Title:
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On one mathematical model of creep in superalloys (English) |
Author:
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Vala, Jiří |
Language:
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English |
Journal:
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Applications of Mathematics |
ISSN:
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0862-7940 (print) |
ISSN:
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1572-9109 (online) |
Volume:
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43 |
Issue:
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5 |
Year:
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1998 |
Pages:
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351-380 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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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. (English) |
Keyword:
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Strain and stress distributions in superalloys |
Keyword:
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high-temperature creep |
Keyword:
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viscoelasticity |
Keyword:
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interface diffusion |
Keyword:
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PDE’s of evolution |
Keyword:
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method of discretization in time |
Keyword:
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Rothe sequences |
MSC:
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73F05 |
MSC:
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73F15 |
MSC:
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74D05 |
MSC:
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74D10 |
MSC:
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74H99 |
idZBL:
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Zbl 1042.74511 |
idMR:
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MR1644132 |
DOI:
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10.1023/A:1022286318503 |
. |
Date available:
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2009-09-22T17:58:41Z |
Last updated:
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2020-07-02 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/134393 |
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Reference:
|
[Ap] Appell J., Zabrejko P.P.: Nonlinear Superposition Operators.Cambridge University Press, Cambridge, 1990. MR 1066204 |
Reference:
|
[De] Denis S., Hazotte A., Wen I.H., Gautieu E.: Micromechanical approach by finite elements to the microstructural evolutions and mechanical behaviour of two-phase metallic alloys.IUTAM’95 symposium on micromechanics of plasticity and damage of multiphase materials in Paris, Pineau A., Zaoui A. (eds.), Kluwer Academic Publishers, Dordrecht, 1995, pp. 289–296. |
Reference:
|
[Ga] Gajewski H., Gröger K., Zacharias K.: Nonlinear Operator Equations and Operator Differential Equations (in German).Akademie Verlag, Berlin, 1974. |
Reference:
|
[Gr] Greguš M., Švec M., Šeda V.: Ordinary Differential Equations (in Slovak).Alfa, Bratislava, 1985. |
Reference:
|
[Ka$^1$] Kačur J.: Solution to strongly nonlinear parabolic problem by a linear approximation scheme. Preprint M2-96.Comenius University (Faculty of Mathematics and Physics), Bratislava, 1996. MR 1670689 |
Reference:
|
[Ko] Kolář V.: Nonlinear mechanics (in Czech).ČSVTS, Ostrava, 1985. |
Reference:
|
[Ma] Maz’ya V.G.: Sobolev spaces (in Russian).Leningrad University Press, Leningrad (St. Petersburg), 1985. MR 0807364 |
Reference:
|
[Ne] Nečas J., Hlaváček I.: Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction.Elsevier, Amsterdam, 1981. MR 0600655 |
Reference:
|
[Pe] Petterman H.E., Böhm H.J., Rammerstorfer F.G.: An elasto-plastic constitutive law for composite materials.Modelling in materials science and processing, Rappaz M., Kedro M. (eds.), European Commission (COST 512 Action Management Committee), Brussels, 1996, pp. 384–392. |
Reference:
|
[Sv] Svoboda J., Lukáš P.: Modelling of kinetics of directional coarsening in Ni-superalloys.Acta materialia 44 (1996), 2557–2565. 10.1016/1359-6454(95)00349-5 |
Reference:
|
[Sv$^1$] Svoboda J., Vala J.: Micromodelling of creep in composites with perfect matrix/particle interfaces.Metallic Materials 36 (1998), 109–126. |
Reference:
|
[Va] Vala J., Svoboda J., Kozák V., Čadek J.: 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. |
Reference:
|
[Va$^1$] Vala J.: 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. |
Reference:
|
[Va$^2$] Vala J.: Micromechanical considerations in modelling of superalloy creep flow.Numerical Modelling in Continuum Mechanics 3 (1997), Proceedings of the conference in Prague, pp. 483–489. |
Reference:
|
[Vs] Valanis K.C.: A gradient theory of finite viscoelasticity.Archives of Mechanics 49 (1997), 589–609. Zbl 0877.73025, MR 1468561 |
Reference:
|
[Yo] Yosida K.: Functional Analysis (in Russian).Mir, Moscow, 1967. MR 0225130 |
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