Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched and Tempered Steel
Flow stress variations of 49MnVS3 non-quenched and tempered steel are studied in isothermal compression tests on a Gleeble-1500D thermal simulated test machine at a deformation temperatures of 950, 1000, 1150, and 1200° C, and strain rates of 0.1, 1, 5, and 10 s⁻¹, with obtaining the strain ha...
Gespeichert in:
| Datum: | 2014 |
|---|---|
| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут проблем міцності ім. Г.С. Писаренко НАН України
2014
|
| Schriftenreihe: | Проблемы прочности |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/112699 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched and Tempered Steel / Y.F. Chen, X.D. Peng, H.B. Xu, H.D. Jiang, G.H. Guan // Проблемы прочности. — 2014. — № 2. — С. 54-65. — Бібліогр.: 14 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-112699 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1126992020-12-20T14:24:18Z Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched and Tempered Steel Chen, Y.F. Peng, X.D. Xu, H.B. Jiang, H.D. Guan, G.H. Научно-технический раздел Flow stress variations of 49MnVS3 non-quenched and tempered steel are studied in isothermal compression tests on a Gleeble-1500D thermal simulated test machine at a deformation temperatures of 950, 1000, 1150, and 1200° C, and strain rates of 0.1, 1, 5, and 10 s⁻¹, with obtaining the strain hardening exponent n and deformation activation energy Q of the alloy. Thus, the constitutive equations and processing maps of compression flow behavior for 49MnVS3 non-quenched and tempered steel at high temperatures are established. It shows that the peak stress is shownto significantly reduced with a decrease in the strain rate and increase in deformation temperature when the alloy deforms at high temperature, and the deformation activation energy is 350.98 kJ/mol. When the true strain of 49MnVS3 non-quenched and microalloyed steel high-temperature deformation is 0.5, the optimum process parameters of the alloy are determined to be 1150–1200° C for the deformation temperature and 2–10 s⁻¹ for the strain rate, based on the criterion that the process parameters of higher power dissipation efficiency values should be chosen in the dynamic recrystallization region as the best processing technology. Изменение напряжения течения незакаленной и закаленной стали 49MnVS3 исследовали путем проведения испытаний на изотермическое сжатие на установке Gleeble-1500D, моделирующей высокотемпературные условия, при температурах деформации 950, 1000, 1150, 1200° C и скоростях деформации 0,1; 1; 5 и 10 c⁻¹ с показателем степени деформационного упрочнения n и значением энергии активации деформации сплава Q. Установлены определяющие уравнения и схемы обработки компрессионного режима течения для незакаленной и закаленной стали 49MnVS3 при высокой температуре. Анализ уравнений показал, что максимальное значение напряжения значительно уменьшается при снижении скорости деформации и повышении температуры деформации, если сплав подвергается деформации при высокой температуре, а значение энергии активации деформации составляет 350,98 кДж/моль. Если значения истинной деформации незакаленной стали 49MnVS3 и высокотемпературной деформации микролегированной стали составляют 0,5, то оптимальные параметры процесса обработки сплава определяются при температуре деформирования 1150…1200° C и скорости деформации 2…10 c⁻¹ на основе критерия, который способствует отбору параметров с более высокой эффективностью рассеивания мощности в области динамической рекристаллизации в качестве оптимальной технологии обработки. Зміну напруження течії незагартованої і загартованої сталі 49MnVS3 досліджували шляхом проведення випробувань на ізотермічний стиск на установці Gleeble-1500D, що моделює високотемпературні умови, за температур деформації 950, 1000, 1150, 1200° C та швидкості деформації 0,1; 1; 5 і 10 c⁻¹ із показником степеня деформаційного зміцнення n і значенням енергії активації деформації сплаву Q. Установлено визначальні рівняння і схеми обробки компресійного режиму течії для незагартованої і загартованої сталі 49MnVS3 за високої температури. Аналіз рівнянь показав, що максимальне значення напруження значно зменшується зі зниженням швидкості деформації і підвищенні температури деформації, якщо сплав зазнає деформації за високої температури, а значення енергії активації деформації дорівнює 350,98 кДж/моль. Якщо значення істинної деформації незагартованої сталі 49MnVS3 і високотемпературної деформації мікролегованої сталі дорівнюють 0,5, то оптимальні параметри процесу обробки сплаву визначаються за температури деформування 1150...1200° C і швидкості деформації 2...10 c⁻¹ на основі критерію, який сприяє відбору параметрів із більш високою ефективністю розсіяння потужності в області динамічної рекристалізації як оптимальної технології обробки. 2014 Article Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched and Tempered Steel / Y.F. Chen, X.D. Peng, H.B. Xu, H.D. Jiang, G.H. Guan // Проблемы прочности. — 2014. — № 2. — С. 54-65. — Бібліогр.: 14 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/112699 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Научно-технический раздел Научно-технический раздел |
| spellingShingle |
Научно-технический раздел Научно-технический раздел Chen, Y.F. Peng, X.D. Xu, H.B. Jiang, H.D. Guan, G.H. Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched and Tempered Steel Проблемы прочности |
| description |
Flow stress variations of 49MnVS3 non-quenched
and tempered steel are studied in isothermal compression
tests on a Gleeble-1500D thermal simulated
test machine at a deformation temperatures
of 950, 1000, 1150, and 1200° C, and strain rates
of 0.1, 1, 5, and 10 s⁻¹, with obtaining the strain
hardening exponent n and deformation activation
energy Q of the alloy. Thus, the constitutive
equations and processing maps of compression
flow behavior for 49MnVS3 non-quenched and
tempered steel at high temperatures are established.
