Abstract
This paper is concerned with modeling the strongly inhomogeneous hydrogen distribution over a sample by means of the micropolar continuum approach. The presence of micro-cracks covering the lateral surface of the sample is modeled by means of a distributed couple stress prescribed as a boundary condition. The applied couple stress produces a longitudinal displacement in return, which quickly fades away from the surface. The tensile displacement increases the intergranular space in the vicinity of the sample boundary and initiates hydrogen absorption from the environment. A comparison between widths of the surface layer that were experimentally determined and the ones that were analytically obtained allows estimating a value of one of the non-classical elastic parameters.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
References
Adomeit G (1968) Mechanics of Generalized Continua (Edited by E. Kroner), chapter Determination of elastic constants of a structured material. lUTAM Symposia, Springer-Verlag Berlin Heidelberg
Aifantis EC (1984) On the microstructural origin of certain inelastic models. Journal of Engineering Materials and technology 106(4):326–330
Altenbach J, Altenbach H, Eremeyev VA (2010) On generalized Cosserat-type theories of plates and shells: a short review and bibliography. Archive of Applied Mechanics 80(1):73–92
Andronov DY, Arseniev DG, Polyanskiy AM, Polyanskiy VA, Yakovlev YA (2017) Application of multichannel diffusion model to analysis of hydrogen measurements in solid. International Journal of Hydrogen Energy 42(1):699–710
Askar A (1972) Molecular crystals and the polar theories of the continua experimental values of material coeffcients for kno3. International Journal of Engineering Science 10(3):293–300
Askar A, Cakmak AS (1968) A structural model of a micropolar continuum. International Journal of Engineering Science 6(10):583–589
Belyaev AK, Grishchenko AI, Polyanskiy VA, Semenov AS, Tretyakov DA, Shtukin LV, Arseniev DG, A YY (2017a) Acoustic anisotropy and dissolved hydrogen as an indicator of waves of plastic deformation. In: Days on Diffraction, 2017, pp 39–44
Belyaev AK, Polyanskiy VA, Yakovlev YA, Mansyrev DE, Polyanskiy AM (2017b) Surface effect of the waves of plastic deformation and hydrogen distribution in metals. In: Days on Diffraction, 2017, pp 45–50
Betekhtin VI, Gilyarov VL, Kadomtsev AG, Korsukov VE, Korsukova MM, Obidov BA (2009) Fractalization of the surface relief of an amorphous alloy as an indication of rupture. Bulletin of the Russian Academy of Sciences: Physics 73(10):1419
dell’Isola F, Seppecher P (1997) Edge contact forces and quasi-balanced power. Meccanica 32(1):33–52
dell’Isola F, Seppecher P, Madeo A (2012) How contact interactions may depend on the shape of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”. Zeitschrift für angewandte Mathematik und Physik 63(6):1119–1141
dell’Isola F, Corte AD, Giorgio I (2017) Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives. Mathematics and Mechanics of Solids 22(4):852–872
Ellis RW, Smith CW (1967) A thin-plate analysis and experimental evaluation of couple-stress effects. Experimental Mechanics 7(9):372–380
Eremeyev VA, Pietraszkiewicz W (2012) Material symmetry group of the non-linear polar-elastic continuum. International Journal of Solids and Structures 49(14):1993–2005
Eremeyev VA, Pietraszkiewicz W (2014) Refined theories of plates and shells. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik 94(1-2):5–6
Eremeyev VA, Pietraszkiewicz W (2016) Material symmetry group and constitutive equations of micropolar anisotropic elastic solids. Mathematics and Mechanics of Solids 21(2):210–221
Eremeyev VA, Lebedev LP, Altenbach H (2012) Foundations of micropolar mechanics. Springer Science & Business Media
Eringen AC, Kafadar CB (1976) Polar field theories. In: Continuum Physics, Volume 4, Elsevier, pp 1–73
Gauthier RD, Jahsman WE (1975) A quest for micropolar elastic constants. Journal of Applied Mechanics 42:369–374
