Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure

We propose a flow stress characteristic of SUS430F steel that takes in account the effects of temperature, strain rate and their deformation history. In the framework of this characteristic, the history effects of strain rate and temperature are estimated through the plastic strain energy stor...

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Datum:	2002
Hauptverfasser:	Shirakashi, Т., Yoshino, М.
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Sprache:	English
Veröffentlicht:	Інститут проблем міцності ім. Г.С. Писаренко НАН України 2002
Schriftenreihe:	Проблемы прочности
Schlagworte:	Научно-технический раздел
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Zitieren:	Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure / T. Shirakashi, M. Yoshino // Проблемы прочности. — 2002. — № 3. — С. 22-29. — Бібліогр.: 6 назв. — англ.

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spelling	irk-123456789-467572013-07-07T12:11:08Z Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure Shirakashi, Т. Yoshino, М. Научно-технический раздел We propose a flow stress characteristic of SUS430F steel that takes in account the effects of temperature, strain rate and their deformation history. In the framework of this characteristic, the history effects of strain rate and temperature are estimated through the plastic strain energy stored. The formulated characteristic (σ) may be shown as the function of temperature (θ), strain rate (ε), and the stored energy (W) or the reference stress (σst). The energy is stored through plastic deformation and released during annealing process. The energy is also re ferred by the yield flow stress (ost), which is measured under the reference condition. The discussion on the characteristic is extended to the material under high temperature (1073-1473 K) with α + γ phase in the given phase ratio. The equilibrium ratio of α or γ phase under given temperature can be estimated on the basis of an equilibrium phase diagram. In order to introduce the flow stress characteristic with phase transformation using the proposed formulation, we also analyze the phase transformation rate from α to α + γ with temperature elevation, and from α to γ + α in cooling process based on “time-temperature- transformation” diagram that includes the quenching process as well. The flow stress characteristic and phase ratio are estimated simultaneously for a hot forging process. Предложена новая характеристика текучести стали SUS430F, учитывающая влияние температуры, скорости деформации и истории деформирования материала. В рамках данного подхода влияние истории деформирования на скорость деформации и температуру оценивается по величине накопленной энергии пластической деформации. Предложенная характеристика текучести (σ) может быть представлена в виде функции температуры (θ), скорости деформации (ε), накопленной энергии (W) или базового напряжения (σst). Энергия накапливается в процессе пластического деформирования, а выделяется при отжиге. Ее величина соотносится с пределом текучести, измеряемым в исходных условиях деформирования. Анализ предложенной характеристики распространен на данный материал для высоких температур (1073...1473 К) при наличии (α + γ)-фазы с определенным соотношением фаз. Равновесное распределение соотношения α- или γ-фазы при любой температуре может быть оценено на основе диаграммы равновесия фаз. Новая характеристика текучести для случая фазового превращения может быть использована по предложенной формулировке с учетом скорости фазового превращения из α- в (α + γ)-фазу при повышении температуры и из α- в (γ + α)-фазу при охлаждении. При этом основой служит диаграмма время-температура-фазовое превращение, учитывающая также процесс закалки. Выполнена оценка предложенной характеристики текучести с учетом соотношения фаз для случая горячей ковки материала. Запропоновано нову характеристику текучості сталі SUS430F, яка враховує вплив температури, швидкості деформування та історії деформування матеріалу. У рамках даного підходу вплив історії деформування на швидкість деформації і температуру оцінюється по величині накопиченої енергії пластичної деформації. Характеристика текучості (σ) може бути представлена у вигляді функції температури (θ), швидкості деформації (ε), накопиченої енергії (W) або базового напруження (σst). Енергія накопичується в процесі пластичного деформування, а виділяється при відпалу. Її величина співвідноситься з границею текучості, що вимірюється в початкових умовах деформування. Аналіз запропонованої характеристики розповсюджується на даний матеріал для високих температур (1073...1473 К), якщо має місце (α + γ )-фаза з визначеним співвідношенням фаз. Рівноважний розподіл співвідношення