It shows that the peak stress is shownto
significantly reduced with a decrease in the
strain rate and increase in deformation temperature
when the alloy deforms at high temperature,
and the deformation activation energy is
350.98 kJ/mol. When the true strain of
49MnVS3 non-quenched and microalloyed steel
high-temperature deformation is 0.5, the optimum
process parameters of the alloy are determined
to be 1150–1200° C for the deformation
temperature and 2–10 s⁻¹ for the strain rate,
based on the criterion that the process parameters
of higher power dissipation efficiency values
should be chosen in the dynamic
recrystallization region as the best processing
technology. |
| format |
Article |
| author |
Chen, Y.F. Peng, X.D. Xu, H.B. Jiang, H.D. Guan, G.H. |
| author_facet |
Chen, Y.F. Peng, X.D. Xu, H.B. Jiang, H.D. Guan, G.H. |
| author_sort |
Chen, Y.F. |
| title |
Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched and Tempered Steel |
| title_short |
Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched and Tempered Steel |
| title_full |
Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched and Tempered Steel |
| title_fullStr |
Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched and Tempered Steel |
| title_full_unstemmed |
Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched and Tempered Steel |
| title_sort |
constitutive equations and processing maps for 49mnvs3 non-quenched and tempered steel |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2014 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/112699 |
| citation_txt |
Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched and Tempered Steel / Y.F. Chen, X.D. Peng, H.B. Xu, H.D. Jiang, G.H. Guan // Проблемы прочности. — 2014. — № 2. — С. 54-65. — Бібліогр.: 14 назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
AT chenyf constitutiveequationsandprocessingmapsfor49mnvs3nonquenchedandtemperedsteel AT pengxd constitutiveequationsandprocessingmapsfor49mnvs3nonquenchedandtemperedsteel AT xuhb constitutiveequationsandprocessingmapsfor49mnvs3nonquenchedandtemperedsteel AT jianghd constitutiveequationsandprocessingmapsfor49mnvs3nonquenchedandtemperedsteel AT guangh constitutiveequationsandprocessingmapsfor49mnvs3nonquenchedandtemperedsteel |
| first_indexed |
2025-07-08T04:25:34Z |
| last_indexed |
2025-07-08T04:25:34Z |
| _version_ |
1837051396804837376 |
| fulltext |
UDC 539.4
Constitutive Equations and Processing Maps for 49MnVS3 Non-Quenched
and Tempered Steel
Y. F. Chen,
a,b,1
X. D. Peng,
a,2
H. B. Xu,
b,3
H. D. Jiang,
b,4
and G. H. Guan
b5
a School of Materials Science and Engineering, Chongqing University, Chongqing, China
b School of Materials Science and Engineering, Chongqing University of Technology, Chongqing,
China
1 chenyuanfang@cqut.edu.cn
2 pengxiaodong@cqu.edu.cn
3 xuhb@cqut.edu.cn
4 307173732@qq.com
5 Guohua Guan@cqut. edu.cn)
ÓÄÊ 539.4
Îïðåäåëÿþùèå óðàâíåíèÿ è ñõåìà îáðàáîòêè íåçàêàëåííîé è çàêàëåííîé
ñòàëè 49MnVS3
Þ. Ô. ×åí
à,á,1
, Ê. Ä. Ïåíã
à,2
, Õ. Á. Êñó
á,3
, Õ. Ä. Äæàíã
á,4
, Ã. Õ. Ãóàí
á,5
à Ôàêóëüòåò ìàòåðèàëîâåäåíèÿ è ìàøèíîñòðîåíèÿ, ×îíãêèíñêèé óíèâåðñèòåò, ×îíãêèíã, Êèòàé
á Ôàêóëüòåò ìàòåðèàëîâåäåíèÿ è ìàøèíîñòðîåíèÿ, ×îíãêèíñêèé òåõíîëîãè÷åñêèé óíèâåðñèòåò,
×îíãêèíã, Êèòàé
Èçìåíåíèå íàïðÿæåíèÿ òå÷åíèÿ íåçàêàëåííîé è çàêàëåííîé ñòàëè 49MnVS3 èññëåäîâàëè
ïóòåì ïðîâåäåíèÿ èñïûòàíèé íà èçîòåðìè÷åñêîå ñæàòèå íà óñòàíîâêå Gleeble-1500D, ìîäå-
