1. MMC
  2. All Volumes and Issues
  3. Volume 3, Number 1, 2016
  4. To modeling admixtures influence on the size effects in a thin film

To modeling admixtures influence on the size effects in a thin film

MMC.
2016;
Volume 3, Number 1
: pp. 12-22
https://doi.org/10.23939/mmc2016.01.012
Received: December 28, 2015

Math. Model. Comput. Vol. 3, No. 1, pp. 12-22 (2016)

Authors:
  1. B. Bozhenko
  2. T. Nahirnyj
  3. K. Tchervinka
1
Centre of Mathematical Modeling of IAPMM named after Ya. S. Pidstryhach; Opole University of Technology
2
Centre of Mathematical Modeling of IAPMM named after Ya. S. Pidstryhach; Faculty of Mechanical Engineering, University of Zielona Góra
3
Ivan Franko National University of Lviv

There are formulated the key systems of equation describing  structurally nonhomogeneous two-component solid solutions.  As the key functions there are chosen the stress tensor (displacement vector) and the densities of admixture and skeleton.  On this basis the near-surface nonhomogeneity densities of skeleton and admixture, stresses and  size effects of surface tension and intensity of the power load causing the thin film fracture are studied.  The attention is paid to the admixture influence on size effects.

solid solutions
near-surface non-homogeneity
thin films
size effects
  1. Stark J. P. Solid state diffusion. Wiley. 237 p. (1976).
  2. Borg R. J., Dienes G. J. An Introduction to Solid State Diffusion. ACADEMIC PRESS Inc. 360 p. (1988).
  3. Wilkinson D. S. Mass transport in solids and fluids. Cambridge University Press. 270 p. (2000).
  4. Barton C. Prorok, Yong Zhu, Horacio D. Espinosa, Zaoyang Guo, Zdenek P. Bazant, Yufeng Zhao, Boris I. Yakobson. Micro- and Nanomechanics, in Encyclopedia of Nanoscience and Nanotechnology, Edited by H. S. Nalwa. Vol. 5, 555–600 (2004).
  5. Mazurkiewicz A., Dobrodziej J., Poteralska B. Nanonauki i nanotechnologie: stan i perspektywy rozwoju. W-wo Instytutu Technologii Eksploatacji, Radom. 605 s. (2007).
  6. Burak Y., Nahirnyj T., Tchervinka K. Local gradient thermomechanics. Encyclopedia of Thermal Stresses. 2794–2801 (2014).
  7. Nahirnyj T., Tchervinka K. Basics of mechanics of local non-homogeneous elastic bodies. Bases of nanomechanics II. Lviv, Rastr-7. 168 p. (2014).
  8. Nahirnyj T., Tchervinka K. Mathematical modeling of structural and near-surface non-homogeneities in thermoelastic thin films. Int. J. Eng. Sci. 91, 49–62 (2015).
  9. Nahirnyj T., Tchervinka K. Thermodynamical models and methods of thermomechanics taking into account near-surface and structural nonhomogeneity. Bases of nanomechanics I. Lviv, Spolom. 264 p. (2012).
  10. Nahirnyj T., Chervinka K., Boiko Z. On the choice of boundary conditions in problems of the local gradient approach in thermomechanics. Journal of Mathematical Sciences. 186, n. 1, 130–138 (2012).
  11. de Groot S. R., Mazur Р. Non-equilibrium Thermodynamics. North-Holland Publishino Company, Amsterdam. 457 p. (1962).
  12. Münster A. Chemische Thermodynamik. Berlin, Akademie Verlag. 295 p. (1969).
  13. Fracture Mechanics and Strength of Materials: Handbook: in 4 vol. / Ed. Panasyuk V. V. Kyev, Nauk. dumka. Vol. 3: Characteristics of short-time crack resistance of materials and methods of their determination. 436 p. (1988).
  14. Lambert P. Surface Tension in Microsystems. Engineering Below the Capillary Length. Springer-Verlag, Berlin. 327 p. (2013).
  15. Timoshenko S. P., Goodier J. N. Theory of Elasticity. McGraw-Hill International Editions (1970).