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Mathematical Modeling of Failure and Deformation Processes in Metal Alloys and Composites

Received: 13 May 2020     Accepted: 3 July 2020     Published: 17 July 2020
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Abstract

Based on experimental examples, the strength characteristics of metal alloys and composites under tensile and compressive loads are considered to demonstrate both their similarity and difference. Under tensile loads, their behavior is essentially the same. Under compressive loads, the composite shows different properties, but similar to the behavior of a metal alloy under tension. When tensioned and compressed, it fractured as a material with a different structure. When a metal alloy is cyclically compressed, the damage accumulation process is attenuated, which reduces the alloy longevity during subsequent tension. The analysis of experimental data for various types of loading from the standpoint of the kinetic concept of fracture is carried out. Instead of a number of incompatible approaches or a formal description of experimental data, that based on the theory of reaction rates is used. Mathematical modeling of processes is carried out using rheological models of the material. Structural models of the material, called physical media, reflect the thermodynamic processes of flow, failure, and changes in the structure of the material. Parametric identification of structural models is carried out on the basis of the minimum necessary basic experiment: loading of specimens with different speeds at several temperature values and by the amplitude dependence of inelasticity. Based on results of these experiments, the scope of applicability conditions for this material and test modes necessary for parametric identification of models are selected. One fracture criterion is used, which formally corresponds to the achievement of a threshold concentration of micro-damage in any volume of the material, leading to macro-fracture. The application of mathematical models for calculating the longevity of materials depending on the temperature and force loading conditions and the nature of their changes is shown. Calculations of longevity under constant, monotonously increasing and variable loads under conditions of constant or changing temperatures are based on the relationship of plastic flow and failure processes distributed over the volume of the material. They are performed numerically by time steps depending on the ratio of the rate of change of temperature and stresses.

Published in American Journal of Physics and Applications (Volume 8, Issue 4)
DOI 10.11648/j.ajpa.20200804.11
Page(s) 46-55
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2020. Published by Science Publishing Group

Keywords

Creep, Fatigue, Damage, Thermal Activation Analysis, Inelasticity, Rheology, Mathematical Modeling

References
[1] D. A. Gokhfeld and O. F. Chernyavskii. Bearing capacity of structures under repeated loads. Moskva (USSR): Mashinostroenie, 1979. Russian.
[2] M. G. Petrov. Strength and life of structural components: an approach based on model of material as a physical medium. Saarbrücken (DE): Lambert Academic Publishing; 2015. Russian.
[3] V. A. Stepanov, N. N. Peschanskaya, V. V. Shpeizman, and G. A. Nikonov (1975). Longevity of solids at complex loading. International Journal of Fracture, 11 (5): 851–867.
[4] A. R. Michetti (1977). Fatigue analysis of structural components through math-model simulation. Experimental mechanics, 2: 69–76.
[5] M. G. Petrov (1998). Rheological properties of materials from the point of view of physical kinetics. Journal of Applied Mechanics and Technical Physics, 39 (1): 104–112.
[6] V. A. Petrov, A. Ya. Bashkarev, V. I. Vettegren. Physical foundations for predicting the longevity of structural materials. S.-Peterburg (Russia): Politekhnika, 1993. Russian.
[7] L. N. Stepanova, M. G. Petrov, V. V. Chernova, V. L. Kozhemyakin, and S. A. Katarushkin (2016). Investigation of the inelastic properties of carbon fiber during cyclic testing of specimens using acoustic emission and tensometry methods. Deformation and fracture of materials, 5: 37–41. Russian.
[8] L. N. Stepanova, M. G. Petrov, V. V. Chernova (2017). Acoustic emission control of inelastic properties of carbon fiber reinforced plastic with various reinforcement schemes under cyclic loading. Control. Diagnostics, 8: 18–25. Russian.
[9] Yu. N. Rabotnov. Creep of structural components. Moskva (USSR): Mashinostroenie, 1966. Russian.
[10] M. G. Petrov. Numerical simulation of fatigue failure of composite materials under compression. V. Fomin and L. Placidi (Eds.). EPJ Web of Conferences Volume 221 (2019): XXVI Conference on Numerical Methods for Solving Problems in the Theory of Elasticity and Plasticity (EPPS-2019 Tomsk, Russia, June 2019).
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[16] M. G. Petrov and A. I. Ravikovich (2001). Kinetic approach to prediction of the life of aluminum alloys under various thermal-temporal loading conditions. Journal of Applied Mechanics and Technical Physics, 42 (4): 725–730.
[17] A. S. Nowick and B. S. Berry. Anelastic relaxation in crystalline solids. New York (NY), London (GB): Academic Press, 1972.
[18] V. I. Shabalin. Investigation of fatigue of metals at stresses above the yield point [dissertation]. Moskva (USSR): VIAM, 1970. Russian.
[19] M. G. Petrov. On estimation of damages of aircraft structures in operation. High Energy Processes in Condensed Matter 2019. AIP Conference Proceedings 2125. (accessed 2019 Sep 11). https://aip-info.org/2FAM-1G5WC-8XI93L-XGDN5-0/c.aspx
[20] J. A. Collins. Failure of materials in mechanical design: analysis, prediction, prevention. New York (NY): John Wiley and Sons, 1981.
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[22] V. S. Yuschenko and E. D. Schukin (1981). Molecular dynamics modeling in studying mechanical properties. Physical and Chemical Mechanics of Materials, 4: 46–59. Russian.
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    Mark Petrov. (2020). Mathematical Modeling of Failure and Deformation Processes in Metal Alloys and Composites. American Journal of Physics and Applications, 8(4), 46-55. https://doi.org/10.11648/j.ajpa.20200804.11