α- або γ-фази за любої температури можна визначити на основі діаграми рівноваги фаз. Нова характеристика текучості у випадку фазового перетворення може бути використана за запропонованим формулюванням з урахуванням швидкості фазового перетворення з α- у (α + γ )-фазу при підвищенні температури та з α- у (γ + α)-фазу при охолодженні. При цьому за основу береться діаграма час-температура-фазове перетворення, яка враховує також процес загартування. У випадку гарячого кування матеріалу оцінено характеристику текучості з урахуванням співвідношення фаз. 2002 Article Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure / T. Shirakashi, M. Yoshino // Проблемы прочности. — 2002. — № 3. — С. 22-29. — Бібліогр.: 6 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/46757 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 Shirakashi, Т. Yoshino, М. Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure Проблемы прочности
description	We propose a flow stress characteristic of SUS430F steel that takes in account the effects of temperature, strain rate and their deformation history. In the framework of this characteristic, the history effects of strain rate and temperature are estimated through the plastic strain energy stored. The formulated characteristic (σ) may be shown as the function of temperature (θ), strain rate (ε), and the stored energy (W) or the reference stress (σst). The energy is stored through plastic deformation and released during annealing process. The energy is also re ferred by the yield flow stress (ost), which is measured under the reference condition. The discussion on the characteristic is extended to the material under high temperature (1073-1473 K) with α + γ phase in the given phase ratio. The equilibrium ratio of α or γ phase under given temperature can be estimated on the basis of an equilibrium phase diagram. In order to introduce the flow stress characteristic with phase transformation using the proposed formulation, we also analyze the phase transformation rate from α to α + γ with temperature elevation, and from α to γ + α in cooling process based on “time-temperature- transformation” diagram that includes the quenching process as well. The flow stress characteristic and phase ratio are estimated simultaneously for a hot forging process.
format	Article
author	Shirakashi, Т. Yoshino, М.
author_facet	Shirakashi, Т. Yoshino, М.
author_sort	Shirakashi, Т.
title	Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure
title_short	Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure
title_full	Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure
title_fullStr	Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure
title_full_unstemmed	Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure
title_sort	flow characteristics of metal with phase transformation and prediction of its microstructure
publisher	Інститут проблем міцності ім. Г.С. Писаренко НАН України
publishDate	2002
topic_facet	Научно-технический раздел
url	http://dspace.nbuv.gov.ua/handle/123456789/46757
citation_txt	Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure / T. Shirakashi, M. Yoshino // Проблемы прочности. — 2002. — № 3. — С. 22-29. — Бібліогр.: 6 назв. — англ.
series	Проблемы прочности
work_keys_str_mv	AT shirakashit flowcharacteristicsofmetalwithphasetransformationandpredictionofitsmicrostructure AT yoshinom flowcharacteristicsofmetalwithphasetransformationandpredictionofitsmicrostructure
first_indexed	2025-07-04T06:12:49Z
last_indexed	2025-07-04T06:12:49Z
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fulltext	UDC 539.4 Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure T. Shirakashia and M. Yoshinob a Department of Precision Machinery Engineering, Tokyo Denki University, Tokyo, Japan b Department of Mechano-Aerospace Engineering, Tokyo Institute of Technology, Tokyo, Japan УДК 539.4 Реологические свойства металла с фазовым превращением и прогнозированием его микроструктуры Т. Ширакашиа, М. Йошино6 а Отделение точного машиностроения, Токийский университет, Токио, Япония 6 Отделение механико-аэрокосмической техники, Токийский технологический институт, Токио, Япония Предложена новая характеристика текучести стали SUS430F, учитывающая влияние температуры, скорости деформации и истории деформирования материала. В рамках данного подхода влияние истории деформирования на скорость деформации и температуру оценивается по величине накопленной энергии пластической деформации. Предложенная характеристика текучести (а) может быть представлена в виде функции температуры (в), скорости деформации (е), накопленной энергии (W) или базового напряжения (аst). Энергия накапливается в процессе пластического деформирования, а выделяется при от жиге. Ее величина соотносится с пределом