ELASTIC PROPERTIES OF ALLOY ZE10 SHEETS EVALUATION BY KERNS TEXTURE PARAMETERS

Valentin Usova,*, Natalia Shkatulyaka,†, Elena Savchukb,††, Nadezhda Rybaka,††† aSouth Ukrainian National Pedagogical University named after K. D. Ushinsky Str. Staroportofrankovskaya, 26, Odessa, 65020, Ukraine bNational University "Odessa Maritime Academy", Str. Didrikhson, 8, Odessa, 65000, Ukraine *Corresponding Author: E-mail address: valentinusov67@gmail.com †E-mail: shkatulyak56@gmail.com, ††E-mail: z9816@yandex.ua, †††E-mail: tesha1994@mail.ru Received 18 December, 2020; accepted February 18, 2021


EEJP. 1 (2021)
Valentin Usov, Natalia Shkatulyak et al This work aimed the Kearns texture parameters to find and evaluating on this base the elastic and mechanical properties of sheets of magnesium alloy ZE10 after industrial processing and subsequent alternating bending (AB). Such approach to evaluating of the elastic and mechanical properties of sheets of magnesium alloy ZE10 has not been used before.

MATERIALS AND METHODS
Sheets of ZE10 magnesium alloy (1.3% Zn, 0.15% Zr, 0.2% rare earth metals (REM), among REM mainly cerium) were obtained by processing [9], which consisted of ingot extrusion at a temperature of 350°C, after which a slab 6 mm thick and 60 mm wide was obtained. Next, the slab was rolled sequentially in the longitudinal direction to a thickness of 4.5 mm in 2 passes in combination with heating to 350 ° C after each pass. Further rolling to a thickness of 2 mm was performed in the transverse direction in combination with heating to 350°C after each pass. The degree of deformation for each pass was approximately 10 %. From a thickness of 2 mm, the direction of rolling was changed by 90° after each pass with a degree of deformation of approximately 10 % in combination with heating to 350°C, and thus obtained sheets with a thickness of 1 mm (original sheets).
The alternating bending (AB) was simulated on a manual bending device that included three rollers. The diameter of the bending roller was 50 mm. The speed of metal movement during bending was ~ 150 mm/s. The study was performed after 0.5; 1.0, 3.0 and 5.0 cycles. One cycle of alternating bending consisted of bending in one direction (0.25 cycles), straightening to a flat state (0.5 cycles), bending in the other direction (0.75 cycles) and straightening (1.0 cycle).
The three series of samples for mechanical testing in every from the three direction namely rolling direction (RD), diagonal direction (DN, i. e. at an angle of 45° to the RD), and transverse direction (TD) were cut out from original sheet as well as from the sheets after bending for 0.5, 1, 3 and 5 cycles. Mechanical tests of abovementioned samples were performed at room temperature on the tensile-testing machine Zwick Z250 / SN5A with a force sensor at 20 kN. The total length of the samples was 90 mm. The length and width of the working part of the samples was 30 mm and 12.5 mm, respectively.
For the Young's modulus measuring were cut out the samples through every 15° from the rolling direction (RD) up to the transverse direction (TD) (by three samples in every direction) from original sheet as well as from the sheets after AB. The length and width of the samples were respectively100 mm and 10 mm.
The Young's modulus was measured dynamically by the frequency of natural bending oscillations of flat specimens. The error Young's modulus measuring did not exceed 1% [10].
The average value by three series of measured and tested specimens in each according direction were taken as values of the elastic and mechanical properties.
Samples to the texture study were cut also. Before studying the texture, the samples were chemically polished to a depth of 0.1 mm to remove the distorted surface layer. The crystallographic texture was investigated on the two surfaces of the sheets, as well as in the rolling direction of the samples after above number of the RB cycles by means of the inverse pole figures (IPF) of the normal direction (ND IPF) and the rolling direction (RD IPF) on a DRON-3m diffractometer in filtered Kα-Mo X-ray. A typesetting sample was used to record of RD IPF. The sample without texture was made of fine recrystallized sawdust of the investigated alloy. Morris normalization was used in the construction of the IPFs [11].

