KnE Engineering | XIX International scientific-technical conference “The Ural school-seminar of metal scientists-young researchers” | pages: 47–54

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1. Introduction

The search for new technical solutions directly linked with the study of the physics and mechanics of the metal forming processes, rheology behavior of the material and the formation of the metal structure. The most important characteristic of the material is the strain resistance σs . The σs value must be known to assess the heterogeneity of strength and mechanical properties in the volume of the metal, to calculate the power parameters of the process, which determine the stable flow of the metal deformation process. Many works are devoted to the development of adequate mathematical models for strain resistance calculations [1-10]. Most of the studies based on the plastometer tests, which allow to consider the influence of degree ϵu , rate ξu and temperature θ of deformation on σs .

2. Determination of the Influence of Thermomechanical Parameters of the Tensile Process on the Strain Resistance

The staff of the Metal Forming Department of Ural Federal University (Ekaterinburg, Russia) together with the scientists of Czestochowa Technological University (Czestochowa, Poland) conducted studies of the dependence of the thermomechanical parameters of the tensile processon the strain resistance of low-carbon steel. For this purpose, the samples were tested on the torsion plastometer «STD 812»of Czestochowa Technological University. Chemical composition of the steel is presented in the Table 1.

The determinants varied in the following range: deformation temperature θ = 800 С ÷ 1200 С; strain degree εu , = 0 ÷ 6,5; strain rate ξu was 0,1 s -1 ; 1,0 s -1 and 10,0 a -1 . The tests were carried out at constant temperature and strain rate in a vacuum chamber.

Table 1

Chemical composition of the sample material during testing on the plastometer, %.


C Mn Si P S Cr Ni Cu Al Mo
0,21 0,97 0,10 0,014 0,009 0,26 0,07 0,17 0,024 0,014
N Pb Al As Cb V Ti B Zn Sn
0,0119 0,001 0,020 0,007 0,002 0,004 0,047 0,0030 0,018 0,012

Equations (1) and (2) were used to calculate the degree and speed of torsional deformation and to determine the strain resistance equation (3) was used [2-4]:

ϵu=2·π·r·N3·Lτ;

(1)

ϵ˙u=2·π·r·N˙3·60·L;ϵ˙u=2·π·r·N˙3·60·L;

(2)

σs=3·3·M2·π·r3,

(3) where: r – sample radius, L – sample length, N – number of sample rotations, N – rotation speed, M – torque.

Figure 1 shows deformation hardening curves of steel depending on the strain degree and strain rate at temperature 1200 С.

fig-1.jpg
Figure 1
Change of strain resistance depending on the degree and rate of deformation at temperature 1200 ∘ С.

Similar dependences are observed for other thermomechanical parameters of the process. It is found that at the beginning of the test there is an intensive increase in the strain resistance, and when strain degree ϵu reaches a certain value, the metal is practically not strengthened, and with further deformation, the strain resistance decreases, i.e., the material is softening.

3. Processing of the plastometer tests results for determination of strain resistance

For determination of strain resistance σs the equation proposed in the work [11] is widely used:

σs=Aϵunξukexp(pθ),

(4) where ϵu , ξu , θ- degree, rate and temperature of deformation; n, k and p–empirical coefficients. The linearized equation has the following form:

lnσS=lnA+nlnϵu+klnξupθ,

(5)

The parameters of the model (5) are convenient to represent in normalized form:

X1=lnϵulnϵu'Jlnϵu;X2=lnξulnξu'Jlnξu;X3=θθ'Jθ,

where ϵu' , ξu' , θ'- values of the model parameters in the center point of the experiment, which have typical values for the technological process of the railway wheel manufacturing; Jlnϵu , Jlnξu , Jθ- variability intervals of the parameters of the model.

The regression equation takes the following form:

y=b0+b1X1+b2X2+b3X3+b12X1X2+b13X1X3+b23X2X3+b123X1X2X3+b11X1'+b22X2'+b33X3'

Parameters that affect σs were set, during the experiment design basic level (BL), variability intervals ( Δ X), as well as upper and lower factor levels (-1/+1) were determined (Table 2).

Table 2

Factors affecting yield stress.


Factors -1 BL +1 Δ X
X 1 –straindegree εu , % 0,25 0,45 0,65 0,2
X 2 - strain rate ξu , s -1 5 10 15 5
X 3 – test temperature, θ,𝙲 900 1000 1100 100

A second-order central composition plan was used, which as a "core" has a matrix of linear orthogonal total factorial experiment 2 3 , to which tests in the center point of the experiment and tests in the so-called "star points" with coordinates( ± α,0,0), (0, ± α,0), (0,0, ± α) were added.