текучести, измеряемым в исходных условиях деформирования. Анализ предложенной характеристики распространен на данный мате риал для высоких температур (1073...1473 К) при наличии (а + у)-фазы с определенным соотношением фаз. Равновесное распределение соотношения а- или у-фазы при любой температуре может быть оценено на основе диаграммы равновесия фаз. Новая характе ристика текучести для случая фазового превращения может быть использована по предло женной формулировке с учетом скорости фазового превращения из а- в (а + у)-фазу при повышении температуры и из а- в (у + а)-фазу при охлаждении. При этом основой служит диаграмма время-температура-фазовое превращение, учитывающая также процесс закал ки. Выполнена оценка предложенной характеристики текучести с учетом соотношения фаз для случая горячей ковки материала. Ключевые слова: характеристика текучести, скорость деформации, темпера тура, история деформирования, энергия деформации, фазовое превращение. Introduction. The flow stress characteristic provides a very important information for the analysis of a metal forming process. During this process, a material is deformed under variable strain rate, temperature and their deformation histories, and when temperature is high enough, phase transformation is also to be expected. However, no useful flow stress characteristic equation, which can be applied to a complex deformation process, is available yet. © T. SHIRAKASHI, M. YOSHINO, 2002 22 ISSN 0556-171X. Проблемы прочности, 2002, № 3 Flow Characteristics o f Metal with Phase Transformation Metals deformed under various strain rates show different work hardening rates even if their total equivalent strains are the same [1-5]. This means that the deformation history affects the flow stress characteristic. The same feature is also present in the temperature history, because metallurgical phenomena in hot forming processes (e.g., recovery, phase transformation, or re-crystallization) can be expected. Since conventional flow stress equation is only a function of the equivalent strain, strain rate and temperature, but does not depend on deformation histories of temperature and strain rate, the equation is not used to analyze the usual hot forming process. In this paper, the effects of strain rate and temperature histories on the flow stress are discussed, and a new flow stress equation, which can be applied to any kind of deformation process, is proposed. The equation is expressed to the hot forming process, where phase transformation is expected, and the microstructure (phase ratio) combined with the flow stress is also estimated. Flow Stress Characteristics of Multiphase Metals with Effect of Strain Rate and Temperature Histories without Phase Transformation. In this paper, the flow stress characteristic of SUS430F metal (ferrite stainless steel) is discussed, as an example. Figure 1 shows the equilibrium phase diagram for SUS430F material, which has three regions: ferrite phase (a) for temperatures less than 1073 K, ferrite and austenite phase (a + y) for temperatures from 1073 to 1473 K, and ferrite phase (a) once again for temperatures over 1473 K. Fig. 1. E quilibrium phase d iagram o f Fe and Cr. Fig. 2. C om bined effect o f strain rate and tem perature on the flow stress. If phase transformation is not expected (at temperatures less than 1073 K), the flow stress characteristics with effect of histories of both strain rate and temperature have been proposed as the function of strain rate/temperature at the moment of straining and material state (work hardening rate) shown by Eq. (1) [6], and the material state is estimated by the stored energy (W) in straining through the forming process shown in Fig. 2, a = f (e, T, W), (1) where £, T, and W are strain rate, temperature and stored energy, respectively. ISSN 0556-171X. Проблемы прочности, 2002, N2 3 23 T. Shirakashi and M. Yoshino The energy is stored through plastic deformation and released by annealing process as shown in Eq. (2), dw = ode — kwpdt, (2) where o, e, k, p, w, and t are flow stress, strain, material constants, stored energy, and time, respectively. The energy released during annealing is shown in Fig. 3 and also expressed by Eq. (3) and Fig. 4, dw/dt =—kWn, k = ks exp(—C/T), (3) where ks and C are the material constants. Equation (1) is also applicable to a + y phase of given ratio under high temperatures between 1073 and 1473 K shown in Figs. 4 and 5. The stored energy (W) is uniquely estimated by the reference stress sst, which is measured under the reference condition such as room temperature and high strain rate 1500 s—1 shown in Fig. 5. Fig. 3. B ehavior o f stress-strain relation by annealing (room tem perature). Fig. 4. Stress strain relation o f a + y phase (high tem perature T = 1273 K). Open symbol 0 T = 1273K - £ = 1 Cr'sec"' A T = 1173K Solid symbol □ T = 1073K _ £ = 1 0 2sec-1 nDo a o = ° “ ° DDDn ■ o f . — — “" V AA A A A ^ A A M loooooooooo _L SUS430F i . i . Fig. 5. R elation betw een plastic deform ation energy and reference stress. 