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МАТЕР1АЗНАВСТВО
UDC 669.141.24:539.431.015
I. A. VAKULENKO1*, S. V. PROYDAK1
1 Dep. «Materials Technology», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (056) 373 15 56, e-mail dnyzt_texmat@ukr.net 1Dep. «Materials Technology», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, Ukraine, 49010, tel. +38 (056) 373 15 56, e-mail dnyzt_texmat@ukr.net
THE INFLUENCE MECHANISM OF FERRITE GRAIN SIZE ON STRENGTH STRESS AT THE FATIGUE OF LOW-CARBON STEEL
Purpose. Explanation of the influence mechanism of ferrite grain size on the fatigue strength of low-carbon steel. Methodology. Material for research is the low-carbon steel with 0.1% of carbon contnent. The different size of ferrite grain was obtained due to varying the degree of cold plastic deformation and temperature of annealing. The estimation of grain size was conducted using methodologies of quantitative metallography. The microstructure of metal was investigated under a light microscope with increase up to 1 500 times. As a fatigue response the fatigue strength of metal - a maximal value of load amplitude with endless endurance limit of specimen was used. Fatigue tests were carried out using the test machine «Saturn-10», at the symmetric cycle of alternating bend loading. Findings. On the basis of research the dependence for fatigue strength of low-carbon steel, which is based on an additive contribution from hardening of solid solution by the atoms of carbon, boundary of the ferrite grain and amount of mobile dislocations was obtained. It was established that as the grainy structure of low-carbon steel enlarges, the influence of grain size on the fatigue strength level is reduced. For the sizes of grains more than 100 mcm, basic influence on fatigue strength begins to pass to the solid solution hardening, which is determined by the state of solid solution of introduction. Originality. From the analysis of the obtained dependences it ensues that with the increase of ferrite grain size the required amount of mobile dislocations for maintenance of conditions for spreading plastic deformation becomes less dependent from the scheme of metal loading. Practical value. The obtained results present certain practical interest when developing of recommendations, directed on the increase of resource of products work from low-carbon steels in the conditions of cyclic loading. Estimation of separate contribution of the studied processes of structural changes with fatigue load allows one to choose a rational solution - to use the hardening effect from the ferrite alloying or to change the grain size of ferrite. Keywords: ferrite; grain size; fatigue strength; solid solution; carbon
Introduction
In the process of loading the ferrite grain size determines most of the properties of single-phase alloys and carbon steels [1]. Gradual accumulation of defects in crystalline structure and their localization during cyclic loading can lead (in certain microvolumes of metallic material) to the forming of the breakdown sites, as in the case of unidirectional static deformation.
Taking into account the heterogeneity of strain distribution, especially in the initial stages of plastic flow of unidirectional loading in the metal volumes near to the grain boundaries will increasingly occur the processes of accumulation of crystal structure defects.
Under cyclic loading the magnitude of cycle deformation, the temperature [2] and the dislocations ability to nonconservative movement [3] will to some extent determine the processes, which cause
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the metal hardening. In this case, the rate of dislocations accumulation and the beginning of formation of substructure units, such as fragment walls and dislocation cellular structure in some ferrites, which are favorably oriented with respect to the actual stresses, can be considered as the beginning of the incubation period of the metal destruction process.
One of the known mechanisms explaining the process of microcrack initiation [10] is based on the initiation of breakdown site resulting from the step forming in the place of slip band emergence on the sample surface under the cyclic loading. Subsequent recombination of dislocations leads to the irreversible deformations in the specified place on the metal surface. Therefore, it is safe to assume that the gradual accumulation to the maximum permissible concentration of structural defects near the steps, is one of the main reasons leading to the microcracks initiation and the subsequent loading conditions determine the rate of its growth.
There is a sufficient quantity of the experimental results, which indicate the dependence of fatigue processes development in the metal materials from the grain size. This situation is often caused by the lack of accounting of structural change processes in the metal internal structure under cyclic loading, as compared to the conditions of static unidirectional deformation.
Purpose
The work purpose is to explain the influence mechanism of ferrite grain size on the fatigue strength of low-carbon steel.
Findings
Behavior analysis of the single-phase alloys under loading showed that only in some cases the polycrystalline strength according to absolute values is approaching to the quarter of the theoretical strength of a perfect crystal [1, 10]. On the other hand, the strength property level of metal in the grain boundaries reaches the values of the same order with the metal within grains [14]. On the basis of above mentioned, the origin and distribution of dislocations according to crystallographic slip systems, could be the determining factor during metal loading in the region of small plastic deformations. Moreover, the internal structure of the grain boundary itself and the inevitable presence of impurity atoms of implementation can make a definite contribution to the changing nature of the grain size influence.
