (b).
102 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5
R. K. Janutienë and R. K. Dièkuvienë
transformation more than tension. The manufacture declares that after air quenching
from 1050–1090�C temperature, the quantity of retained austenite in Hotvar steel is 5%
[12].
T a b l e 5
Determined Lattice Parameters used for Calculation of R Values
Austenizing
temperature
(�C)
Specimen
surface
2� , deg Lattice parameter (Å)
Austenite Martensite Austenite Martensite
a a c
1050 Stretched 50.48 64.36 3.598 2.8506 2.8829
Compressed 50.66 64.66 3.601 2.8504 2.8784
1070 Stretched 50.82 64.50 3.590 2.8495 2.8808
Compressed 50.42 64.46 3.617 2.8509 2.8800
1090 Stretched 50.54 64.68 3.596 2.8537 2.8839
Compressed 50.72 64.56 3.597 2.8577 2.8809
T a b l e 6
Parameters of (200) Peaks of Austenite
Austenizing
temperature
(�C)
Specimen
surface
2� ,
deg
� ,
deg
f FF * p LPF e M 2 R� I�
1050 Stretched 50.48 25.24 17.47 4885.08 6 8.56 0.94 107.90 100.09
Compressed 50.66 25.33 17.48 5637.10 6 8.47 0.95 124.14 89.60
1070 Stretched 50.82 25.41 17.45 4873.47 6 8.41 0.94 108.50 136.32
Compressed 50.42 25.21 17.52 4912.27 6 8.57 0.95 106.54 87.50
1090 Stretched 50.54 25.27 17.47 4881.21 6 8.44 0.94 107.99 94.50
Compressed 50.72 25.36 17.52 4883.10 6 8.45 0.94 107.96 48.40
T a b l e 7
Parameters of (200) Peaks of Martensite
Austenizing
temperature
(�C)
Specimen
surface
2� ,
deg
� ,
deg
f FF * p LPF e M 2 R� I�
1050 Stretched 64.36 32.18 15.27 932.56 6 4.92 0.92 45.03 744.85
Compressed 64.66 32.33 15.23 927.96 6 4.88 0.92 43.90 660.33
1070 Stretched 64.50 32.25 15.29 934.77 6 4.92 0.92 46.10 715.20
Compressed 64.46 32.23 15.28 933.27 6 4.93 0.92 46.10 771.50
1090 Stretched 64.68 32.34 15.23 927.61 6 4.88 0.91 45.00 436.30
Compressed 64.56 32.28 15.16 919.30 6 4.90 0.92 44.90 738.90
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5 103
External Stress Effect on Microstructure ...
At the air quenching of specimens after heating at austenizing temperature martensitic
transformation did not begin immediately, but after 3–4 minutes when the specimen was
withdrawn from the furnace, i.e., when the temperature dropped to 220–250�C. This was
clearly seen when the specimens started to bend immediately after heating (Fig. 5). When
the specimen started bending already during the originated martensite transformation, i.e.,
at 4th or 5th minute of cooling, they immediately began bending (Fig. 7). However, the
deflections were nearly 30–40% lower than in the first case (see the total deflection at
Fig. 5). Later loading of specimens resulted in a higher loss of plasticity, because at the last
stage of the transformation, the nuclear binds became stronger.
2.3. Self-Deformation of Steel. An interesting phenomenon has been observed, when
steel specimens were unloaded at the beginning of the air quenching, i.e., at 4th or 5th
minutes of the test, and the monitoring of deflection of specimen was continued. It was
noted that curved and unloaded specimens successfully bent in the same direction as they
were bent, but with a less intensity (Fig. 8). In this case, the external stress has a direct
impact on transformation plasticity passing as bending load generated compression and
tension stresses in specimen at the same moment. Compression stimulates martensitic
transformation more than tension as compressed surfaces of specimens’ show higher
diffraction intensities for martensite.
The influence of tension and compression stresses that were generated in the
specimens is different for the martensitic transformation start temperature M s and its
intensity. This phenomenon is related to anisotropy of volume changes that creates
T a b l e 8
Calculated Quantity of Retained Austenite
Austenizing
temperature (�C)
Quantity of austenite in layer of specimen (%)
Stretched Compressed
1050 5.3 4.9
1070 6.5 4.7
1090 5.6 2.7
Fig. 7. Plastic deformation of specimens after bending that began at 4th and 5th minutes of cooling.