The orthogonality of the central compositional plan is provided by the appropriate selection of the star shoulder α (for three factors α = 1,215) and special transformation of quadratic variables x i2 by equation X' i =x i2 -d, where d – correction factor, depending on the number of factors, f or three factors d = 0,73. The significance of regression coefficients was tested by Student criterion. Experiment matrix to establish dependence σs=f(ϵu,ξu,θ) is shown in Table3.The right extreme column of the matrix shows the experimental values of lnσs , obtained during plastometric testing by upsetting steel samples with chemical composition, %: 0,55С; 1,0 Mn; 0,5 Si; 0,2 V; 0,25 Cr; 0,25 Ni; 0,25 Cn; S, P < 0.04. [14].

Due to the orthogonality of the planning matrix, its coefficients are calculated using the following formulas:

bi=j=1nxijyij=1nxij2;bii,=j=1nxij,yij=1nxij,2;bij=j=1n(xijxui)yjj=1n(xijxiu)2.

By the calculations results were determined: b0 = 2,960; b1 = 0,075; b2 = 0,118; b3 = 0,316;

b1u=0,02;b2u=0,012;b3u=0,033;b12=0;b13=0;b23=0;b123=0.
Table 3

Second order orthogonal plan for three factors.


Factors (coded value) Factors (nominal value) Response variable lnσs
X 1 X 2 X 3 x˜1 x˜2 x˜3 y
Plan core 1 -1 -1 -1 0,25 5 900 3,084 3,085
2 +1 -1 -1 0,65 5 900 3,232 3,232
3 -1 +1 -1 0,25 15 900 3,320 3,321
4 +1 +1 -1 0,65 15 900 3,468 3,467
5 -1 -1 +1 0,25 5 1100 2,453 2,454
6 +1 -1 +1 0,65 5 1100 2,601 2,595
7 -1 +1 +1 0,25 15 1100 2,689 2,706
8 +1 +1 +1 0,65 15 1100 2,837 2,853
Star points 9 -1.215 0 0 0,21 10 1000 2,871 2,889
10 +1.215 0 0 0,69 10 1000 3,051 3,058
11 0 -1.215 0 0,45 1,59 1000 2,817 2,818
12 0 +1.215 0 0,45 18,41 1000 3,104 3,105
13 0 0 -1.215 0,45 10 831,8 3,344 3,344
14 0 0 +1.215 0,45 10 1168,2 2,577 2,580
Plan center point 15 0 0 0 0,45 10 1000 2,851 2,851
16 0 0 0 0,45 10 1000 2,851 2,848
17 0 0 0 0,45 10 1000 2,852 2,856
18 0 0 0 0,45 10 1000 2,851 2,859
19 0 0 0 0,45 10 1000 2,851 2,854
20 0 0 0 0,45 10 1000 2,851 2,845

The significance of the coefficients is checked by the Student criterion

ti=biS bi ,

for that the reproducibility dispersion is determining by five parallel experiments in the central point of the plan

Seocn2=i=16(y0iy0¯)261=161i=15yoi216i=15y0i2=0,008.

The dispersion of the regression equation coefficients is determined by the following formulas:

Sbi2=Seocn2j=1nxij2;Sbii2=Seocn2j=1nxij2;Sbiu2=Seocn2j=1n(xijxiu)2.

By the calculations results were determined:

Sb0=0,02;Sb1=Sb2=Sb3=0,027;Sb1u=Sb2u=Sb3u=0,033.

The Student t-test for each of the coefficients was: tb0 = 148,036; tb1 = 2,76; tb2 = 4,38; tb3 = 11,68; tb1u = 0,549; tb2u = 0,36; tb3u = 1.Because the critical value t0,05;6-1 =2,571 (Student t-test), then all coefficients except b 0 , b 1 ; b 2 ub 3 , can be considered not significant. Therefore, finally the regression equation can be written as:

y=2,96+0,075X1+0,0118X2+0,0316X3.

The response values y obtained by this equation for the experiment plan points are shown in Table 3. Comparing the obtained y values with the experimental y i the adequacy dispersion was found, given that the number of significant coefficients in the regression equation is four:

S042=i=120(yiyi)2204=0,005.

The adequacy of the equation is checked by Fisher criterion:

F=S042Seocn2=0,625.

The equation is adequate, since composed F-ratio is less than the theoretical F < F 0,05;m1;m2 = 4,74, where m 1 =n-l=20-10=10 – number of freedom degrees of adequacy dispersion, m 2 =n 0 -1=6-1=5 – number of freedom degrees of reproducibility dispersion. Considering the normalization of the model parameters (4-5), obtained the following equation

lnσS=4,78+0,191lnϵu+0,176lnξu0,00286·θ,

then the mathematical model

σs=119ϵu0,191ξu0,176exp(0,00286·θ)

can be considered adequate and recommended for technological and strength calculations.

