Chebyshevskii Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Chebyshevskii Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Chebyshevskii Sb., 2019, Volume 20, Issue 1, Pages 405–423 (Mi cheb741)  

HISTORY OF MATHEMATICS AND APPLICATIONS

Historical aspects of mathematical analysis of metal material deformation diagrams

A. N. Chukanova, A. E. Gvozdeva, A. N. Sergeeva, S. N. Kutepova, P. N. Medvedeva, D. V. Maliya, A. A. Yakovenkob, I. F. Shirokya

a Tula State Lev Tolstoy Pedagogical University, Tula
b “OOO Metallurg-Tulamash” Ltd, Tula

Abstract: The article presents a retrospective of the formation and development of one of the methods to study the materials strain hardening – mathematical analysis of strain diagrams. Discussed in detail the most important mathematically reasonable direction of the analysis of the diagrams of deformation based on the use of their rebuild in the coordinates, due to the defined model representations, describe the process of strain hardening. The paper illustrates changing of analysis methods of stretching curves (load-elongation) and their mathematical description starting from representations of the 17$ ^{th}$–18$ ^{th}$ centuries in the works by L. da Vinci, R. Hooke, I. Newton up to the present day. A phased development of the mathematical description of strain hardening using strain diagrams from phenomenological approaches within the theories of Ludwik, Hollomon, Jaul-Krussard to modern physical theories of strain hardening by J. Taylor, N.F. Mott, E. Orovana, Ya.I. Frenkel, Ya.B. Friedman, A. Zeger, A. Cottrell, J. Reed, based on the analysis of the evolution of complexes of structural defects, the results of metallographic grounded thin metalphysical experiments. A critical analysis of the shortcomings of modern mathematical methods for estimating the parameters of strain diagrams in terms of the degradation and destruction (damage) development in the testing process is given. For example, mild steel experimental testing of the use of the listed model representations in comparison with the approaches Ludvika, Hollomon, Joule-Crosara to assess their conformity with modern views on the contribution of degradation and destruction processes (damage) to work hardening. The quantitative analysis of the coefficients of hardening, q-factor and destruction, which allowed to link the stages of deformation hardening with the parallel development of two main processes: the transformation of dislocation substructure and the development of deformation damage such as microcracks and pores. The critical values of deformation determining the boundaries of the ranges of sharp changes in the parameters of deformation hardening and destruction are revealed.

Keywords: metal alloys, hardening, strain, mathematical analysis, diagram, tensile, damage, steel, mathematical model, fracture, load, plasticity.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation RFMEF 157717X0271
The work was carried out within the framework of the Federal target program "Research and development in priority areas of development of the scientific and technological complex of Russia for 2014--2020" (unique project ID RFMEF 157717X0271).


DOI: https://doi.org/10.22405/2226-8383-2018-20-1-405-423

Full text: PDF file (730 kB)
References: PDF file   HTML file

UDC: 539.21:621.785
Received: 25.12.2018
Accepted:10.04.2019

Citation: A. N. Chukanov, A. E. Gvozdev, A. N. Sergeev, S. N. Kutepov, P. N. Medvedev, D. V. Maliy, A. A. Yakovenko, I. F. Shiroky, “Historical aspects of mathematical analysis of metal material deformation diagrams”, Chebyshevskii Sb., 20:1 (2019), 405–423

Citation in format AMSBIB
\Bibitem{ChuGvoSer19}
\by A.~N.~Chukanov, A.~E.~Gvozdev, A.~N.~Sergeev, S.~N.~Kutepov, P.~N.~Medvedev, D.~V.~Maliy, A.~A.~Yakovenko, I.~F.~Shiroky
\paper Historical aspects of mathematical analysis of metal material deformation diagrams
\jour Chebyshevskii Sb.
\yr 2019
\vol 20
\issue 1
\pages 405--423
\mathnet{http://mi.mathnet.ru/cheb741}
\crossref{https://doi.org/10.22405/2226-8383-2018-20-1-405-423}


Linking options:
  • http://mi.mathnet.ru/eng/cheb741
  • http://mi.mathnet.ru/eng/cheb/v20/i1/p405

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:46
    Full text:8
    References:3

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021