MATHEMATICAL MODELING OF MECHANICAL PROPERTIES OF STRUCTURAL STEELS

Аннотация

On the basis of available published data and with the aid of a personal computer found equations of the dependence of the yield strength σ 0,2, of reduction of area φ and of impact toughness a 1 of a group of a structural steels on their tensile strength σ u with correlation coefficients.

Толық мәтін

According to published data [1] there exists a certain-dependence of the yield strength ct02, of reduction of area p and of impact toughness ai of structural steels alloyed with various elements on the tensile strength ctu. In article [1] processed the data of more than 400 publications with a computer by method of multiple regression analysis and obtained quantitative dependences suitable for calculating the mechanical properties of steels (12 marques) from the known chemical composition. On the basis of the data on the correlation between the mechanical properties of metals [3] compare in the present work the results of [1] and [2] The data of [1] on the mechanical characteristics of steels were processed by methods of correlations and variance analysis so as to obtain mathematical models of the dependences of yield strength ct02, reduction of area p and impact strength a1 on ultimate resistance ct„. The calculations were with software presented in [4]. To make the programs suitable for the computer, they were analyzed and translated into Turbo Pascal-5. For the dependences of ct0 2, p and a1 on ou were obtained the following equations (type y = a = bx) with the correlation coefficients rxy = 0,978 and 0,985, respectively: ct0,2 = 297,321 + 0,652 ct„ (1) p = 85,724 - 0,023 ct„ (2) For a1 was obtained the equation (type y = b0-xb1 with rxy = 0,980): a1 = 10197977,89 ctu4’645. (3) The curves of the experimental and of the calculated dependences by equations (1)-(3) are presented in fig. 1. An evaluation of the of the error of the theoretical data compared with experimental ones showed that for the dependence ct02 = fau) the range of the maximal deviations lies in the range from + 12,93 % to - 9,3 %, for p = fau) - from + 10,97 % to - 5,3 %, and a1 = flau) - from + 18,1 % to - 23,1 % (fig. 2). Carried out a comparative analysis of the deviations of the calculated data on mechanical properties (ct02, p and a1) from experimental ones (fig. 2). It was established that the scatter of the values of these characteristics calculated for the data [1] was somewhat larger than the data [2] because in the former case the values of ctu were averaged for an entire group of steels (in [1] neither the amount nor the marks of the of the steels was given). In [2] the mechanical properties were calculated from data obtained for 12 marks of steels, but each characteristic was calculated separately and with a view to the principal factors affecting the mechanical properties (content of alloying elements, conditions of heat treatment). 135 Технологические процессы и материалы Fig. 1. Dependences of ct0,2, p and a1 of structural steels on au. o - experimental data; • - calculated data Fig. 2. Deviation (n) of the calculated values of the mechanical properties of structural steels on the experimental values when the regression equations for the data of [1] and [2] were used: 1 - for the groups steels [1]; 2-7 - for actual steels [2]: 2 - 10ХН3; 3 - 10Х2Н4; 4 - 20ХН4; 5 - 15Х; 6 - 25Х2ГС; 7 - 25ХГС The range of deviations of the calculated values of the properties for this case is smaller because fig. 2 presents the mechanical properties of separate marks of steel, and not their entirety. Nevertheless, the theoretical determination of the mechanical properties of steels and alloys from some single characteristic is of a practical value because it makes it possible to evaluate the quality of products fairly reliably [5].