Influence of deformation degree on grains size and borders between them in metal alloys during cold rolling of sheets

The internal structure of metal products was investigated and it was identified that it affects quality and workability of equipment parts. Changes that occur in metal products structure during cold treatment by pressure, which lead to changes in physical and mechanical properties of products, have been analyzed. It was established that grains and borders between them, which determine internal structure of metal products, change their shape and size during cold rolling, depending on percentage reduction value. It is offered to consider grain borders as amorphous layer. Methodology has been developed to study influence of deformation degree during cold rolling to grain size of metal internal structure and intergranular layer volume. Intergranular surface area, its volume and part of surface volume from metal volume were determined. Parameters of internal structure of low-carbon steel were calculated depending on reduction value during cold rolling. According to study results, interconnection between grains size and deformation degree was established; and percentage reduction influence to grain size and borders between them was determined, obtaining a minimum standard grain size with percentage reduction of over 80 %; yield strength and its growth for metal alloy during cold rolling are established, which allows controlling the strength of steel by adjusting the grain size and their junction surface. It is shown that with an increase in deformation degree, yield strength of metal product material increases in hyperbolic dependence, and fraction of amorphous layer and strength properties of low-carbon steel change almost equally in exponential functions. It is revealed that during cold rolling, it is possible to control internal properties of obtained product by adjusting reduction value.


Introduction
During the process of mechanisms and machines structures manufacture, requirements for their strength, quality and reliability are constantly increasing.Detail properties are determined by internal structure of metal, which was used for manufacturing.In order to improve metal products quality, it is necessary to find opportunity to control strength of metal and alloys during their manufacture, due to improving internal structure of metal products.
Metals and alloys have certain properties that are divided into physical (specific weight, melting point, heat capacity, electrical conductivity, linear expansion coefficient, magnetic properties); mechanical (strength, hardness, resistance to impact, resistance to fatigue), which determine metals workability; technological (forging property, flowability, weldability, machining by cutting), which determine ability of metals and alloys to undergo different methods of hot and 1254 (2023) 012006 IOP Publishing doi:10.1088/1755-1315/1254/1/012006 2 cold processing; chemical (corrosion resistance, high-temperature resistance, high-temperature strength), which determine stability of metals in aggressive environments at normal and high temperatures.All these properties depend on nature of metal and its internal structure, which consists of grains of various sizes.The finer grains in internal structure of metal are, the higher its strength and plastic properties.Therefore, investigation of metal structure change under influence of external factors is a relevant problem, and solution of this problem will enable to manage steel strength during rolling by means of identification of rational treatment modes and will improve metal products quality.

Analysis of literature data and problem definition
Within the framework of the program of stable development of metallurgy, the team of scientists of the Department of Metallurgy of Ferrous Metals and Foundry Production of the Kryvyi Rih National University is solving the following important tasks: improving the technology of foundry and rolling production and improving the quality of manufactured products [1,2].
For correct choice of material for mechanisms structures manufacture with further adding mechanical and other properties that affect reliability and workability of machines, it's necessary to know internal structure of material at micro level.Metals and alloys consist of large number of small crystals of irregular shape -grains and borders between them [3,4].Borders between grains form inner surface of metal.This surface area is area of intergranular borders in units of volume or mass of metal [5][6][7].As it can be seen from sources, inner surface parameters significantly affect mechanical properties of metal products.Mentioned surface is characterized by its value, which depends on grains number and size (diameter), dislocations density, metal porosity and density, disorientation (angles magnitude between grains surfaces) and other parameters, i.e. thickness and volume of surface and fraction volume from total metal volume.
Structural features of crystalline grids of metals and alloys are formed when they crystallize.The faster cooling (crystallization) of melt is carried out, the more and smaller size of equiaxial grains is formed.Distance between the nearest atoms (crystal grid parameter) is less in completely solidified steel comparing to liquid state [6].During solid steel cooling, grains jointing in it continues due to atoms diffusion, which is accompanied by decrease in intergranular borders.In this case, smaller grains having a larger surface curvature are gradually absorbed by larger grains with less surface curvature.Diffusion process is known of being quite slow.There may also be other behavior of grains and intergranular borders in steel during products deformation: they change shape, collapse, forming new additional surfaces due to grains crushing and formation of new dislocations -vacancies, pores and cracks [4,6,7].
During treating metals by pressure, plastic deformation of original material occurs, and it causes changes in its shape and size (figure 1) [2].
During cold rolling hammering harden, grinding and elongation of ferrite grains along the rolling direction occurs.Summarized reduction during cold treatment determines final texture of deformed material.In case of high degree of cold deformation, fine grain is formed.Ability of metals and alloys to plastic deformation is determined by material yield strength, which also depends on its internal structure.Metal alloys yield strength can change with treatment by pressure, which is especially noticeable during metal rolling of cold state.During metals treatment by pressure or during heat treatment, material strength and plasticity change due to change in internal structure -grains are crushed or enlarged, and number of dislocations or vacancies decreases in grains, pores appear and disappear, that means that junction surface between grains changes in metals volume [3,4].During cold rolling metal density usually decreases.This is due to the fact that during deformation intergranular cavities and cracks are formed.