Hadam U, Zakroczymski T (2009) Absorption of hydrogen in tensile strained iron and high-carbon steel studied by electrochemical permeation and desorption techniques. International Journal of Hydrogen Energy 34(5):2449–2459
Jones RH (2017) Stress-Corrosion Cracking, Materials performance and evaluation. ASM international
Khrustalev YA, Simakov YS, Glazunov MP, Gubin VV (1989) Formation of hydrogen under the metal friction (in russian). Russian Journal of Physical Chemistry A 63(5):1355–1357
Koyama M, Akiyama E, Tsuzaki K (2012) Hydrogen-induced delayed fracture of a fe–22mn–0.6 c steel pre-strained at different strain rates. Scripta Materialia 66(11):947–950
Kramer DE, Savage MF, Levine LE (2005) Afm observations of slip band development in al single crystals. Acta Materialia 53(17):4655–4664
Kyoung HS, Ji SK, Young SC, Kyung-Tae P, Young-Kook L, Chong SL (2009) Hydrogen delayed fracture properties and internal hydrogen behavior of a fe–18mn–1.5 al–0.6 c twip steel. ISIJ International 49(12):1952–1959
Lake R (1995) Experimental methods for study of Cosserat elastic solids and other generalized elastic continua. Continuum models for materials with microstructure pp 1–25
Lake RS (1983) Size effects and micromechanics of a porous solid. Journal of Materials Science 18(9):2572–2580
Liebold C, Müller WH (2015) Are microcontinuum field theories of elasticity amenable to experiments? a review of some recent results. In: Differential Geometry and Continuum Mechanics, Springer, pp 255–278
Liebold C, Müller WH (2016) Applications of higher-order continua to size effects in bending: Theory and recent experimental results. In: Generalized Continua as Models for Classical and Advanced Materials, Springer, pp 237–260
Martinsson A, Sandström R (2012) Hydrogen depth profile in phosphorus-doped, oxygen-free copper after cathodic charging. Journal of Materials Science 47(19):6768–6776
Mindlin RD (1964) Micro-structure in linear elasticity. Archive for Rational Mechanics and Analysis 16(1):51–78
Omura T, Nakamur J, Hirata H, Jotoku K, Ueyama M, Osuki T, Terunuma M (2016) Effect of surface hydrogen concentration on hydrogen embrittlement properties of stainless steels and ni based alloys. ISIJ International 56(3):405–412
Perkins RW, Thompson D (1973) Experimental evidence of a couple-stress effect. AIAA Journal 11(7):1053–1055
Schijve J (1966) Note on couple stresses. Journal of the Mechanics and Physics of Solids 14(2):113–120
Steffens T, Schwink C, Korner A, Karnthaler HP (1987) Transmission electron microscopy study of the stacking-fault energy and dislocation structure in cumn alloys. Philosophical Magazine A 56(2):161–173
Wu R, Ahlström J, Magnusson H, Frisk K, Martinsson A (2015) Charging, degassing and distribution of hydrogen in cast iron. Swerea KIMAB pp 1–41
Yagodzinskyy Y, Todoshchenko O, Papula S, Hänninen H (2011) Hydrogen solubility and diffusion in austenitic stainless steels studied with thermal desorption spectroscopy. steel research international 82(1):20–25
Yang JFC, Lakes RS (1981) Transient study of couple stress effects in compact bone: torsion. Journal of Biomechanical Engineering 103(4):275–279
Zhang S, Huang Y, Sun B, Liao Q, Lu H, Jian B, Mohrbacher H, Zhang W, Guo A, Zhang Y (2015) Effect of nb on hydrogen-induced delayed fracture in high strength hot stamping steels. Materials Science and Engineering: A 626:136–143
Acknowledgements
Support of this work by a grant from Russian Science Foundation by RSF grant no. 18-19-00160 is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Frolova, K., Vilchevskaya, E., Polyanskiy, V., Alekseeva, E. (2019). Modelling of a Hydrogen Saturated Layer Within the Micropolar Approach. In: Abali, B., Altenbach, H., dell'Isola, F., Eremeyev, V., Öchsner, A. (eds) New Achievements in Continuum Mechanics and Thermodynamics. Advanced Structured Materials, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-030-13307-8_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-13307-8_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-13306-1
Online ISBN: 978-3-030-13307-8
eBook Packages: EngineeringEngineering (R0)