Conditions of unidirectional static loading the reduction of the grain size of the low-carbon steel is accompanied by the increase in resistance value of microplastic deformation (c0), which is the part of the deformation curve equation [15]:
c = c0 + Ksm, (1)
where K - is the constant value, s - is true strain, m - is power index. As the yield stress (aT) the value c0 obeys to the Hall-Petch dependence [5] (Fig. 1):
_ 1
a0 =°, + ky d 2, (2)
Methodology
Material for research was the low-carbon steel with 0.1% of carbon content. The different size of ferrite grain was obtained due to varying the degree of cold plastic deformation and temperature of annealing. The estimation of grain size was conducted using methodologies of quantitative metallography [4]. The microstructure of metal was investigated under a light microscope with increase up to 1500 times. As a fatigue response the maximum value of load amplitude (c_j) when reaching the conditions of unlimited specimen endurance was used. Fatigue tests were carried out using the test machine «Saturn-10», at the symmetric cycle of alternating bend loading.
ст0, MPa
d 2,
mm
Fig. 1. Execution of the relation (2) for the value ct„ of low-carbon steel
2
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where o - is the friction stress of ferrite crystalline lattice, value ky - determines the influence of
grain boundaries, d - is the ferrite grain size.
Taking into account that in the initial stages of cyclic loading of dislocation displacement one is limited by the volume of ferrite grain of low-carbon steel, the state of solid solution should have some influence (if not the main one) on the process of microcracks initiation. On the other hand, the end of the incubation stage of microcrack growth is most often associated with the intersection of the first angular grain boundary [3, 10]. On the basis of the above mentioned, starting from the specified moment (the accelerated growth stage) the process of fatigue crack propagation becomes dependent on the presence of the ferrite grain boundaries [17].
As a result of cyclic loading of the investigated steel with different ferrite grain size the fatigue strength values () were obtained. Dependence 1
o_ = f (d 2) is shown in Fig. 2.
According to external characters the change o_1 from ferrite grain size (Fig. 2) is subject to a similar dependence (2):
c-i = С + ky d 2.
(3)
where oi and ky are the constants, similar to the corresponding characteristics of equation (2).
с
MPa
d
mm
Fig. 2. Dependence ct_ on the ferrite grain size of low-carbon steel
As a result, the graphical solution of the equa-
_ i
tion ct_j = f (d 2 ) the values ai and k were ob-
tained, which are respectively equal to 90MPa and 12.5N/mm3/2. Taking into account that the stress
oi naturally should characterize the resistance to dislocation displacement within the ferrite grain (friction stress of the crystalline lattice), the level 90MPa is much higher than the known values of the specified characteristics. Indeed, according to numerous studies [1, 10, 12, 16], the friction stress of the iron crystalline lattice is 8-17MPa, and taking into account that the ferrite is a solid interstitial solution the body-centered cubic lattice of the iron contains about 12MPa of carbon atoms [5].
For the conditions of unidirectional loading of investigated steel values of the equation constants (2) were determined. They are correspondingly
3
equaled: = 50MPa and ky = 10N/mm2 (Fig. 1).
Comparative analysis of the obtained characteristics shows that for oi the difference is 38MPa, which is explained by the hardening effects because of the presence of a certain concentration of carbon atoms in the ferrite lattice [1, 2].
Under cyclic loading, the specified difference is equaled to 78MPa (90MPa-12MPa). Thus, the observed increase of the magnitude during fatigue can be first of all associated with more efficient blocking of reciprocating dislocations by carbon atoms. Confirmation of this phenomenon may be possibility increase of multiple dislocation slip on different crystallographic systems. For the crystalline lattice of body-centered cubic type the dislocation displacement is possible according to three crystallographic slip systems {110}, {112) and {123}, at <111> [9]. On the basis of the above mentioned it is safe to assume that under cyclic loading of low carbon steel, the reversible dislocation displacement is accompanied not only by annihilation, but also by the transition into the other slip systems [1, 13]. In this case, the possibility of dislocations blocking by carbon atoms should increase. Consequently, the value o] can be written as:
с =с
(4)
where A - is the value of solid-solution ferrite strengthening in reverse loading.