Figure 1. Deformation scheme:
ABB A is strain zone; h 0 is sheet thickness before rolling; h 1 is sheet thickness after rolling; b 0 is strip width before rolling; b 1 is strip width after rolling; α is capture angle during rolling; h 0 , h 1 -initial and final thickness of strip accordingly R is roll radius; F k is contact area of the sheet with the rolls; l d is length of the strain zone; M is metal flow before entering the strain zone; N is metal flow when leaving the strain zone.
According to authors, research in this area shall be continued and influence of reduction value during cold rolling on grain size and borders between them shall be considered, which will allow to control strength and plasticity of products by adjusting value of reduction during cold rolling of steel.

Purpose and tasks of research
Purpose of work: to analyze influence of deformation degree during cold rolling on grain size and volume of metal internal structure joint surface In order to reach this goal, following tasks were set: to determine dependencies between metal alloy grains size and borders between them from reduction value during cold rolling; to establish regularities of the impact of the amount of crimp on the grain sizes of the metal alloy, the boundaries between them and the strengthening of the metal.

Methodology of research
Low-carbon steel was used in research.The microstructure of cast low-carbon steel (figure 2) was studied and compared with the structure after cold rolling (figure 3), which shows the changes in the shape and size of the grains during pressing.
Using data from list of references [14,15], geometric characteristics of metal were identified, i.e. intergranular surface area and its volume, and surface volume fraction from metal volume.Intergranular surface volume V M Z was calculated according to formula: where d z -grain size in form of cube, m; n -number of grains, contained in 1 m 3 ; t -intergranular surface thickness, t = 0,6 • 10 −3 m.Grain size was calculated according to figure 4 based on standard [15].According to Hall-Petch law, yield strength σ T equals to [16]: where σ 0 -some stress that is required to slip dislocations (for low-carbon steel σ 0 = 170 MPa); K -constant that depends on material grade, Hall-Petch coefficient (for calculations K = 60 [16]).Increase of yield strength ∆σ was calculated according to formula: ∆σ = σ T − σ 0 .Metal yield strength during cold rolling is calculated according to formula: where a, n -coefficients that take into consideration influence of chemical composition of a = 33.4;n = 0.6; ε Σ -summarized deformation degree (in case if rolling is performed in several stages), %.Deformation degree during study varied from 10 to 80 %.Deformation degree was determined by the formula [13]: where ∆h is absolute reduction, Equating formulas ( 2) and ( 3), after corresponding transformations, reduction value, which provides specified grain size during cold rolling was determined: After completing mathematical transformations, we receive dependence of grain size in metal, obtained during rolling, from reduction value: Offered dependence will enable to adjust grain size changing value of percentage reduction, which determines prospects for controlling steel strength.

Results and their explanation
Executed research enabled to identify fraction of intergranular amorphous volume, metal yield strength and its strengthening according to value of reduction during cold rolling.Strengthening value is specified in %. Results of study are presented in table 1.
For more visual observation of changes in amorphous volume fraction, reduction value obtained by formula (3) and metal strengthening value, depending on grain size of internal structure, we draw appropriate graphs (figure 5).
From reference list it is known [17,18] that fine-grained materials exhibit high plasticity under certain temperature and velocity deformation conditions.Following dependence has been established: the smaller grains size in material is, the more intensive intergranular slipping is developed, and the higher velocity of superplastic deformation and the higher percentage elongation of samples is.These parameters are very important for introduction of technologies that are based on superplasticity effect usage.During cold rolling, internal properties of treated sheets, i.e. grains size and borders between them, metal yield strength and its changes, can be controlled by reduction value.For this purpose, we investigated grain size changes according to formula (7), depending on reduction degree (figure 6).
It shall be noted that grain size decreases with increase in reduction value according to hyperbolic function of n-th order (figure 6).Studies showed that with summarized reduction of more than 80 % during cold rolling, sheets with internal structure having a minimum standard grain size and is characterized with maximum intergranular borders is obtained.
Influence of reduction value to strengthening of metal alloy and fraction of intergranular surface volume is presented in figure 7, where it is clear that these indicators increase almost equally with increased degree of deformation.
Approximation of obtained graphical dependences made it possible to determine that influence of these parameters is performed according to linear function.Studies used least square method, which enabled to obtain following dependencies: where A -fraction of intergranular amorphous volume, %; C -metal strengthening, %.

Conclusions
Changes that occur in internal structure of metal products during treatment by pressure were analyzed, it allowed to determine dependencies between metal alloy grains size and borders between them from reduction value during cold rolling.
Regularities of reduction value influence on grains sizes of metal alloy, borders between them and metal strengthening are determined.It is shown that grain size decreases with increase of deformation degree according to hyperbolic function of n-th order, while fraction of intergranular amorphous volume and metal strengthening increase according to linear functions, which enable to control steel strength by adjusting grains size and their joint surface, i.e. changing reduction value.

Figure 3 .
Figure 3. Microstructure of low-carbon steel after rolling.

Figure 6 .
Figure 6.Influence of reduction value on grain size.

Table 1 .
Parameters of internal structure and properties of steel.