Calculation of the elastic modulus of steel during tensile

Abstract

The rational use of resources in the design of vessels and devices and ensuring their growing needs requires the performance of strength and stability calculations, which require the use of appropriate values of the modulus of elasticity during tension E. The purpose of the article is to improve the definition of the modulus of elasticity of steels during tension, the value of which is normalized by the current in Ukraine by regulatory documents. On the basis of standard tables, dot graphs of changes in modulus of elasticity of carbon, low-alloy, heat-resistant, corrosion-resistant chromium, heat-resistant and heat-resistant austenitic steels and iron-nickel-based alloys during tension E depending on temperature t were constructed and analyzed. It is proposed to approximate these dependencies with simple mathematical equations. As a result, it was determined that the dependence E = f (t) for carbon and low-alloy steels in the range of changing t from 20 oС to 300 oС is described by a simple linear equation E = – 100t + 2.01.105. When changing t from 300 oС to 450 oС inclusive, it is proposed to apply cubic regression E = – 5.33.10–3t3 + 5.2t2 – 1.827.103t + 3.95.105. In the above and further proposed formulas, the temperature t is substituted in °C, and the result is obtained in MPa. Heat-resistant and corrosion-resistant chromium steels in the temperature range t from 20 oС to 100 oС inclusive are characterized by the same modulus of elasticity during tension E = 2.15.105 MPa. The dependence of E = f (t) in the range of changing t from 100 oС to 250 oС inclusive can be described by the cubic regression E = 1.33.10–3t3 – 2.63.102t + 2.4.105, and when changing t from 250 oС to 600 oС inclusive – by cubic regression E = – 7.5.10–4t3 + 0.722t2 – 3.426.102t + 2.4748.105. The value of the modulus of elasticity during tension for heat-resistant and heat-resistant austenitic steels and iron-nickel-based alloys E = 2.15.105 MPa in the temperature range t from 20 oС to 100 oС. The dependence of E = f (t) in the range of changing t from 100 oС to 700 oС inclusive is described by the quadratic regression E = – 0.152t2 + 9.101t + 2.009.105. The obtained formulas make it possible to abandon the use of standard tables and additional interpolation of intermediate values of the modulus of elasticity of steels during tension when performing calculations, which in turn simplifies both the calculation itself and the development of appropriate computer programs. The average error value of the performed approximations is in the range from 0 % to 0.218 %, which indicates a high level of coincidence of the regression equations with the actual values. The use of the proposed formulas for calculating the modulus of elasticity of steels during tension makes it possible to simplify the calculation of vessels and devices for strength and stability.