Austenizing temperature 1070�C.
104 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5
R. K. Janutienë and R. K. Dièkuvienë
self-deformation of steel parts, so called, self-deformation, even in that way, when the value
of external stresses is � � 0 [11].
The self-deformation of bent, unloaded at the certain moment and exposed to the
following load-free cooling specimens has reached about 28 and 12% of plastic deflection
when specimen was unloaded at 4 or 5 min of total cooling time, respectively.
Altogether, martensitic transformation is very sensitive to stress, thus, deforming the
initial structure – austenite, the martensitic transformation occurs at higher temperatures
than M s [6]. In addition, it was found that at the quenching of steel, the transformations
(decomposition of austenite and self-tempering of martensite) proceeds at different stages
in stretched and compressed sides [31]. Therefore, it must be assumed that the tensile and
compressive stresses exhibit different effects on quenching and tempering transformations.
As the bent and unloaded specimens get curved further at the cooling process, the stretched
volume of specimens is increased. It was determined that the specific volume of austenite is
the smallest, and the one of martensite is the largest [6, 20].
Obviously, that martensitic transformation was inhibited in stretched volume of
specimen, so, unloading was following by increasing of volume as the result of intensive
formation of new martensite crystals. Decomposition of austenite into martensite inside the
compressed part of specimen has started before, so its proceeding has been interrupted.
When transformation performs at different intensities, the volumetric changes can make the
specimen to bend to one or other one. The value of deflection alteration has shown the
quantitative differences in transformations.
C o n c l u s i o n s
1. Microstructure of Hotvar tool steel air quenched from 1050–1090�C temperature is
composed of martensite, carbides, mainly of vanadium and molybdenum, and small content
of retained austenite (3–6%).
2. The transformation plasticity of Hotvar tool steel specimens increases from 8 to
15% when austenizing temperature rises from 1050 to 1090�C, respectively. It is quite
possible that interstitial carbon atoms positioned in [001] crystallographic direction have
the main influence on reducing the atomic binds.
Fig. 8. The phenomenon of self-deformation of Hotvar steel after unloading of specimens
bent and air quenched from 1070�C.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5 105
External Stress Effect on Microstructure ...
3. The air quenched Hotvar steel has slightly tetragonal lattice. The influence of
tension and compression on the c a ratio is different – usually, the stretched surfaces
showed higher magnitudes of c a.
4. The transformations that occur during air quenching are dependent on stress mode.
X-ray analysis revealed that the compressed layers had higher contents of martensite. The
content of retained austenite was determined 2.7–4.9 and 5.3–6.5% in compressed and
stretched layers of specimens depending on austenizing temperature.
5. It was determined that the loss of transformation plasticity is about 30–40% when
the bending was started at temperatures lower than M s .
6. The specimens were self-bending in the same direction as they were bent when the
load was removed at the temperatures below M s . It proves assumption that the stretched
side of specimen had less martensite comparing to the compressed one at the moment of
unloading.
Acknowledgment. This work has been performed in collaboration with Lithuanian
Institute of Energy.
