THE INFLUENCE MECHANISM OF FERRITE GRAIN SIZE ON STRENGTH STRESS AT THE FATIGUE OF LOW-CARBON STEEL

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 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


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 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.

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 ( 1 − σ ) 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.

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 ( 0 σ ), which is the part of the deformation curve equation [15]: where Kis the constant value, εis true strain, mis power index.As the yield stress ( Т σ ) the value 0 σ obeys to the Hall-Petch dependence [5] (Fig. 1): 0 , MPa σ where i σis the friction stress of ferrite crystalline lattice, value y kdetermines 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 lowcarbon 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 ( 1 − σ ) were obtained.Dependence is shown in Fig. 2. According to external characters the change 1 − σ from ferrite grain size (Fig. 2) is subject to a similar dependence (2): σ 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 equaled: 50 10N/mm y k = (Fig. 1).
Comparative analysis of the obtained characteristics shows that for i σ 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 ' i σ 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 ' i σ can be written as: where ∆ -is the value of solid-solution ferrite strengthening in reverse loading.Another characteristic -' After conversion of ratio (3) similar to that performed for (2) [2], it becomes possible to evaluate the stress ( 1 σ ) required for dislocation displacement from their source to the grain boundaries: 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 2 Then the ratio (5) should be rewritten: from the ferrite grain size is represented in Fig. 4.
Based on this dependence (Fig. 4), one can estimate the value 2 σ using the well-known relation [13]: where α -is a coefficient, which takes the values from 0.1 to 1.0, µ -is the shear modulus, b -is the Burgers vector and ρis the density of mobile dislocations.
2 ,MPa σ Considering the observed components in general terms the value of the fatigue strength of lowcarbon steel may be written as: The obtained values ρ 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 ( ρ ) from the ferrite grain size of low-carbon steel under cyclic loading.Comparative analysis of ρ with similar charac- teristics of investigated steel (Fig. 6) for the conditions of static strain ( 1ρ ) showed that as the size of ferrite grain increases the difference between them decreases.Thus, for the ferrite grain size d = 15.6-16mcm: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 1 − σ transits to the solid solution hardening, that is determined by the concentration of carbon atoms in the ferrite, i.e. by the value ' i σ 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.

Fig. 1 .
Fig. 1.Execution of the relation (2) for the value 0 σ of low-carbon steel

Fig. 2 . 1 −σk
Fig. 2. Dependence 1 − σ on the ferrite grain size of low-carbon steel As a result, the graphical solution of the equation

Fig. 4 .
Fig. 4. Influence of ferrite grain size on the value 2 σ σ and ∆ the values ρ were calculated.

Fig. 5 .
Fig. 5. Influence of ferrite grain size on ρ of low-carbon steel