Abstract
The paper is concerned with modeling of stress-induced diffusion within the framework of the micropolar approach. The specificity of the model accounting for stress-strain state of the host material by means of additional thermodynamic driving force in the form of gradient of chemical potential is discussed. The considered model represents a generalization of the known corresponding model developed within the framework of the classical approach. The proposed generalization allows one to account for size effects while modeling the diffusion process. The main focus is on modeling of the skin effect manifested near the perturbation surface. It is shown that accounting for couple stress interactions between material particles results in a significant excess of diffusing impurity in the vicinity of the border. An axially symmetric problem is solved and investigated in detail. Various types of boundary condition on the outer border are used to demonstrate the general specificity of the developed model. Qualitative and quantitative effect of non-classical material parameters is discussed.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Koyama M, Akiyama E, Lee Y-K, Raabe D, Tsuzaki K (2017) Overview of hydrogen embrittlement in high-Mn steels, Int J Hydrog Energy 42(17):12706-12723.
Wasim M, Djukic MB (2020) Hydrogen embrittlement of low carbon structural steel at macro-, micro-and nano-levels, Int J Hydrogen Energy 45(3):2145-2156.
Wu TI, Wu JC (2008) Effects of cathodic charging and subsequent solution treating parameters on the hydrogen redistribution and surface hardening of Ti–6Al–4V alloy, J Alloys Compd 466(1-2):153-159.
Martinsson Å, Sandström R (2012) Hydrogen depth profile in phosphorusdoped, oxygen-free copper after cathodic charging, J Mater Sci 47(19):6768-6776.
Polyanskiy VA, Belyaev AK, Alekseeva EL, Polyanskiy AM, Tretyakov DA, Yakovlev YA (2019) Phenomenon of skin effect in metals due to hydrogen absorption, Continuum Mech Thermodyn 31(6):1961-1975.
Aifantis EC (1980) On the problem of diffusion in solids, Acta Mech 37(3):265-296.
Indeitsev D, Mochalova Y (2014) Mechanics of multi-component media with exchange of mass and non-classical supplies, In: Irschik H, Belyaev AK (Eds) Dynamics of Mechanical Systems with Variable Mass, pp 165-194, Springer, Vienna.
Indeitsev DA, Mochalova YA (2017) On the problem of diffusion in materials under vibrations, In: Altenbach H, Goldstein R, Murashkin E (Eds) Mechanics for Materials and Technologies, pp 183-193, Springer, Cham.
Belyaev AK, Polyanskiy VA, Yakovlev YA (2012) Stresses in a pipeline affected by hydrogen, Acta Mech 223(8):1611-1619.
Wu CH (2001) The role of Eshelby stress in composition-generated and stressassisted diffusion, J Mech Phys Solids 49(8):1771-1794
Li JCM, Oriani RA, Darken LS (1966) The thermodynamics of stressed solids, Z Phys Chem 49(3-5):271-290.
Larché F, Cahn JW (1973) A linear theory of thermochemical equilibrium of solids under stress, Acta Metall 21(8):1051-1063.
Larchté, F.C., Cahn, J.L.: The effect of self-stress on diffusion in solids. Acta Metall. 30(10), 1835–1845 (1982)
Eshelby JD (1975) The elastic energy–momentum tensor, J Elast 5(3-4):321-335.
Mindlin RD (1965) Second gradient of strain and surface-tension in linear elasticity, Int J Solids Struct 1(4):417-438.
Mindlin RD, Eshel NN: On first strain-gradient theories in linear elasticity, Int J Solids Struct 4(1):109-124.
Toupin R (196(2) Elastic materials with couple-stresses, Arch Ration Mech Anal 11(1):385-414.
Aifantis EC (2003 Update on a class of gradient theories, Mech Mater 35(3-6), 259-280.
Altenbach, H., Eremeyev, VA (2012) Generalized Continua - from the Theory to Engineering Applications, Springer Science & Business Media.
Eremeyev VA, Lebedev LP, Altenbach H (2012) Foundations of micropolar mechanics. Springer Science & Business Media (2012)
Maugin GA, Metrikine AV (Eds): Mechanics of Generalized Continua, Springer, New York (2010)
Eremeev VA, Zubov LM Phase-equilibrium conditions in nonlinear-elastic media with microstructurel Doklady Akad Nauk Minerologia USSR 322(6):1052-1056.
Lazar M, Kirchner HOK (2007) The Eshelby stress tensor, angular momentum tensor and scaling flux in micropolar elasticity, Int J Solids Struct 44(14-15):4613-4620.
Frolova KP, Vilchevskaya EN, Bessonov NM (2022) On modeling of stressinduced diffusion within micropolar and classical approaches, ZAMM - Z für Angew Math Mech 102(6):e202100505 (2022)
Cui Z, Gao F, Qu J (2012) A finite deformation stress-dependent chemical potential and its applications to lithium ion batteries, J Mech Phys Solids 60(7):1280-1295.
Nowacki W (1974) The linear theory of micropolar elasticity In: Nowacki W, Olszak W (Eeds) Micropolar Elasticity, International Centre for Mechanical Sciences, vol 151, pp 1-43, Springer, Vienna.
Eringen AC (1999) Theory of micropolar elasticity. Microcontinuum field theories, Springer, New York, NY.
Lakes R (2001) Elastic and viscoelastic behavior of chiral materials, Int J Mech Sci 43(7):1579-1589.
Frolova K, Vilchevskaya E, Bessonov N, Müller W, Polyanskiy V, Yakovlev Y (2022) Application of micropolar theory to the description of the skin effect due to hydrogen saturation, Math Mech Solids 27(6):1092-1110.
Alekseeva EL, Belyaev AK, Zegzhda AS, Polyanskiy AM, Polyanskiy VA, Frolova KP, Yakovlev YA (2018) Boundary layer influence on the distribution of hydrogen concentrations during hydrogen-induced cracking test of steels, Diagnostics, Resource and Mechanics of Materials and Structures 3:43-57.
Merson E, Kudrya AV, Trachenko VA, Merson D, Danilov V, Vinogradov A (2016) The Use of Confocal Laser Scanning Microscopy for the 3D Quantitative Characterization of Fracture Surfaces and Cleavage Facets, Procedia Struct Integr 2:533-540.
Samarskii AA (2001) The Theory of Difference Schemes, vol. 240, CRC Press, Boca Raton.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Frolova, K., Bessonov, N., Vilchevskaya, E. (2023). Application of Nonlocal FICK’s Law Within Micropolar Approach. In: Altenbach, H., Berezovski, A., dell'Isola, F., Porubov, A. (eds) Sixty Shades of Generalized Continua. Advanced Structured Materials, vol 170. Springer, Cham. https://doi.org/10.1007/978-3-031-26186-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-031-26186-2_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-26185-5
Online ISBN: 978-3-031-26186-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)