539.26 Analysis of empirical models of deformation curves of elastoplastic materials (review). Part 2

Golovina N. Y. (Industrial University of Tyumen), Belov P. A. (Institute of Applied Mechanics of RAS)


doi: 10.18698/2309-3684-2022-2-1427

This article is a continuation of the review of works devoted to the study of the properties of elastic-plastic materials. In the first part, universal laws of deformation containing less than four formal parameters considered. As result of the review, requirements for the formulation of empirical laws of deformation of elastic-plastic materials formulated.In particular, it concluded that the deformation law must be at least four-parameter. In the second part of this paper, empirical laws of deformation containing four or more parameters considered and analyzed. Comparison of the considered empirical curves with a sample of experimental points carried out according to the standard procedure of minimization of the total quadratic deviation and using the method of gradient descent to determine the minimum of a function of many variables. A representative sample of 158 experimental points of the deformation curve of the Russian titanium alloy VT6 used to evaluate the predictive ability of the models for experimental agreement. Universal empirical strain laws containing four formal parameters allow describing the strain curve with specified stresses and tangential moduli at the ends of the curve. This fact allows us to state that the elastic-plastic properties of materials can expressed through the geometric parameters of the strain curve. In turn, the relationship between the elastic-plastic properties of the material and the geometry of the strain curve can interpreted as the principle of "geometrization" of the elastic-plastic properties of materials.

Golovina N.Ya., Belov P.A. Analysis of empirical models of deformation curves of elastoplastic materials (review). Part 2. Mathematical Modeling and Computational Methods, 2022, no. 1, pp. 63–96.
Bell J.F. Mechanics of Solids: Volume I: The Experimental Foundations of Solid Mechanics. Springer, 1984, 813 p.
Hodgkinson E. Experiments to prove that all bodies are in some degree inelastic, and a proposed law for estimating the deficiency. Report of the 13th Meeting of the British Association for the Advancement of Science, 1843, pp. 23–25.
Ramberg W., Osgood W.R. Description of stress–strain curves by three parameters. Washington DC, NASA, 1943, 29 p.
Ludwigson D.C. Modified stress–strain relation for FCC metals and alloys. Metallurgical and material handling B, 1971, no. 2(10), pp. 2825–2828.
Golovina N.Y. On one empirical model of nonlinear deformation of elastoplastic materials. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2020, vol. 17, no. 3, pp. 48–55.
Golovina N.Ya., Belov P.A. Model of a curve of nonlinear deformation of steel 20HGR and steel 35. Problems of Strength and Plasticity, 2020, vol. 82, no. 3, pp. 305–316.
Dimitrienko Yu.I. Osnovy mekhaniki tverdogo tela. T.4. Mekhanika sploshnoj sredy [Fundamentals of solid mechanics. Vol.4. Continuum mechanics]. Moscow, BMSTU Publ., 2013, 624 p.
Dimitrienko Yu.I. Nonlinear Continuum Mechanics and Large Inelastic Deformations. Springer, 2010, 722 p.
Golovina N.Ya., Belov P.A. Deformation curve as a functional extremal. Science and Business: Ways of Developmen, 2019, no. 10 (100), pp. 44–52.
Golovina N.Ya. The nonlinear stress-strain curve model as a solution of the fourth order differential equation. International Journal of Pressure Vessels and Piping, 2021, vol. 189, art. no. 104258.
Krivosheeva S.Ya., Golovina N.Ya. Study of axial stiffness effect on the performance of pliable metal pipelines. Scientific review, 2016, no. 16, pp. 213–216.
Bowen A.W., Partridge P.G. Limitations of the Hollomon strain-hardening equation. Journal of Physics D: Applied Physics, 1974, vol. 7, no. 7, pp. 969–978Papirno R. Goodness of fit of the ramberg-osgood analytic stress-strain curve to tensile test data. Journal of Testing and Evaluation, 1982, vol. 10, no. 6, pp. 263–268.
Rasmussen K. Full range stress-strain curves for stainless steel alloys. Journal of Constructional Steel Research, 2003, vol. 59, iss. 1, pp. 47–61.
Gardner L. Experiments on stainless steel hollow sections – part 1: material and cross-sectional behavior. Journal of Constructional Steel Research, 2004, no. 60, pp. 1291–318.
Abdella K. Inversion of a full-range stress–strain relation for stainless steel alloys. International Journal of Non-Linear Mechanics, 2006, vol. 41, iss. 3, pp. 456–463.
Quach W.M., Huang J.F. Two-stage stress-strain models for light-gauge steels. Advances in Structural Engineering, 2014, vol. 17, no. 7, pp. 937–949

Головина Н.Я., Белов П.А. Анализ эмпирических моделей кривых деформирования упругопластических материалов (обзор). Часть 2. Математическое моделирование и численные методы, 2022, № 2, с. 16–29

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