Ð å ç þ ì å
Äîñë³äæóºòüñÿ çì³íà ïëàñòè÷íîñò³ òà ì³êðîñòðóêòóðè æàðîì³öíî¿ ³íñòðóìåíòàëüíî¿
ñòàë³ ïðè ìàðòåíñèòíîìó ïåðåòâîðåíí³. Çðàçêè ï³ääàâàëè àñòåí³òèçàö³¿ òà çàêàëþâàí-
íþ íà ïîâ³òð³. Ó ïðîöåñ³ îõîëîäæåííÿ ¿õ íàâàíòàæóâàëè ñòàòè÷íèì çãèíîì ³ç íîì³-
íàëüíèì íàïðóæåííÿì 100 ÌÏà çà òðüîìà ñõåìàìè: ñòàòè÷íèé çãèí çðàçê³â ï³ñëÿ ¿õ
âèëó÷åííÿ ç ïå÷³, ïðè öüîìó â³äì³÷àëèñü äåôîðìàö³ÿ ïî÷àòêîâîãî àóñòåí³òó ³ ôîðìó-
âàííÿ ìàðòåíñèòó ï³ä 䳺þ íàâàíòàæåííÿ; çãèí ï³ñëÿ ïî÷àòêó ìàðòåíñèòíîãî ïåðå-
òâîðåííÿ ç äåôîðìàö³ºþ ìàðòåíñèòó; ðîçâàíòàæåííÿ ç ìîìåíòó ïî÷àòêó ìàðòåíñèò-
íîãî ïåðåòâîðåííÿ ç ïåðåâàæàþ÷îþ äåôîðìàö³ºþ àóñòåí³òó, ïðè öüîìó âèì³ðþâàëàñü
äåôîðìàö³ÿ ïðè ðîçâàíòàæåíí³. Ïðè îõîëîäæåíí³ çðàçê³â äî ê³ìíàòíî¿ òåìïåðàòóðè
âèì³ðþâàëàñü âåëè÷èíà ¿õ ïëàñòè÷íîãî ïðîãèíó. Ïîêàçàíî, ùî ìàðòåíñèòíå ïåðå-
òâîðåííÿ õàðàêòåðèçóºòüñÿ ñóòòºâèì ï³äâèùåííÿì ïëàñòè÷íîñò³. гçíèé âïëèâ íà
ìàðòåíñèòíå ïåðåòâîðåííÿ ðîçòÿæíèõ ³ ñòèñêàëüíèõ íàïðóæåíü îö³íþâàëè øëÿõîì
âèì³ðþâàííÿ äåôîðìàö³¿ çðàçê³â ïðè ðîçâàíòàæåíí³. ̳êðîñòðóêòóðà ðîçòÿãíóòèõ ³
ñòèñíóòèõ ïîâåðõíîñòåé çðàçê³â äîñë³äæóâàëàñü ìåòîäàìè ðåíòãåí³âñüêî¿ äèôðàêòî-
ìåòð³¿, åëåêòðîííî¿ ì³êðîñêîﳿ ³ åëåêòðîííî-äèñïåðñ³éíî¿ ñïåêòðîñêîﳿ.
1. Z. Gronostajski, M. Kaszuba, M. Hawryluk, and M. Zwierzchowski, “A review of the
degradation mechanisms of the hot forging tools,” Arch. Civil Mech. Eng., 14,
528–539 (2014).
2. A. Medvedeva, J. Bergström, S. Gunnarsson, and J. Anderson, “High-temperature
properties and microstructural stability of hot-work tool steels,” Mater. Sci. Eng. A,
523, 39–46 (2009).
3. E. Brinksmeier, Th. Lübben, U. Fritsching, et al., “Distortion minimization of disks
for gear manufacture,” Int. J. Mach. Tools Manuf., 51, 331–338 (2011).
4. J. R. Cho, W. J. Kang, M. G. Kim, et al., “Distortions induced by heat treatment of
automotive bevel gears,” J. Mater. Process. Technol., 153-154, 476–481 (2004).
5. K. Amini, A. Akhbarizadeh, and S. Javadpour, “Investigating the effect of the quench
environment on the final microstructure and wear behaviour of 1.2080 tool steel after
deep cryogenic heat treatment,” Mater. Design, 45, 316–322 (2013).
6. Yu. M. Lachtin and V. P. Leont’eva, Materials Science. Handbook [in Russian],
Mashinostroenie, Moscow (1980).
106 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5
R. K. Janutienë and R. K. Dièkuvienë
7. R. K. Janutienë, “The investigation of plasticity and microstructure of Hotvar steel
during martensitic transformation,” in: Proc. of Europ. Conf. on Heat Treatment and
21st IFHTSE Congress (Munich, Germany, 2014), pp. 407–414.
8. N. Ausmanas, R. K. Janutienë, and J. Þvinys, “Investigation of plastic properties of
Hotvar hot work tool steel during martensitic transformation,” Mater. Sci.
(Medþiagotyra), 21, No. 1, 18–22 (2015).
9. R. K. Janutienë and J. Þvinys, “Low carbon chromium steel transformation plasticity
during tempering,” Mater. Sci. (Medþiagotyra), 12, No. 2, 101–105 (2006).
10. J. Þvinys and R. K. Janutienë, “Carbon and tempering temperature influence on steel
kinetic plasticity,” Mater. Sci. (Medþiagotyra), 6, No. 3, 172–174 (2000).
11. A. I. Tyshchenko, W. Theisen, A. Oppenkowski, et al., “Low-temperature martensitic
transformation and deep cryogenic treatment of a tool steel,” Mater. Sci. Eng. A, 527,
7027–7039 (2010).