ëèðóþùåé âûñîêîòåìïåðàòóðíûå óñëîâèÿ, ïðè òåìïåðàòóðàõ äåôîðìàöèè 950, 1000, 1150,
1200�C è ñêîðîñòÿõ äåôîðìàöèè 0,1; 1; 5 è 10 c�1 ñ ïîêàçàòåëåì ñòåïåíè äåôîðìàöèîííîãî
óïðî÷íåíèÿ n è çíà÷åíèåì ýíåðãèè àêòèâàöèè äåôîðìàöèè ñïëàâà Q. Óñòàíîâëåíû îïðåäåëÿ-
þùèå óðàâíåíèÿ è ñõåìû îáðàáîòêè êîìïðåññèîííîãî ðåæèìà òå÷åíèÿ äëÿ íåçàêàëåííîé è
çàêàëåííîé ñòàëè 49MnVS3 ïðè âûñîêîé òåìïåðàòóðå. Àíàëèç óðàâíåíèé ïîêàçàë, ÷òî ìàêñè-
ìàëüíîå çíà÷åíèå íàïðÿæåíèÿ çíà÷èòåëüíî óìåíüøàåòñÿ ïðè ñíèæåíèè ñêîðîñòè äåôîðìàöèè
è ïîâûøåíèè òåìïåðàòóðû äåôîðìàöèè, åñëè ñïëàâ ïîäâåðãàåòñÿ äåôîðìàöèè ïðè âûñîêîé
òåìïåðàòóðå, à çíà÷åíèå ýíåðãèè àêòèâàöèè äåôîðìàöèè ñîñòàâëÿåò 350,98 êÄæ/ìîëü. Åñëè
çíà÷åíèÿ èñòèííîé äåôîðìàöèè íåçàêàëåííîé ñòàëè 49MnVS3 è âûñîêîòåìïåðàòóðíîé äåôîð-
ìàöèè ìèêðîëåãèðîâàííîé ñòàëè ñîñòàâëÿþò 0,5, òî îïòèìàëüíûå ïàðàìåòðû ïðîöåññà
îáðàáîòêè ñïëàâà îïðåäåëÿþòñÿ ïðè òåìïåðàòóðå äåôîðìèðîâàíèÿ 1150…1200�C è ñêîðîñòè
äåôîðìàöèè 2…10 c�1 íà îñíîâå êðèòåðèÿ, êîòîðûé ñïîñîáñòâóåò îòáîðó ïàðàìåòðîâ ñ
áîëåå âûñîêîé ýôôåêòèâíîñòüþ ðàññåèâàíèÿ ìîùíîñòè â îáëàñòè äèíàìè÷åñêîé ðåêðèñòàë-
ëèçàöèè â êà÷åñòâå îïòèìàëüíîé òåõíîëîãèè îáðàáîòêè.
Êëþ÷åâûå ñëîâà: íåçàêàëåííàÿ è çàêàëåííàÿ ñòàëü 49MnVS3, íàïðÿæåíèå ïîòîêà,
îïðåäåëÿþùåå óðàâíåíèå, ñõåìà îáðàáîòêè.
Introduction. 49MnVS3 non-quenched and tempered steel is a microalloyed medium-
carbon steel with microstructure of ferrite and pearlite. There is tiny vanadium-containing
precipitated phase in pro-eutectoid ferrite and pearlite. The 49MnVS3 alloy has been
applied to various significant parts in automobiles, engineering machinery and machine
© Y. F. CHEN, X. D. PENG, H. B. XU, H. D. JIANG, G. H. GUAN, 2014
54 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
tools due to its excellent comprehensive performance, such as manufacture of critical
automotive parts of bent axle, knuckle spindle and constant velocity cardan joints at hot
forging state without quenching and tempering treatment. However, the plasticity of
49MnVS3 alloy processed at room temperature is poor. Thereby, the plastic processing is
generally performed at high temperatures, usually employing forging as the processing
technique [1, 2].
The flow stress value of the metal in the plastic processing is not only an important
index to measure plastic processing capacity of material, but is also the basis of equipment
selection and basic premise of design of mold and related devices. The flow stress in
thermal deformation is one of the basic material properties at high temperatures, occupying
extremely important positions in terms of developing a reasonable thermal processing
technology, as well as theoretical research in the plastic deformation of metals [3]. The
constitutive equations of materials describe the quantitative relationships between flow
stress and strain and between strain rate and temperature deformation in material
deformation. Thus, the constitutive equations are the basic data for developing thermal
processing technology and are also instrumental for the finite element method to simulate
manufacturing process [4, 5]. The thermal processing map is superposition of dynamic
material model-based energy consumption diagram and instability diagram, and is capable
of proper description of the relation between structural change and plasticity parameters of
the material deformation at high temperatures, providing the option range for determining
process parameters in the alloy deformation [6, 7].