4. Summary

Studies of the dependence on the strain resistance of low-carbon steel in dependence of the thermomechanical parameters of the tensile process were conducted. It is found that at the beginning of the test there is an intensive increase in the strain resistance, and when strain degree reaches a certain value, the metal is practically not strengthened, and with further deformation, the strain resistance decreases, i.e., the material is softening. The correction algorithm of the strain resistance value of mathematical model is presented. A mathematical model of the relation between the strain resistance and the thermomechanical parameters of the tensile process was obtained. The adequacy of the model and the possibility of its use to study the influence on the strain resistance of thermomechanical parameters independently of each other were proved based on the application of statistical analysis methods.

Acknowledgements

The study was made within the base part of state job in the field of scientific activity №11.9538.2017/8.9, supported by Act 211 of the Government of the Russian Federation (agreement No. 02.A03.21.0006)

References

1 

Polukhin P.I., Gorelik S.S., Vorontsov V.K., Fizicheskie osnovy plasticheskoi deformatsii (Physical Mechanisms of Plastic Deformation), Moscow: Metallurgiya, 1984.

2 

Bogatov A.A., Mizhiritskii I.O., Smirnov, S.V., Resursp lastichnosti metallov pri obrabotke davleniem (Resource of Metal Plasticity under Pressure Treatment), Moscow: Metallurgiya, 1984.

3 

Andreyuk L.V. Tyulenev G.G., Strain resistance of steels and alloys, in Teoriya i praktikametallurgii (The Theory and Practice in Metallurgy), Sb. Nauch. Tr. Nauchno-Issled. Inst. Metall., Chelyabinsk: Yuzh.-Ural. Knizh. Izd.11 (1970) 101–123.

4 

Tret'yakov A.V. Zyuzin V.I., Mekhanicheskie svoistva metallov i splavov pri obrabotke metallov davleniem (Mechanical Properties of Metals and Alloys at Metal Forming), Moscow: Metallurgiya, 1973.

5 

Galkin A.M., Badania Plastometryczne Metali i Stopów, Politechnika Czestochowska, Monografie, Czestochowa: Wyd. Politech. Czestochowskiej, 1990

6 

Vainblat Yu. M., Diagrams of structural states and maps of structures of aluminum alloys, Metally, 2 (1982) 82–88.

7 

Dyja H., Tussupkaliyeva E., Bajor T., Laber K., Physical Modeling of Plastic Working Conditions for Rods of 7xxx Series Aluminum Alloys, Archives of Metallurgy and Materials. 62 (2017) 2, 515-521.

8 

Laber K., KawałekA., Sawicki, S., (...), Lesniak D., Jurczak H., Investigations of Plasticity of Hard-Deformed Aluminium Alloys of 5xxx Series Using Torsion Plastometer, Archives of Metallurgy and Materials. 61 (2016) 1853-1860.

9 

Smirnov A.S., Konovalov A.V., Belozerov G.A., Shveikin V.P., Smirnova E.O., Peculiarities of the rheological behavior and structure formation of aluminum under deformation at near-solidus temperatures, International Journal of Minerals, Metallurgy and Materials. 23 (2016)563–571.

10 

Chen F., Qi K., Cui Z.S., Lai X.M., Modeling the dynamic recrystallization in austenitic stainless steel using cellular automaton method, International Journal of Minerals, Comput. Mater. Sci.83 (2014)2014.

11 

Laber K.B., Dyja H.S., Kawalek A.M., Bogatov A.A., Nukhov D.S., Influence of the temperature and strain rate on the deformability of low-alloy carbon steel, Steel in Translation. 46 (2016) 620–623.

12 

Dyja H., Galkin A., Knapinski M., Reologia Metali Odksztalcanych Plastycznie, Monografie, Czestochowa: Wyd. Politech. Czestochowskiej, 2010.

13 

Grosman F. Hadasik E., Technologiczna Plastycznosc Metali. Badania Plastometryczne, Gliwice: Wyd. Politech. Slaskiej, 2005.

14 

Szyndler J., Grosman F., Tkocz M., Madej L., Numerical and Experimental Investigation of the Innovatory Incremental-Forming Process Dedicated to the Aerospace Industry, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science. 47 (2016)5522–5533.

15 

Bogatov A.A. Kushnarev A.V., Modeling of the thermomechanical state of the metal and the evolution of grain structure in the mechanics of metal forming, Proizvod. Prokata. 6(2013) 42–48.

16 

Smirnov N.V., Dunin-Barkovskii I.V., Kursteorii veroyatnostei i matematicheskoi statistiki (A Course of Probability Theory and Mathematical Statistics), Moscow: Nauka, 1965.

17 

Prosser M., Trigwell K., Student evaluations of teaching and courses: Student study strategies as a criterion of validity, Higher Education. 20 (1990) 135–142.

18 

Meyer J.P., Doromal J. B., Wei X., Zhu S.,A Criterion-Referenced Approach to Student Ratings of Instruction, Research in Higher Education. 58 (2017) 545–567.

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