ISSN (print) 1995-2732
ISSN (online) 2412-9003




Problem Statement (Relevance): The current yield criteria enable to predict the behavior of anisotropic materials under plastic deformation conditions. However, they do not appear to allow for the physical basis of anisotropy, i.e. the crystalline structure of the material and the texture formed under severe plastic strain. Therefore, it would not be possible to solve the inverse problem using the above criteria. In other words, we cannot use the above criteria to determine what crystalline structure, which has to be obtained in semi-finished products, would be most adequate to the requirements of metal forming processes. Objectives: The objective is to derive a plasticity criterion and constitutive assumptions of the plasticity theory for orthotropic material allowing for the lattice constants and the parameters of the predominant crystallographic structure typical of the stress state. Methods Applied: The plasticity criterion was derived based on the specific distortion strain energy and using some tensor calculus and invariant theory elements. The constitutive assumptions of the anisotropic medium plasticity theory were proved to be correct through experiment. The experiment was based on the comparison between the hardening curve obtained as a result of the tensile testing of longitudinal and transverse samples and the calculated curve. Originality: Basic equations of the orthotropic medium plasticity theory were developed, which explicitly account for the crystallographic nature of anisotropy. Findings: It was established that in order to determine the relationships between stress and strain in different directions, one needs to build a hardening curve in just one direction. And then, based on the texture orientation and the crystal lattice parameters, one can obtain the hardening curves for the other directions. In this case the calculation error does not appear to be more than 2-3%. Practical Relevance: The proposed variant of the plasticity theory allows to ensure improved processability and performance of the products by designing the texture components.


Anisotropy, yield criterion, crystal lattice, texture, crystallographic orientation, hardening curve, tension test.

Yaroslav A. Erisov – Ph.D. (Eng.), Associate Professor

Samara University, Samara, Russia. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID:

Fedor V. Grechnikov – D.Sc. (Eng.), Academician of RAS, First Deputy Chairman of Samara Scientific Center of the Russian Academy of Sciences, Head of Metal Forming Department

Samara University, Samara, Russia. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID:

Sergei V. Surudin – Ph.D. (Eng.), Engineerat the Metal Forming Department

Samara University, Samara, Russia. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.. ORCID:

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