On one mathematical model of creep in superalloys

Jiří Vala

Applications of Mathematics (1998)

  • Volume: 43, Issue: 5, page 351-380
  • ISSN: 0862-7940

Abstract

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In a new micromechanical approach to the prediction of creep flow in composites with perfect matrix/particle interfaces, based on the nonlinear Maxwell viscoelastic model, taking into account a finite number of discrete slip systems in the matrix, has been suggested; high-temperature creep in such composites is conditioned by the dynamic recovery of the dislocation structure due to slip/climb motion of dislocations along the matrix/particle interfaces. In this article the proper formulation of the system of PDE’s generated by this model is presented, some existence results are obtained and the convergence of Rothe sequences, applied in the specialized software CDS, is studied.

How to cite

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Vala, Jiří. "On one mathematical model of creep in superalloys." Applications of Mathematics 43.5 (1998): 351-380. <http://eudml.org/doc/33015>.

@article{Vala1998,
abstract = {In a new micromechanical approach to the prediction of creep flow in composites with perfect matrix/particle interfaces, based on the nonlinear Maxwell viscoelastic model, taking into account a finite number of discrete slip systems in the matrix, has been suggested; high-temperature creep in such composites is conditioned by the dynamic recovery of the dislocation structure due to slip/climb motion of dislocations along the matrix/particle interfaces. In this article the proper formulation of the system of PDE’s generated by this model is presented, some existence results are obtained and the convergence of Rothe sequences, applied in the specialized software CDS, is studied.},
author = {Vala, Jiří},
journal = {Applications of Mathematics},
keywords = {Strain and stress distributions in superalloys; high-temperature creep; viscoelasticity; interface diffusion; PDE’s of evolution; method of discretization in time; Rothe sequences; high-temperature creep; viscoelasticity; interface diffusion; weak formulation of evolution PDE; Rothe method},
language = {eng},
number = {5},
pages = {351-380},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On one mathematical model of creep in superalloys},
url = {http://eudml.org/doc/33015},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Vala, Jiří
TI - On one mathematical model of creep in superalloys
JO - Applications of Mathematics
PY - 1998
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 43
IS - 5
SP - 351
EP - 380
AB - In a new micromechanical approach to the prediction of creep flow in composites with perfect matrix/particle interfaces, based on the nonlinear Maxwell viscoelastic model, taking into account a finite number of discrete slip systems in the matrix, has been suggested; high-temperature creep in such composites is conditioned by the dynamic recovery of the dislocation structure due to slip/climb motion of dislocations along the matrix/particle interfaces. In this article the proper formulation of the system of PDE’s generated by this model is presented, some existence results are obtained and the convergence of Rothe sequences, applied in the specialized software CDS, is studied.
LA - eng
KW - Strain and stress distributions in superalloys; high-temperature creep; viscoelasticity; interface diffusion; PDE’s of evolution; method of discretization in time; Rothe sequences; high-temperature creep; viscoelasticity; interface diffusion; weak formulation of evolution PDE; Rothe method
UR - http://eudml.org/doc/33015
ER -

References

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  10. 10.1016/1359-6454(95)00349-5, Acta materialia 44 (1996), 2557–2565. (1996) DOI10.1016/1359-6454(95)00349-5
  11. Micromodelling of creep in composites with perfect matrix/particle interfaces, Metallic Materials 36 (1998), 109–126. (1998) 
  12. Modelling discontinuous metal matrix composite behavior under creep conditions: effect of diffusional matter transport and interface sliding, Scripta metallurgica et materialia 30 (1994), 1201–1206. (1994) 
  13. Software package CDS for strain and stress analysis of materials consisting of several phases (in Czech), Programs and Algorithms of Numerical Mathematics 8 (1996), Proceedings of the summer school in Janov nad Nisou, pp. 199–206. 
  14. Micromechanical considerations in modelling of superalloy creep flow, Numerical Modelling in Continuum Mechanics 3 (1997), Proceedings of the conference in Prague, pp. 483–489. 
  15. A gradient theory of finite viscoelasticity, Archives of Mechanics 49 (1997), 589–609. (1997) Zbl0877.73025MR1468561
  16. Functional Analysis (in Russian), Mir, Moscow, 1967. (1967) MR0225130

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