Another characteristic - ky to a lesser extent differs from the value ky, which once again points to the role of influence of the ferrite grain bounda-
© I. A. Vakulenko, S. V. Proydak, 2014
2
2
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ries on the development of fatigue fracture of low-carbon steel.
After conversion of ratio (3) similar to that performed for (2) [2], it becomes possible to evaluate the stress (Cj) required for dislocation displacement from their source to the grain boundaries:
c, =
2yfl'
(5)
k„
42d
(6)
During the formal application of the values c calculated according to (6), for the same values d against the corresponding values c_ it is found out an unambiguous relationship with a sufficiently high correlation coefficient (Fig. 3).
Analysis of absolute values shows that the value Cj several times less than c_ . At the same time, the rougher grain structure of the metal, the greater the difference between these characteristics.
Considering the total contribution to the value c_j from ci, A and c , the difference should be atributed to the metal hardening from the
cl5 MPa
c_l5 MPa
interaction of mobile dislocations with the blocked by carbon atoms dislocations ( c2). Changing c2 from the ferrite grain size is represented in Fig. 4.
Based on this dependence (Fig. 4), one can estimate the value c2 using the well-known relation
[13]:
c2 = а ц
N/p,
(7)
where l - is the distance of dislocations source from the ferrite grain boundaries. Considering that l in general can take values from 0 (the source of dislocations are the angular ferrite grain boundaries [1, 2]) to l = d (intragranular source location), we
take the average value l = d .
Then the ratio (5) should be rewritten:
where a - is a coefficient, which takes the values from 0.1 to 1.0, ^ - is the shear modulus, b - is the Burgers vector and p - is the density of mobile dislocations.
c2,MPa
d
mm
Fig. 4. Influence of ferrite grain size on the value c2
Considering the observed components in general terms the value of the fatigue strength of low-carbon steel may be written as:
k„
-J2d
+ ац ô^/p
(8)
After substitution into (8) of a = 0.6 (the average value of interval 0.1-1.0), ^ = 8.2-104MPa (for
carbon steel), b = 2.48 -10_7mm (for ferrite), the experimental values c_1 , ci and A the values p were calculated.
The obtained values p represent the density of mobile dislocations, which is necessary for maintaining the conditions of plastic deformation propagation for a loading cycle. Fig. 5 shows the dependence of this characteristic ( p ) from the ferrite grain size of low-carbon steel under cyclic loading.
Fig. 3. Mutual change of c, and c_,
C_1 = c
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р, x105mm 2
0 2 4 б 8 10
_1 _i d 2,mm 2
Fig. 5. Influence of ferrite grain size on p of low-carbon steel
Comparative analysis of p with similar characteristics of investigated steel (Fig. 6) for the conditions of static strain ( p1 ) showed that as the size of ferrite grain increases the difference between them decreases. Thus, for the ferrite grain size d =
15.6-16mcm: p = 7.5-106mm_2, p1 = 107mm_2; for d = 22-24mcm: p = 2.9 -106mm_2, p1 = 4-106mm_2 and for d = 115-120mcm: p = 4.4 • 105mm_2, p1 = 4.2 -105mm_2.
p1, x 106mm_2
55 30 25 20 15 10 5 0
0 5 10 15
_ 1
d 2, mm _2
Fig. 6. Influence of ferrite grain size on pj of low-carbon steel
The obtained results show that with increase of ferrite grain size the required amount of mobile dislocations, to maintain the conditions of propagation of plastic deformation becomes less dependent
on metal loading scheme. Analysis of the equation is the confirmation of the above mentioned (8). Thus, as the grain structure of the low carbon steel coarsens the influence of grain size on the level of the fatigue strength decreases. For the grain sizes greater than 100 mcm, the main influence on the values o_1 transits to the solid solution hardening, that is determined by the concentration of carbon atoms in the ferrite, i.e. by the value oi from the ratio (4).
Originality and practical value
The analysis of obtained dependencies shows that as the ferrite grain size increases the required amount of mobile dislocations to maintain the conditions of plastic deformation propagation becomes less dependent on the metal loading scheme. The obtained results are of particular interest in the development of practical recommendations aimed at improving the operation life of the products of low-carbon steels under cyclic loading. Evaluation of separate contribution of structural components at certain stages of fatigue loading development, allows one to choose a rational solution - to use the hardening effect of changes in the state of solid solution of low-carbon steel or vary ferrite grain size.
Conclusions
1. The analysis shows that the level of fatigue strength of low-carbon steel is determined by the additive contribution from the condition of solid solution, ferrite grain size and hardening, caused by the interaction of blocked and mobile dislocations.