The 49MnVS3 steel is non-quenched and tempered steel which is widely used for
crankshaft of heavy-duty automobile. The aim of present investigation was to establish the
constitutive equations and processing maps for the thermal deformation behavior of the
alloy by calculating and simulating the stress and strain data of 49MnVS3 non-quenched
and tempered steel obtained at different temperatures and strain rates via thermal simulated
test machine, and supply the theoretical basis for the selection of processing parameters in
alloy deformation.
1. Experimental Materials and Test Methods. The tested material is 49MnVS3
non-quenched and tempered steel under hot-rolled state with composition of Si�0.6%,
0.6%�Mn�1.0%, P�0.035%, 0.045%�S�0.065%, 0.008�V�0.13%, and 0.42%�C
�0.50%.
The thermally compressed specimen taken from the air-cooled hot-rolled bar is
subjected to isothermal compression test on Gleeble1500D thermal simulated test machine.
The specimen for compression test has a size of � �10 12 mm with 0.2 mm-deep grooves
at both ends. In order to reduce influence of friction on the stress state, graphite is casted to
both ends of the specimen, and then graphite sheets are pasted to the ends. The deformation
temperature is set as 950, 1000, 1150, and 1200�C, and strain rate is set as 0.1, 1, 5, and
10 s�1, respectively. At first, the tested specimen is heated to 1250�C with heating rate of
10 �C/s and then incubated for 3 min at 1250�C. Then the specimen is cooled to the
deformation temperature with a rate of 5 �C/s and incubated for 30 s at deformation
temperature, in order to eliminate the temperature gradient. Finally, the isothermal
deformation proceeds at deformation temperature. Argon protection is used to prevent the
surface of the specimen from oxidation. After the deformation is finished, water quenching
starts immediately. The strain rate is kept constant during the compression process. The
temperature is automatically compensated by computer system of Gleeble1500D thermal
simulated test machine and is maintained constant. The data on stress, strain, and
temperature are collected automatically by Gleeble1500D thermal simulated test machine
so as to plot curve of true stress–true strain.
2. Results and Discussion.
2.1. True Stress–True Strain Curve. Figure 1 shows the true stress–true strain curve
of isothermal compression of 49MnVS3 non-quenched and tempered steel. As can be seen
Constitutive Equations and Processing Maps ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 55
from Fig. 1, the process parameters, such as heating temperature, deformation and strain
rate, have a significant impact on the flow stress.
During the thermal compression deformation of 49MnVS3 non-quenched and tempered
steel, the flow stress increase first rapidly and then slower with the increase of strain. Under
higher temperatures and lower strain rates, the stress is gradually decreased after peak value
appears and the peak stress gradually decreases with rise of deformation temperature when
the strain rate is constant. Under lower temperatures and higher strain rates, the stress
shows a slow upward trend instead of the apparent stress peak, and the material deformation
exhibits a significant dynamic softening phenomenon as the temperature rises. In the
experimental temperature range, the flow stress increases with the lift of strain rate in case
of constant temperature.
2.2. Establishment of Constitutive Equation. The strain rate is an important factor
affecting the flow stress. As can be seen from Fig. 1, under the same deformation
temperature, the stress level of the material is increased with the rise of strain rate,
indicating that the material is positively sensitive to strain rate. The reported studies have
demonstrated that there are various expressions to describe relationship between the strain
rate of the flow stress and deformation temperature under the high temperature deformation
[4, 5, 8, 9], such as exponential relationship, power exponent relationship and hyperbolic
sine formula, revealed as follows:
� exp ,� �
�
�
�
�
�A
Q
RT
n
1
1 (1)
Y. F. Chen, X. D. Peng, H. B. Xu, et al.
56 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
a b
c d
Fig. 1. True stress–strain curves of 49MnVS3 steel during hot compression.
� exp( )exp ,� ��
�
�
�
�
�A
Q
RT
2 (2)
� [sinh( )] exp ,� ��
�
�
�
�
�A
Q
RT
n
(3)
where �� is strain rate, A is structural factor, A1 and A2 are constants, n1 and � are
material constants, � is parameter of stress level, � is material flow stress, n is hardening
exponent of stress, Q is deformation activation energy which reflects the ease or difficulty
of material thermal deformation, R is molar gas constant, and T is the absolute
deformation temperature.
Taking the natural logarithm on both sides of formulas (1) and (2), respectively, the
following equations can be obtained:
ln � ln ln ,� � � �A n
Q
RT
1 1 (4)
ln � ln .� �� � �A
Q
RT
2 (5)
From formula (4) and (5) it can be seen that n1
� �
� �
ln �
ln
and �
� �
��
ln �
. Based on the
experimental data of flow stress and strain rate under different compression conditions, the
corresponding relational graphs of ln � ln� �� p and ln �� �� p are plotted as shown in
Fig. 2, wherein the value of � p is set as peak stress.
