539.26 Analysis of empirical models of deformation curves of elastoplastic materials (review). Part 3

Golovina N. Y. (Industrial University of Tyumen)

MATHEMATICAL MODEL OF THE DEFORMATION CURVE, EMPIRICAL STRESS-STRAIN CURVES, NONLINEAR ELASTICITY LAW, ELASTOPLASTIC MATERIAL PROPERTIES, PHYSICAL PARAMETERS OF ELASTOPLASTIC MATERIALS, PROCESSING OF EXPERIMENTAL DATA


doi: 10.18698/2309-3684-2023-1-331


This article is the third part of a review of works devoted to the study of the properties of elastic-plastic materials. The first and second parts were devoted to the analysis of universal empirical laws of deformation, which model the material properties over the entire range of deformation, up to fracture. It was concluded that in order to create a model of the material response to stress growth, the deformation law must be at least four-parametric. The empirical Ramberg-Osgood law was found to be the most qualitative, at least for the titanium alloy VT6 considered. However, despite its accuracy, it does not reflect the material properties in the zone of large plastic strains, including in the vicinity of the point of ultimate strength. This paper presents an analysis of multilink models describing the relationship between strain and stress by different laws in the elastic zone and in the plastic zone. The review includes two-link models by Nadai, Mirambell-Real, Rasmussen, Abdella, formulated for materials whose strain curve has no positive curvature section. Also considered in the review are the three-link models of Quach; Hertele; Belov-Golovina, which allow modeling of deformation curves with a positive curvature region. The evaluation of the quality of empirical laws and their correspondence to the sample of experimental points was carried out by minimizing the standard quadratic deviation and using the method of gradient descent to determine the minimum of the function of many variables. The material for the comparative analysis of empirical models is titanium alloy VT6; for the Hertele and Belov-Golovina models — steel St3sp. It is shown that the models built on the basis of multi-line splines determine the properties of elastic-plastic materials more accurately than the models built on the basis of universal laws.


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