2. As the ferrite grain size increases the required amount of mobile dislocations to maintain the conditions of plastic deformation propagation becomes less dependent on the metal loading scheme.
3. Coarsening of the ferrite structure is accompanied by decrease in the contribution of grain boundaries and increase of the role of solid solution hardening in improving fatigue strength.
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И. А. ВАКУЛЕНКО1*, С. В. ПРОЙДАК1
1 Каф. «Технология материалов», Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (056) 373 15 56, эл. почта dnyzt_texmat@ukr.net
'Каф. «Технология материалов», Днепропетровский национальный университет железнодорожного транспорта имени академика В. Лазаряна, ул. Лазаряна, 2, Днепропетровск, Украина, 49010, тел. +38 (056) 373 15 56, эл. почта dnyzt_texmat@ukr.net
МЕХАНИЗМ ВЛИЯНИЯ РАЗМЕРА ЗЕРНА ФЕРРИТА НА УСТАЛОСТНУЮ ПРОЧНОСТЬ НИЗКОУГЛЕРОДИСТОЙ СТАЛИ
Цель. Объяснение механизма влияния размера зерна феррита на усталостную прочность низкоуглеродистой стали. Методика. Материалом для исследования служила низкоуглеродистая сталь с содержанием углерода 0,1 %. Различный размер зерна феррита получали за счет варьирования степенью холодной пластической деформации и температурой отжига. Оценку величины зерна проводили, используя методики количественной металлографии. Микроструктуру металла исследовали под световым микроскопом при увеличениях до 1 500 раз. В качестве характеристики усталости использовали усталостную прочность металла -
Дншропетр. нац. ун-ту зал1зн. трансп. - Д., 2008. - Вип. 21. - С. 266-268.
9. Коттрелл, А. Х. Дислокации и пластическое течение в кристаллах / А. Х. Коттрелл. - М. : Металлургиздат, 1958. - 255 с.
10. Нотт, Дж. Ф. Основы механики разрушения / Дж. Ф Нотт. - М. : Металлургия, 1978. - 256 с.
11. Atkinson, J. D. The Work - hardening of Copper -Silica: IV. The Bauschinger Effect and Plastic Relaxation / J. D. Atkinson, L. M. Brown, W. B. Stobs // Philosophical Magazine. - 1974. -Vol. 30, № 6. - P. 1247-1280.
12. Crist, B. W. Comparison of the Hall - Petch parameters of Zone - refined Iron Determined by the Grain Size and Extrapolation Methods / B. W. Crist, C. V. Smith // Acta Metallurgica. -1967. - Vol. 15, № 5. - P. 809-816.
13. Garofalo, F. Factors Affecting the Propagation of a Luders Band and the Lower Yield and Flow Stressers / F. Garofalo // Metallurgical Transactions. - 1971. - Vol. 2, № 8. - P. 2315-2317.
14. Gleiter, H. High - Grain Boundaries / H. Gleiter, B. Chalmers // Progress in Materials Science. -1972. - Vol. 16. - 375 p.
15. Hollomon, John H. Tensile Deformation / John H. Hollomon // AIME. -1945. - Vol. 162. -P. 268-290.
16. Holzman, M. Determination of Friction stress in BCC polycristalls / M. Holzman, J. Man // J. of the Iron and Steel Inst. - 1966. - Vol. 204, № 3. - P. 230-234.
17. Vakulenko, I. A Mechanism of the Effect of the Ferrite Grain Size on the Fatigue Strength of a Low - Carbon Steel / I. A. Vakulenko, O. N. Perkov, V. G. Razdobreev // Russian Metallurgy. - 2008. - № 3. - P. 225-228.
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максимальное значение амплитуды нагружения при бесконечной выносливости образца. Испытания на усталость осуществляли на испытательной машине «Сатурн-10» при симметричном цикле знакопеременного нагружения изгибом. Результаты. На основе проведенных исследований получена зависимость для усталостной прочности низкоуглеродистой стали, которая основана на аддитивном вкладе от упрочнения твердого раствора атомами углерода, границ зерна феррита и количества подвижных дислокаций. В работе установлено, что по мере укрупнения зернистой структуры низкоуглеродистой стали влияние размера зерна на уровень усталостной прочности снижается. При размерах зерен более 100 мкм основное влияние на усталостную прочность начинает переходить к твердо растворному упрочнению, определяемому состоянием твердого раствора внедрения. Научная новизна. Из анализа полученных зависимостей следует, что с ростом размера зерна феррита требуемое количество подвижных дислокаций для поддержания условий распространения пластической деформации становится в меньшей степени зависимым от схемы нагружения металла. Практическая значимость. Полученные результаты представляют практический интерес при разработке рекомендаций, направленных на повышение ресурса работы изделий с низкоуглеродистой стали в условиях циклического нагружения. Оценка раздельного вклада от рассмотренных процессов структурных изменений на определенных этапах развития усталостного нагружения позволит выбрать оптимальное решение - использовать эффект упрочнения от легирования феррита либо уменьшить размер его зерна.