It can be seen from formulas (4) and (5) that ln �� is linearly related to � p and ln .� p
The values of n1 and � can be calculated as the average slopes through monadic linear
regression with the minimum multiplication, respectively. The slopes of the curves in Fig. 2
mean values of n1 and �, respectively. n1 7 4375 . and � �0 0825 1. MPa are obtained
by calculating and averaging. Then, � � n1 0 011092. .
Taking the natural logarithm on both sides of formula (3) and assuming that
deformation activation energy is irrelevant of temperature, when the temperature is
constant, the following relation can be obtained:
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 57
Constitutive Equations and Processing Maps ...
a b
Fig. 2. Relation between strain rate and peak stress of 49MnVS3 steel.
ln � ln ln[sinh( )].� ��� �
Q
RT
A n (6)
It can be found from formula (6) that ln �� and ln[sinh( )]�� have a linear relationship
whose slope is the stress hardening index n. On the basis of true stress–strain curve of
49MnVS3 non-quenched and tempered steel and a constant strain of 50%, a straight line is
fitted out with ln[sinh( )]�� as x coordinate and ln �� as y coordinate, as shown in Fig. 3.
The stress exponent n 5 44. is acquired by calculating the slope of the curves in Fig. 3
and taking the average. Thus, the strain rate sensitivity index m n 1 0 1838. is obtained.
Under a constant strain rate, assuming that Q remains unchanged within a certain
temperature range, and taking the logarithm on both sides of formula (3), the following
equation can be obtained:
ln[sinh( )] ln
�
.��
�
�
1 1
n A n
Q
RT
(7)
As can be seen from formula (7), ln[sinh( )]�� has a linear relationship with 1 T.
Through fixing the strain as 50% and incorporating the values of peak stress under different
deformation conditions into formula (7), linear regression is conducted to draw the
corresponding ln[sinh( )]�� p T�1 curve, obtaining the relational graph between flow
stress and deformation temperature as shown in Fig. 4.
Figure 4 indicates that for the same rheological rate, a linear relationship exists
between the logarithm of hyperbolic sine of flow stress and the reciprocal of temperature,
suggesting that � and T fairly meet the linear relationship of formula (7), demonstrating
that under high-temperature deformation the relationship between flow stress � of
49MnVS3 non-quenched and tempered steel and deformation temperature T satisfies the
Arrehenius relation, and also stating that the thermal compression plasticity deformation of
49MnVS3 non-quenched and tempered steel is also controlled by the heat-activated
reaction.
Treating the data in Fig. 4 by linear regression analysis, an average slope of 0.77 is
obtained for the four curves, that is
Q
Rn
0 77. . (8)
58 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
Y. F. Chen, X. D. Peng, H. B. Xu, et al.
Fig. 3. Relation between strain rate and flow stress for 49MnVS3 steel.
Through formula (8) the deformation activation energy Q of 49MnVS3 non-quenched
and tempered steel is calculated to be 350.98 kJ/mol.
According to the definition of Zener–Hollomon parameter, formula (9) can be
derived:
Z Q RT � exp[ ( )].� (9)
Taking natural logarithm on both sides of formula (9), the following equation is
established:
ln ln � .Z
Q
RT
�� (10)
By inserting the deformation activation energy Q and deformation conditions into
formula (10), the corresponding values of ln Z under different test conditions can be
calculated (Table 1).
By combining Eqs. (3) and (9), it can be obtained that
Z Q RT A n � exp[ ] [sinh( )] .� �� (11)
Constitutive Equations and Processing Maps ...
Fig. 4. Relation between flow stress and temperature of 49MnVS3 steel.
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 59
T a b l e 1
ln Z Values of 49MnVS3 Non-Quenched and Tempered Steel
under Different Deformation Conditions
Strain rate
�,� s�1
Temperature T , K
1223 1273 1423 1473
0.1 32.2154 30.8597 27.3640 26.3570
1 34.5180 33.1623 29.6666 28.6596
5 36.1275 34.7717 31.2760 30.2690
10 36.8206 35.4648 31.9692 30.9622
Formula (12) is presented as follows by taking natural logarithm on both sides of
formula (11):
ln[sinh( )] ln ln .�� �
1 1
n
Z
n
A (12)
Substituting � into formula (12) with steady-state stress � ss , and utilizing
ln[sinh( )]�� ss and ln Z to the plot, the relationship between flow stress and Z parameter
is acquired, as shown in Fig. 5.
According to the definition of hyperbolic sine function, formula (12) is solved to
obtain
�
�
� �
1
11 2 1 2ln{( ) [( ) ] }./ / /Z A Z An n
(13)
It can be seen from formula (12) that 1 n is the slope of ln[sinh( )] ln�� ss Z� curve,
while ( ) ln1 n A is the intercept. Disposing the data in Fig. 5 with linear regression
analysis, the average slope of the straight line is obtained to be 0.1894, that is 1 n 0.1894,
thus n 5.28, and the average intercept of the straight line is acquired as �6 06. , that is
( ) ln( ) . ,1 1 6 06n A� � then A �7 8711 1013. .