0 20 40 60 80 100 Deformotion energy W / MJrrf3 Fig. 6. Plastic deform ation energy and reference energy relation o f a + y under h igh tem perature. 24 ISSN 0556-171X. npo6n.eubi npounocmu, 2002, N2 3 Flow Characteristics o f Metal with Phase Transformation The general flow stress characteristic under given phase ratio is expressed by Fig. 6 and Eq. (4) as follows: a = f (e, T, ast ). (4) Phase Transformation Rate. The flow stress under given condition is easily obtained as shown by Eqs. (1) or (4) when the phase ratio is known. In order to estimate the flow stress, the phase ratio must be obtained. o CL 2000 SUS430F 1500 - « . 10001h a ‘to T ^ i 1 1500.Çü I a w I ■ ■■ ■ AA A Annealed OT = 1073K AT = 1173K Heat treatment time d T = 1273K Open symbol: 600s y t = 1373K Sol i d symboi : 1800s <> T - 1 473K I i I__i I ■ 7 ■ v0 200 400 600 800 1000 D efo rm atio n en ergy W / MJm” 3 o 1000 CL 2 3 ^ 800 ” 5 8 < 600 o 'S 400 's s 200 an ' SUS430F O O C 1 0 1273K - A1123K A1373K - O 1173K ■ 1473K V1223K MAmoxO 1273K 1373K . 1 1223K 1173K □ - & 1 1 1 1 1 . ' 1 1 1 O ' 1.0 0 .8 s o 0.6'Su o 0.4~ -< 0.0 0 500' 1000 1500 ~ 2000 Heat tim e t / s Fig . 7. V a ria tio n o f re fe re n c e stress fo r quenching at various tem peratures. Fig. 8. V ariation o f Aast and austenite ratio annealed under various tem peratures. Fig. 9. R eference stress and stored energy relation (m artensite phase). Fig. 10. Effect o f strain rate on flow stress (a and m artensite phase). Temperature increase up to 1073 K results in a-phase transformation into a + y phase, while in the case where the austenite phase is cooled down quickly enough (quenched), the phase transforms to martensite phase. The ratio of austenite phase is measured by the increase of the reference stress Ao st caused by the transformed martensite as shown in Fig. 7. The maximum austenite ratio is determined by the temperature and annealing time as shown in Fig. 8. Based on latter, the transformation rate from ferrite phase (a) to austenite phase (y) is expressed in Eq. (5) dMAldt = h( Ma max - MA ) f , (5) ISSN 0556-171X. npoôëeMbi npounocmu, 2002, N 3 25 T. Shirakashi and M. Yoshino where MA and MA max are, respectively, the austenite ratio and its maximum value which depends on temperature, while h is the material constant. For the martensite phase, the deformation energy can be measured by the reference stress shown in Fig. 9, and flow stress is also obtained from the reference stress, strain rate, and temperature as shown in Fig. 10. Equation (4) is also valid for the martensite phase. Fig. 11. E ffect o f annealing tim e on residual austenite ( a + y ^ a transform ation). F ig. 12. “ T im e -te m p e ra tu re -tra n sfo rm a tio n ” diagram o f ferritic stainless steel. Under temperatures changing from 1123 K (point Ae) and 573 K (point Ms), the a + y phase transforms to ferrite phase (a). Figure 11 shows variation of the austenite ratio with heat treatment time. This change in ratio is shown as “time -temperature-transformation” diagram in Fig. 12 plotted from Fig. 11. The austenite ratio (Ma ) is represented with the use of nondimensional time % defined from the following relation: % _ tj( t fin ~ tstr ), (6) where tfin and tstr are the final and starting time of the transformation, respectively, and t is the transformation time. MA = ( M A ) str expM% Ht X (7) where X and n are the material constants. When temperature changes with time, % in Eq. (6) is rewritten as follows, % = / dt/( tfin - tstr ). (8) The austenite ratio can be estimated using Eqs. (7) and (8). Prediction of Flow Stress and Microstructure. Since phase ratio during forming process can be estimated through Eqs. (5) to (8), the flow stress characteristic can be also obtained using Eqs. (1) to (4). The average flow stress 26 ISSN 0556-171X. npodxeMbi npounocmu, 2002, № 3 Flow Characteristics o f Metal with Phase Transformation characteristic of mixed phase with given ratio is estimated using mixing rule as follows: a= Mf o f + Ma o a or a = (1- M a IM a 50 )o f + ( M a IM a 50)o a 50. (9) where M f and Ma are the phase ratios of ferrite and austenite, respectively, while af and oa are flow stresses of ferrite and austenite phases, respectively. Now we can estimate changes in the flow stress and microstructure during the forming process. Figure 13 shows the outline of this method. When the stored energy and the phase ratio are known at the moment of forming process, the reference stress o st is obtained. The flow