Ключевые слова: феррит; размер зерна; усталостная прочность; твердый раствор; углерод
I. О. ВАКУЛЕНКО1*, С. В. ПРОЙДАК1
1 Каф. «Технолопя матерiалiв», Дтпропетровський нацюнальний ушверситет затзничного транспорту iменi академжа В. Лазаряна, вул. Лазаряна, 2, Дншропетровськ, Укра!на, 49010, тел. +38 (056) 373 15 56, ел. пошта dnyzt_texmat@ukr.net
'Каф. «Технолог1я матерiалiв», Дтпропетровський нацюнальний утверситет залiзничного транспорту iменi академжа В. Лазаряна, вул. Лазаряна, 2, Дншропетровськ, Украша, 49010, тел. +38 (056) 373 15 56, ел. пошта dnyzt_texmat@ukr.net
МЕХАН1ЗМ ВПЛИВУ РОЗМ1РУ ЗЕРНА ФЕРИТУ НА МЩШСТЬ ПРИ ВТОМ1 НИЗЬКОВУГЛЕЦЕВО1 СТАЛ1
Мета. Пояснения мехашзму впливу розмiру зерна фериту на мщшсть при втомi низько вуглецево! сталг Методика. Матерiалом для дослщження слугувала низько вуглецева сталь iз вмютом вуглецю 0,1 %. Рiзний розмiр зерна фериту отримували за рахунок варшвання ступенем холодно! пластично! деформацп й температурою ввдпалу. Оцшку величини зерна проводили, використовуючи методики шльшсно! металографп. Мшроструктуру металу дослщжували тд свiтловим мiкроскопом при збшьшеннях до 1 500 разiв. В якостi характеристики втоми використовували межу мiцностi при втомi металу - максимальне значення амплiтуди навантаження при необмеженiй витривалостi зразку. Випробування на втому здiйснювали на випробуваль-нiй машинi «Сатурн-10» при симетричному циклi знакозмiнного навантаження вигином. Результати. На основi проведених дослiджень отримана залежиiсть для межi мiцностi при втомi низьковуглецево! сталi, яка заснована на адитивному вкладi вiд змщнення твердого розчину атомами вуглецю, меж зерна фериту й кшь-косл рухливих дислокацiй. У роботi встановлено, що в мiру укрупнення зернисто! структури низьковуглецево! сталi вплив розмiру зерна на рiвень меж1 мiцностi при втомi знижуеться. При розмiрi зерен бiльше 100 мкм основний вплив на мщшсть при втомi починае переходити до твердо розчинного змщнення, що визначаеться станом твердого розчину впровадження. Наукова новизна. З аналiзу отриманих залежностей випливае, що зi збiльшенням розмiру зерна фериту необхвдна к1льк1сть рухливих дислокацш для пвдтримки умов поширення пластично! деформацп стае меншою мiрою залежною ввд схеми навантаження металу. Практична значимкть. Отриманi результати становлять певний практичний iнтерес при розробцi рекоме-ндацiй, як1 спрямованi на пвдвищення ресурсу роботи виробiв iз низьковуглецевих сталей в умовах циктч-ного навантаження. Оцшка роздiльного внеску вщ розглянутих процесiв структурних змiн на певних етапах розвитку втомного навантаження дозволить обрати оптимальне ршення - використовувати ефект змщнення вщ легування фериту або зменшити розмiр його зерна.
Ключовi слова: ферит; розмiр зерна; мщшсть при втомц твердий розчин; вуглець
Наука та прогрес транспорту. Вкник Дншропетровського нацюнального ушверситету залiзничного транспорту, 2014, № 1 (49)
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Associate Professor L. I. Kotova, Ph.D. (Tech); Associate Professor O. A. Chaykovskiy, Ph.D. (Tech)
recommended this article to be published
Received: Nov. 11, 2013
Accepted: Jan. 14, 2014