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    ACS Style

    Mark Petrov. Mathematical Modeling of Failure and Deformation Processes in Metal Alloys and Composites. Am. J. Phys. Appl. 2020, 8(4), 46-55. doi: 10.11648/j.ajpa.20200804.11

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    AMA Style

    Mark Petrov. Mathematical Modeling of Failure and Deformation Processes in Metal Alloys and Composites. Am J Phys Appl. 2020;8(4):46-55. doi: 10.11648/j.ajpa.20200804.11

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  • @article{10.11648/j.ajpa.20200804.11,
      author = {Mark Petrov},
      title = {Mathematical Modeling of Failure and Deformation Processes in Metal Alloys and Composites},
      journal = {American Journal of Physics and Applications},
      volume = {8},
      number = {4},
      pages = {46-55},
      doi = {10.11648/j.ajpa.20200804.11},
      url = {https://doi.org/10.11648/j.ajpa.20200804.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20200804.11},
      abstract = {Based on experimental examples, the strength characteristics of metal alloys and composites under tensile and compressive loads are considered to demonstrate both their similarity and difference. Under tensile loads, their behavior is essentially the same. Under compressive loads, the composite shows different properties, but similar to the behavior of a metal alloy under tension. When tensioned and compressed, it fractured as a material with a different structure. When a metal alloy is cyclically compressed, the damage accumulation process is attenuated, which reduces the alloy longevity during subsequent tension. The analysis of experimental data for various types of loading from the standpoint of the kinetic concept of fracture is carried out. Instead of a number of incompatible approaches or a formal description of experimental data, that based on the theory of reaction rates is used. Mathematical modeling of processes is carried out using rheological models of the material. Structural models of the material, called physical media, reflect the thermodynamic processes of flow, failure, and changes in the structure of the material. Parametric identification of structural models is carried out on the basis of the minimum necessary basic experiment: loading of specimens with different speeds at several temperature values and by the amplitude dependence of inelasticity. Based on results of these experiments, the scope of applicability conditions for this material and test modes necessary for parametric identification of models are selected. One fracture criterion is used, which formally corresponds to the achievement of a threshold concentration of micro-damage in any volume of the material, leading to macro-fracture. The application of mathematical models for calculating the longevity of materials depending on the temperature and force loading conditions and the nature of their changes is shown. Calculations of longevity under constant, monotonously increasing and variable loads under conditions of constant or changing temperatures are based on the relationship of plastic flow and failure processes distributed over the volume of the material. They are performed numerically by time steps depending on the ratio of the rate of change of temperature and stresses.},
     year = {2020}
    }
    

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  • TY  - JOUR
    T1  - Mathematical Modeling of Failure and Deformation Processes in Metal Alloys and Composites
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    Y1  - 2020/07/17
    PY  - 2020
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    T2  - American Journal of Physics and Applications
    JF  - American Journal of Physics and Applications
    JO  - American Journal of Physics and Applications
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    AB  - Based on experimental examples, the strength characteristics of metal alloys and composites under tensile and compressive loads are considered to demonstrate both their similarity and difference. Under tensile loads, their behavior is essentially the same. Under compressive loads, the composite shows different properties, but similar to the behavior of a metal alloy under tension. When tensioned and compressed, it fractured as a material with a different structure. When a metal alloy is cyclically compressed, the damage accumulation process is attenuated, which reduces the alloy longevity during subsequent tension. The analysis of experimental data for various types of loading from the standpoint of the kinetic concept of fracture is carried out. Instead of a number of incompatible approaches or a formal description of experimental data, that based on the theory of reaction rates is used. Mathematical modeling of processes is carried out using rheological models of the material. Structural models of the material, called physical media, reflect the thermodynamic processes of flow, failure, and changes in the structure of the material. Parametric identification of structural models is carried out on the basis of the minimum necessary basic experiment: loading of specimens with different speeds at several temperature values and by the amplitude dependence of inelasticity. Based on results of these experiments, the scope of applicability conditions for this material and test modes necessary for parametric identification of models are selected. One fracture criterion is used, which formally corresponds to the achievement of a threshold concentration of micro-damage in any volume of the material, leading to macro-fracture. The application of mathematical models for calculating the longevity of materials depending on the temperature and force loading conditions and the nature of their changes is shown. Calculations of longevity under constant, monotonously increasing and variable loads under conditions of constant or changing temperatures are based on the relationship of plastic flow and failure processes distributed over the volume of the material. They are performed numerically by time steps depending on the ratio of the rate of change of temperature and stresses.
    VL  - 8
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Author Information
  • Department of Strength and Longevity of Materials and Structural Components, Siberian Aeronautical Research Institute Named After S. A. Chaplygin, Novosibirsk, Russia

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