stress is also estimated based on the reference stress, temperature, and strain rate. Fig. 13. O utline o f the estim ation system o f the m aterial structure and flow stress. Figure 14 shows variation of the flow stress and ferrite ratio during the deformation process with the following loading program. SUS430F material is initially annealed under 1273 K for 1800 s, then it is cooled down to 973 K with cooling speed of 2 K/s, after that the material is compressed with a strain rate of 0.001 s-1 at constant temperature of 973 K. Under these conditions, both work hardening and annealing effects are expected, while phase transformation also occurs. In Fig. 14, both solid lines show the estimated results for the flow stress and ferrite ratio, whereas symbols represent the experimental results for the flow stress and ferrite ratio. Good correlation can be seen between the estimated and experimental results. ISSN 0556-171X. npoôëeMbi npounocmu, 2002, N 3 27 T. Shirakashi and M. Yoshino 0.0 0.2 Fig. 14. E stim ated structure and flow stress. It can be concluded that the proposed flow stress characteristic including phase transformation and deformation history is available to estimate flow stress and microstructure. Conclusions. In order to provide numerical simulation of the deformation process under given condition, mechanical properties of material, such as flow stress during deformation, should be obtained. In this paper, the effects of strain, strain rate, temperature, and their histories on flow stress are discussed, and the available flow stress equation is proposed. In the equation proposed, the energy accumulated during the deformation process, which can take account for the effect of strain rate and temperature histories on flow stress, is included combined with strain rate and temperature at the moment of deformation. The energy is also estimated by the reference stress, which is measured under the reference condition such as high strain rate 1500 s 1 and room temperature. The equation is also applied to the condition with phase transformation, when the phase ratio is given during forming process based on both equilibrium phase diagram and “time-temperature-transformation” diagram. Using this approach, both the flow stress and microstructure during forming process can be estimated. The flow stress equation is applied to simulate a forming process. Moreover, changes in microstructure and phase ratio are also simulated using the proposed system. Good agreement between the simulated and experimental results is shown. Р е з ю м е Запропоновано нову характеристику текучості сталі SUS430F, яка враховує вплив температури, швидкості деформування та історії деформування ма теріалу. У рамках даного підходу вплив історії деформування на швидкість 28 ISSN 0556-171X. Проблемы прочности, 2002, № 3 Flow Characteristics o f Metal with Phase Transformation деформації і температуру оцінюється по величині накопиченої енергії плас тичної деформації. Характеристика текучості (а) може бути представлена у вигляді функції температури (б), швидкості деформації (г), накопиченої енергії (W) або базового напруження (аst). Енергія накопичується в процесі пластичного деформування, а виділяється при відпалу. Її величина спів відноситься з границею текучості, що вимірюється в початкових умовах деформування. Аналіз запропонованої характеристики розповсюджується на даний матеріал для високих температур (1073...1473 К), якщо має місце (а + у )-фаза з визначеним співвідношенням фаз. Рівноважний розподіл спів відношення а- або у-фази за любої температури можна визначити на основі діаграми рівноваги фаз. Нова характеристика текучості у випадку фазового перетворення може бути використана за запропонованим формулюванням з урахуванням швидкості фазового перетворення з а- у (а + у )-фазу при підвищенні температури та з а- у (у + а)-фазу при охолодженні. При цьому за основу береться діаграма час-температура-фазове перетворення, яка вра ховує також процес загартування. У випадку гарячого кування матеріалу оцінено характеристику текучості з урахуванням співвідношення фаз. 1. S. S. Hecker and M. G. Stout, Met. Trans., 13A, 619 (1982). 2. K. S. Chan, Trans. ASME, J. Eng. Mater. Technology, No. 110, 1 (1988). 3. K. E. Hughes, K. D. Nair, and C. M. Sellars, Metal Technology, 1, No. 14, 161 (1974). 4. J. Klepaczko and C. Y. Chiem, Mech. Physics Solids, No. 34, 29 (1986). 5. J. Klepaczko, Mechanics for Working Technologist, No. 5, 143 (1987). 6. T. Shirakashi and E. Usui, Int. J. JSPE, 4, No. 4, 91 (1970). R eceived 14. 11. 2001 ISSN 0556-171X. Проблеми прочности, 2002, № 3 29

Flow Characteristics of Metal with Phase Transformation and Prediction of Its Microstructure

Institution

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