12. Uddeholm Hotvar, http://www.uddeholm.com/files/hotvar-english.pdf.
13. H. Kim, J. Lee, F. Barlat, et al., “Experiment and modeling to investigate the effect of
stress state, strain and temperature on martensitic phase transformation in TRIP-
assisted steel,” Acta Mater., 97, 435–444 (2015).
14. H. K. Yeddu, A. Borgenstam, and J. Ågren, “Stress-assisted martensitic transformations
in steels: A 3-D phase-field study,” Acta Mater., 61, 2595–2606 (2013).
15. W. Kraus and G. Nolze, “POWDER CELL – a program for the representation and
manipulation of crystal structures and calculation of the resulting X-ray powder
patterns,” J. Appl. Cryst., 29, 301–303 (1996).
16. DIFFRACplus. v15.0: EVA (2009) – User’s Manual, Bruker AXS, Karlsruhe,
Germany (2009).
17. M. Maalekian, M. L. Lendinez, E. Kozeschnik, et al., “Effect of hot plastic deformation
of austenite on the transformation characteristics of eutectoid carbon steel under fast
heating and cooling conditions,” Mater. Sci. Eng. A, 454-455, 446–452 (2007).
18. C. Capdevila, F. G. Caballero, and C. Garcia Andres, “Determination of M s
temperature in steels: A Bayesian neural network model,” ISIJ Int., 42, No. 8,
894–902 (2002).
19. M. Fischlschweiger, Th. Antretter and G. Cailletaud, “Transformation hardening and
kinetics for stress assisted and temperature driven martensitic transformation in steels,”
Mech. Res. Commun., 47, 84–88 (2013).
20. I. I. Novikov, Theory of Heat Treatment of Metals [in Russian], Metallurgiya,
Moscow (1978).
21. G. Krauss, “Martensite in steel: strength and structure,” Mater. Sci. Eng. A, 273-275,
40–57 (1999).
22. O. D. Sherby, J. Wadsworth, D. R. Lesuer, and Ch. K. Syn, “The c/a ratio in quenched
Fe–C and Fe–N steels – a heuristic story,” in: Proc. of Conf. THERMEC 2006 (July
4–8, 2006, Vancouver, Canada), https://e-reports-ext.llnl.gov/pdf/329979.pdf.
23. O. D. Sherby, J. Wadsworth, D. R. Lesuer, and Ch. K. Syn, “Revisiting the structure
of martensite in iron-carbon steels,” Mater. Trans., 49, No. 9, 2016–2027 (2008).
24. L. S. Kremnev, “Influence of steel alloying components on martensite tetragonality,”
http://arxiv.org/ftp/ arxiv/papers/1108/1108.3420.pdf.
25. ASTM E975-13. Standard Practice for X-Ray Determination of Retained Austenite in
Steel with Near Random Crystallographic Orientation, ASTM International, West
Conshohocken, PA (2013).
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5 107
External Stress Effect on Microstructure ...
26. T. Gnäupel-Herold and A. Creuziger, “Diffraction study of the retained austenite
content in TRIP steels,” Mater. Sci. Eng. A, 528, 3594–3600 (2011).
27. K. Norrish and R. M. Taylor, “Quantitative analysis by X-Ray diffraction,” Clay
Miner., 5, 98–109 (1962).
28. Y.-Y. Su, L.-H.Chiu, T.-L.Chuang, et al., “Retained austenite amount determination
comparison in JIS SKD11 steel using quantitative metallography and X-Ray
diffraction methods,” Adv. Mater. Res., 482-484, 1165–1168 (2012).
29. M.-X. Zhang, P. M. Kelly, L. K. Bekessy, and J. D. Gates, “Determination of retained
austenite using an X-Ray texture goniometer,” Mater. Character., 45, 39–49 (2000).
30. Ch. Kim, “X-Ray method of measuring retained austenite in heat treated white cast
irons,” J. Heat Treat., 1, No. 2, 43–51 (1979).
31. R. K. Janutienë, J. Þvinys, and A. Baltuðnikas, “Influence of bending stress on
microstructure of tempered high chromium steel,” Mater. Sci. (Medþiagotyra), 10,
No. 3, 201–205 (2004).
Received 23. 12. 2014
108 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2015, ¹ 5
R. K. Janutienë and R. K. Dièkuvienë
|