EXPERIMENTAL RESULTS AND DISCUSSION
The experimental IPFs of the alloy under study are shown in Fig. 1. The texture of the initial sample of the ZE10 alloy ( Fig. 1a,b) is characterized by a wide preferential scattering of normal's to the basal plane in the TD. The maximum deflection angle is 90. Intermediate maxima of the deviation of the hexagonal prism from the ND are observed both towards the TD at 40 and towards the RD by 40, in contrast to the texture, which is usually formed in Mg, Ti, and Zr.
Changes in the character of texture scattering are observed depending on the number of AB cycles ( Fig. 1c -m). The pole density values on the IPFs change also. The observed changes in the pole density distribution at different stages of the AB indicate the occurrence of deformation processes of sliding and twinning [6,7].
The Kearns texture parameters are often used to quantify the texture of hexagonal materials [8]. These coefficients, j f (index j means the corresponding direction ND, RD or TD in the sample) show the degree of coincidence of the c-axes of the crystalline hexagonal cells of grains with a given geometric direction in a polycrystalline material and can be found by the IPFs according to the ratio 2 2 cos cos the normal to the i-th reflex of the corresponding IPF; i  is the angle of deviation from the c axis of the i-th crystallographic direction for the j-th direction in the sample. For hexagonal single crystal, the value of some properties connecting two vector quantities or a tensor with a scalar quantity is determined [13] as: is property in the selected direction, a P and c P are the properties of a single crystal in a direction perpendicular and parallel to the direction  0002 , respectively, φ is the angle between the selected direction and   0002 .
Summing over the entire volume, we get: To find the Kearns texture parameters by formula (1), we used the IPFs in Fig. 1, the values of i A were taken from [12]. To calculate the angles between the crystallographic planes of a hexagonal single crystal using the known formulas [14], it is necessary to know the ratio of the crystal lattice parameters c/a of the alloy under study. According to our data, for magnesium alloy ZE10   1.622 c a  . A similar result was also obtained by the authors of [15].
Kerns showed [8] that if a material property can be described by a tensor (for example, elasticity), then it obeys relation (5). In this case, the sum of j f in the three main directions of the sample should be equal to one and a value of  Fig. 1 as well as TD f found using relation (6) are given in Table. 1. Analysis of the distribution of pole density on the ND IPFs of opposite sides of the sheets after a different number cycles of AB showed certain inconsistencies (Fig. 1, c, d; f, g; i, j; l, m). The cause of these discrepancies is due to the fact that when bent to one side, the metal layers on the convex side of the sheet are subjected to tensile deformation. At the same time, the corresponding metal layers on the concave side of the sheet are deformed by compression. The deformation processes are alternated when the sign of bending is periodical changed. Similar inconsistencies in the distribution of the pole density on the IPFs of the outer and inner sides of the strips obtained after cutting along the axis and subsequent straightening of the tube made of Zr-2.5% Nb alloy were found earlier in [16].
The noted inconsistencies are reflected on the values of the Kearns texture parameters, calculated from the ND IPFs of opposite sides of the sheets after the AB ( (1) ND f , and (2) ND f , Table 1). For further analysis of the AB effect on the properties of investigated alloy in the ND to the sheets plane were used of the Kearns texture parameters averaged over both sides of the sheets after the corresponding number of AB cycles.
The values of the modulus of elasticity, measured every 15 in the rolling plane of the sheets of investigated alloy, are presented in Table 2.     (Table 1) and the single crystal elastic constants of the alloy under study. Earlier in [17], we found the values of the elastic constant 11 S and the combination of the elastic constants 13 11 44 0.5 a S S S    , Now let us estimate the value of the elastic modulus of the sheets of the investigated alloy in three directions of the sheet RD E , TD E , and ND E by a relation of the type (8), using the values of the elastic modulus of the single crystal along and across the hexagonal axis of the ZE10 alloy (11) and (12), as well as the corresponding of the Kerns texture parameters ( Table 1). The calculation results are presented in the Table 6. The experimental values of the modulus of elasticity for

EEJP. 1 (2021)
Valentin Usov, Natalia Shkatulyak et al convenience of comparison are also given in the Table 6. It is seen that the maximum deviation of the calculated and experimental values of the elastic modulus was 5.2%. We could not experimentally measure the elastic modulus in the normal direction ND E to the rolling plane due to the small sheet thickness (1 mm). The value of the ND E in the original sheet of the ZE10 alloy estimated earlier us in [16] was 43.8 GPa. The value of the ND E obtained in this work (Table 6) deviates from the above value by 0.9% (Table 6). Unfortunately, it is impossible to estimate the value of the mechanical characteristics of the alloy under study using the Kearns texture parameters, similar to the above calculations for the elastic modulus, since data on the strength and plastic properties of the single crystal of the alloy ZE10 are missed in the literature. It is known that one of the main causes for the appearance of anisotropy in the physical and mechanical properties of polycrystalline metallic materials is the crystallographic texture formed during deformation. As mentioned above, Kearns texture parameters are often used to quantify the texture of hexagonal materials [19].
Let us analyze the observed changes in the studied characteristics (Tables 2-5) in connection with the crystallographic texture, represented by the Kearns texture parameters ( Table 1). The analysis was showed that there are strong correlations between the values of the modulus of elasticity, mechanical characteristics, on the one hand, and the above-mentioned Kearns texture parameters, on the other hand. The corresponding regression equations and approximation reliability coefficients are represented by the relations (13)  Strong correlations the elastic modulus and mechanical characteristics values with Kearns texture parameters established and quadratic regression equations with approximation reliability coefficients of 0.76 -0.99 were found.
The presented results may be useful to develop a technology for obtaining improved characteristics of the shaping and minimal anisotropy of mechanical characteristics of magnesium alloys sheets.