The material parameter values of n, �, Q, and A (Table 2) are incorporated into
Eq. (3) to obtain the Arrehenius equation for non-quenched and tempered 49MnVS3 steel
under thermal compression, as shown in (14):
Y. F. Chen, X. D. Peng, H. B. Xu, et al.
60 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
Fig. 5. Relation between flow stress and parameter Z.
T a b l e 2
Calculation of Parameters in Modeling Process for Flow Stress
of Non-Quenched and Tempered 49MnVS3 Steel
Parameter Value
Hardening exponent of stress n 5.28
Parameter of stress level � 0.011092
Deformation activation energy Q , kJ/mol 350.98
Structure factor A 7 8711 1013. �
� . [sinh( . )] exp.� � �
�
�
�
�
7 8711 10 0 0115
35098013 5 28
RT
�. (14)
The material parameter values of n, �, Q, and A are put into Eq. (13) to obtain the
expression for Z parameter of steady-state flow stress of 49MnVS3 non-quenched and
tempered steel under thermal compression, as seen from formula (15):
�
�
�
�
�
�
�
� �
�
1
0 0115 7 8711 10 7 8711 1013
1 5 28
13.
ln
. .
/ .
Z Z
�
�
�
�
�
� �
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
!
�
2 5 28 1 2
1
/ . /
, (15)
where Z
RT
�
�
�
�� exp .�
350980
Formula (14) is the constitutive equation of 49MnVS3 non-quenched and tempered
steel under high-temperature conditions. Formula (15) is a high-temperature flow stress
model of 49MnVS3 non-quenched and tempered steel.
2.3. Construction and Analysis of Processing Map.
2.3.1. Theory of Processing Map. In the dynamic material model, the thermal
processing material is considered as a nonlinear energy dissipation body. The power P
absorbed by the material of unit volume per unit time in the thermal processing is converted
into two parts, including power G dissipated by plastic deformation and power J
consumed by the structure change in deformation process [10, 11]. The relation between G
and J can be expressed by the following equation:
J
G
m
� �
� �
(log )
(log � )
, (16)
P G J d d � �""�� � � � �
��
� � � .
�
00
(17)
Here m is the sensitivity factor of strain rate. Under certain temperature and strain
conditions, the stress � born by the workpiece during thermal processing and strain rate ��
are related as follows:
� � K m
� . (18)
The above equation is a dynamic constitutive equation.
By substituting formula (18) into (16) and combining formula (17), the following
equation is obtained [11]:
J k d
m
m
m �
�
"�� � � ��
�
� � � �.
�
0
1
(19)
When the material is in the ideal linear dissipative state, m 1, then J reaches the
maximum value, that is J J mmax ( ) . 1 2� The dimensionless parameter J J max that
reflects the power dissipation characteristic of material is defined as #, and is termed as
energy dissipation efficiency factor. Value of # can reflect microstructure deformation
mechanism of material for certain deformation temperature and rate [12], and is expressed
with the strain rate sensitivity factor as follows:
Constitutive Equations and Processing Maps ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 61
#
�
2
1
m
m
. (20)
The instability graph is based on the extremum principle of irreversible thermo-
dynamics. The dimensionless parameter $ �(� ) is used to represent the criterion for
continuous instability under large-scale plastic deformation. Prasad obtained the instability
criterion according to the maximum entropy principle of material [13]:
$ �
�
� �
(� )
ln[ ( )]
ln �
.
�
� %
m m
m
1
0 (21)
2.3.2. Plotting of Processing Map. The values of true stress under strain of 0.5,
different deformation temperatures and various deformation conditions are supposed to be
calculated by fitting curves in Fig. 1 with a cubic polynomial. The fitting function is as
follows:
log log � (log � ) (log � ) .� � � � � � �a b c d2 3
(22)
The curve log log �� �� is shown in Fig. 6. The values of a b c, , , and d in the fitting
function can be determined. It can be obtained from formula (17) that
m b c d � �
� �
� �
� �
(log )
(log � )
log � (log � ) .2 3 2
(23)
There the sensitivity factor m under different conditions can be gained from the values
of strain rate. Moreover, the values of dissipation efficiency factor # at different deformation
temperatures and different strain rates can be obtained through equation (20). Then the
equivalent contour line of power dissipation efficiency factor # is drawn in the T� log ��
plane, that is the power dissipation efficiency map. Substituting formula (23) into (21), the
variable $ �(� ) is expressed as
$ �
�
� �
�
(� )
log
log �
(log � )
( ) ln
�
�
�
�
�
�
�
�
m
m
m
c d
m m
1 2 6
1 10
�m. (24)
By deriving the values of $ �(� ) under different deformation conditions, the rheological
instability graph can be obtained for a certain deformation temperature and a strain rate.
Then the processing map can be obtained by superimposing power dissipation graph with
instability graph, as shown in Fig. 7, wherein the shadow area is the instability region [that
is the zone of $ �(� )%0], and the contours line represents the order of magnitude of the
values of energy dissipation efficiency #.
2.3.3. Analysis of Processing Map. When the plastic deformation of the alloy proceeds
with the corresponding process parameters in the rheological instability region, there will
be a variety of defects. Thus thermal processing should be avoided in this region. As can be
seen from Fig. 7, as the strain is 0.5, three instability zones (that is the three shadow areas)
appear under the thermal deformation of the alloy. Moreover, the safe processing region
comprises three regions, including region I with strain rate of 2–10 s�1 and temperature of
950–1050�C, region II with strain rate of 0.1–0.5 s�1 and temperature of 1075–1175�C, and
region III with strain rate of 2–10 s�1 and temperature of 1150–1200�C. The contour line
in Fig. 7 represents the dissipation efficiency factor. It can be discovered that the value of
Y. F. Chen, X. D. Peng, H. B. Xu, et al.
62 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
energy dissipation efficiency factor varies in different parts, implying that the deformation
temperature and strain rate have impact on the alloy dynamic consumption. The deformation
of alloy in the low-temperature region is inclined to cause the flow strain localization and
thus initiate shear cracking [14].
The higher dissipation efficiency factor does not necessarily mean that the processing
conditions are more suitable for processing. It can be found from Fig. 7 that although the
dominated region of higher values belongs to safe processing area, part of the region is the
instability zone and is unfit for thermal processing. Remarkably, there is a criterion that the
processing parameters of greater power dissipation efficiency values in dynamic
recrystallization region should be chosen as the best processing technology. According to
Fig. 7, as the strain is 0.5, the optimum thermal processing parameters for this alloy lie in
the region of deformation temperature of 1150–1200�C and strain rate of 2–10 s�1.
Constitutive Equations and Processing Maps ...
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 63
Fig. 6. The interpolating curves obtained from stress and strain rate values.
Fig. 7. Processing map of 49MnVS3 steel at 0.5 true strain.
Conclusions. Hot deformation behavior of 49MnVS3 non-quenched and tempered
steel was analyzed by constitutive equations and processing map. The most noteworthy
results are listed below:
1. In the temperature range of 950–1200�C, the high-temperature compression
deformation behavior of 49MnVS3 non-quenched and tempered steel is greatly influenced
by deformation temperature and strain rate. At the same deformation temperature, flow
stress increases with the rising of strain rate. In case of the same strain rate, the flow stress
decreases with increase of deformation temperature.
2. The basic material constants of 49MnVS3 non-quenched and tempered steel under
high-temperature deformation are calculated by analyzing the flow stress, obtaining
structure factor A �7 8711 1013. , the parameter � of stress level of 0.0115, stress
hardening exponent n 5.28, thermal deformation activation energy Q 350.98 kJ/mol,
and a hyperbolic sine relation for the high-temperature flow stress.
3. For 49MnVS3 non-quenched and tempered steel under high-temperature
compression condition, the flow stress relates with temperature and strain rate.
4. When true strain of non-quenched and tempered microalloyed 49MnVS3 steel is
0.5, the optimum parameters’ range of thermal processing for this alloy is determined to be
deformation temperature of 1150–1200�C and strain rate of 2–10 s�1, according to the
guideline that the optimal processing parameters should be selected from the processing
parameters of greater power dissipation efficiency values in dynamic recrystallization
region.
Acknowledgements. This paper is subsidized by the following project funding: The
National Natural Science Fund, Project Number: 51275548, Chongqing Science and
Technology Natural Science Fund Project: cstc2012jjb70002, the project of Chongqing
Scientific and Technology No. 2009AA3012-2 and Chongqing Municipal Education
Commission Applied Basic Research Program of China (KJ120833).
Ð å ç þ ì å
Çì³íó íàïðóæåííÿ òå÷³¿ íåçàãàðòîâàíî¿ ³ çàãàðòîâàíî¿ ñòàë³ 49MnVS3 äîñë³äæóâàëè
øëÿõîì ïðîâåäåííÿ âèïðîáóâàíü íà ³çîòåðì³÷íèé ñòèñê íà óñòàíîâö³ Gleeble-1500D,
ùî ìîäåëþº âèñîêîòåìïåðàòóðí³ óìîâè, çà òåìïåðàòóð äåôîðìàö³¿ 950, 1000, 1150,
1200�C òà øâèäêîñò³ äåôîðìàö³¿ 0,1; 1; 5 ³ 10 c�1 ³ç ïîêàçíèêîì ñòåïåíÿ äåôîð-
ìàö³éíîãî çì³öíåííÿ n ³ çíà÷åííÿì åíåð㳿 àêòèâàö³¿ äåôîðìàö³¿ ñïëàâó Q. Óñòà-
íîâëåíî âèçíà÷àëüí³ ð³âíÿííÿ ³ ñõåìè îáðîáêè êîìïðåñ³éíîãî ðåæèìó òå÷³¿ äëÿ
íåçàãàðòîâàíî¿ ³ çàãàðòîâàíî¿ ñòàë³ 49MnVS3 çà âèñîêî¿ òåìïåðàòóðè. Àíàë³ç ð³âíÿíü
ïîêàçàâ, ùî ìàêñèìàëüíå çíà÷åííÿ íàïðóæåííÿ çíà÷íî çìåíøóºòüñÿ ç³ çíèæåííÿì
øâèäêîñò³ äåôîðìàö³¿ ³ ï³äâèùåíí³ òåìïåðàòóðè äåôîðìàö³¿, ÿêùî ñïëàâ çàçíàº
äåôîðìàö³¿ çà âèñîêî¿ òåìïåðàòóðè, à çíà÷åííÿ åíåð㳿 àêòèâàö³¿ äåôîðìàö³¿ äîð³âíþº
350,98 êÄæ/ìîëü. ßêùî çíà÷åííÿ ³ñòèííî¿ äåôîðìàö³¿ íåçàãàðòîâàíî¿ ñòàë³ 49MnVS3
³ âèñîêîòåìïåðàòóðíî¿ äåôîðìàö³¿ ì³êðîëåãîâàíî¿ ñòàë³ äîð³âíþþòü 0,5, òî îïòè-
ìàëüí³ ïàðàìåòðè ïðîöåñó îáðîáêè ñïëàâó âèçíà÷àþòüñÿ çà òåìïåðàòóðè äåôîðìó-
âàííÿ 1150...1200�C ³ øâèäêîñò³ äåôîðìàö³¿ 2...10 c�1 íà îñíîâ³ êðèòåð³þ, ÿêèé
ñïðèÿº â³äáîðó ïàðàìåòð³â ³ç á³ëüø âèñîêîþ åôåêòèâí³ñòþ ðîçñ³ÿííÿ ïîòóæíîñò³ â
îáëàñò³ äèíàì³÷íî¿ ðåêðèñòàë³çàö³¿ ÿê îïòèìàëüíî¿ òåõíîëî㳿 îáðîáêè.
1. J. Ding, “Present situation of application and development of microalloyed steel for
automobile,” Heat Treat. Metals, 31, No. 9, 46–48 (2006).
2. Zhaojiu Gen, Miao Yong, Tangxin Min, and Chenjian Ye, “Development of a
microalloy steel for vehicle front axle,” Auto. Technol. Mater., 7, 15–17 (2000).
64 ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2
Y. F. Chen, X. D. Peng, H. B. Xu, et al.
3. X. M. Tang, J. Y. Chen, J. G. Zhao, et al., “Development and application of
non-quenched and tempered steels of bending and extending arms,” Heat Treat.
Metals, 1, 45–47 (2001).
4. H. Shi, A. J. McLaren, C. M. Sellars, et al., “Constitutive equations for high
temperature flow stress of aluminum alloys,” Mater. Sci. Technol., 13, 210–216
(1997).
5. A. Laasraoui and J. J. Jonas, “Recrystallization of austenite after deformation at high
temperature and strain rates-analysis and modeling,” Metall. Trans., 22A, 151–160
(1991).
6. A. Laasraoui and J. J. Jonas, “Prediction of steel flow stresses at high temperatures
and strain rates,” Metall. Trans., 22A, No. 7, 1545–1558 (1991).
7. C. M. Sellars, “Computer modelling of hot-working processes,” Mater. Sci. Technol.,
1, No. 4, 325–332 (1985).
8. C. M. Sellars and W. J. McTegart, “On the mechanism of hot deformation,” Acta
Metall., 14, No. 9, 1136–1138 (1966).
9. C. M. Sellars, “Modeling microstructural development during hot rolling,” Mater. Sci.
Technol., 6, 1072–1081 (1990).
10. Z. M. Zhang, B. C. Yang, K. L. Liu, et al., “Numerical simulation of alloy ZTC4 can
isothermal extrusion,” J. Plasticity Eng., 11, No. 3, 31–34 (2004).
11. Y. V. R. K. Prasad and S. Sasidhara, Hot Working Guide: A Compendium of
Processing Maps, ASM International, Materials Park, OH (1997).
12. B. Bozzini and E. Cerri, “Numerical reliability of hot working processing maps,”
Mater. Sci. Eng. A, 328, No. 1-2, 344–347 (2002).
13. Y. V. R. K. Prasad and T. Seshacharyulu, “Modelling of hot deformation for micro-
structure control,” Int. Mater. Rev., 43, No. 6, 243–258 (1998).
14. R. Raj, “Development of a processing map for use in warm-forming and hot-forming
processing,” Metall. Trans., 12, No. 6, 1089–1097 (1981).
Received 22. 11. 2013
ISSN 0556-171X. Ïðîáëåìû ïðî÷íîñòè, 2014, ¹ 2 65
Constitutive Equations and Processing Maps ...
|