Approximate analytical 2D-solution for the stresses and strains in eigenstrained cubic materials

Acta Mechanica

Volumn 136, Issue 3, 1999, Pages 171-192

  Dreyer, W ^a   Muller W H ^b   Olschewski, J ^c  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

^c BAM FEDERAL INSTITUTE FOR MATERIALS RESEARCH AND TESTING   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ELASTIC MODULI; FOURIER TRANSFORMS; STRAIN; STRESSES;

DISCRETE FOURIER TRANSFORM; EIGENSTRAINED CUBIC MATERIALS; ELASTIC ENERGY;

SOLIDS;

EID: 0342322880     PISSN: 00015970     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01179256     Document Type: Article

References (35)

1. Mader, W.: On the electron diffraction contrast caused by large inclusions. Phil. Mag. A. 55, 59-83 (1987).
2. Bischoff, E., Rühle, M., Sbaizero, O., Evans, A. G.: Microstructural studies of the interfacial zone of a SiC-fiber-reinforced Lithium-Aluminum Silicate glass-ceramic. J. Am. Ceram. Soc. 72, 741-745 (1989).
3. Stevens, R.: An introduction to Zirconia - Zirconia and Zirconia ceramics, 2nd ed., Magnesium Elektron Publication 113, Litho 2000, Twickenham 1986.
4. Hazotte, A., Bellet, D., Ganghoffer, J. F., Denis, S., Bastie, P., Simon, A.: On the contribution of internal mismatch stresses to the high-temperature broadening of gamma-ray diffraction peaks in a Ni-based single crystal. Phil. Mag. Lett. 66, 189-196 (1992).
5. Ignat, M., Buffiere, J.-Y., Chaix, J. M.: Microstructures induced by a stress gradient in a Nickel-base superalloy. Acta Metall. Mater. 41, 855-862 (1993).
6. Socrate, S., Parks, D. M.: Numerical determination of the elastic driving force for directional coarsening in Ni-superalloys. Acta Metall. Mater. 41, 2185-2209 (1993).
7. Hazotte, A., Lacaze, J.: Charactérisation quantitative de la microstructure des superalliages à base de nickel. La Revue de Métallurgie-CIT/Science et Génie des Matériaux, Février 277-294 (1994).
8. Mura, T.: Micromechanics of defects in solids, 2nd rev. ed., Dordrecht: Martinus Nijhoff 1987.
9. Morse, P. M., Feshbach, H.: Methods of theoretical physics, Part I. New York: McGraw-Hill 1953.
10. Sneddon, I. N.: The use of integral transforms. New York: Mc Graw-Hill 1972.
11. Bracewell, R. N.: The Fourier transform and its applications, 2nd rev. ed., New York: McGraw-Hill 1996.
12. Suquet, P.: Une méthode simplifiée pour le calcul de propriétés élastiques de matériaux hétérogènes à structure périodique. C. R. Acad. Sci. Paris. 311, 769-774 (1990).
13. Moulinec, H., Suquet, P.: A fast numerical method for computing the linear and nonlinear mechanical properties of composites. C. R. Acad. Sci. Paris, 318, 1417-1423 (1994).
14. Falk, G.: Theoretische Pysik auf der Grundlage einer allgemeinen Dynamik, Band Ia. Aufgaben und Ergänzungen zur Punktmechanik. Berlin: Springer 1966.
15. Mc Cormack, M., Khachaturyan, A. G., Morris Jr, J. W.: A two-dimensional analysis of the evolution of coherent precipitates in elastic media. Acta Metall. Mater. 40, 325-336 (1992).
16. Withers, P. J.: The determination of the elastic field of an ellipsoidal inclusion in a transversely isotropic medium and its relevance to composite materials. Phil. Mag. 59, 759-781 (1989).
17. Muskhelishvili, N. I.: Some basic problems of the mathematical theory of elasticity, 4th ed., Groningen: Noordhoff 1963.
18. Auld, B. A.: Acoustic fields and waves in solids. Vol. I, 2nd ed., Malabar: Krieger 1990.
19. Müller, W. H., Neumann, S.: An approximate analytical 3D-solution for the stresses and strains in eigenstrained cubic materials. Int. J. Solids Struct. 35 (22), 2931-2958 (1998).
20. ®. Ein System für Mathematik auf dem Computer, 2. Aufl., Bonn: Addison-Wesley 1992.
21. Dreyer, W.: Development of microstructure based viscoplastic models for an advanced design of single crystal hot section components. In: Periodic progress report, development of microstructural based viscoplastic models for an advanced design of single crystal hot section components (Olschewski, J., ed.). Brite/Euram Programme, BAM internal report A.1-17-A.1-29 Berlin (1995).
22. Müller, W. H.: Fourier transforms and their application to the formation of textures and changes of morphology in solids. In: IUTAM Symposium on Transformation Problems in Composite and Active Materials, pp. 61-72, Cairo, Egypt, March 9-12, 1997. Dordrecht: Kluwer Academic Publishers 1998.
23. Moulinec, H., Suquet, P.: A numerical method for computing the overall response of composites from images of their microstructures. In: Microstructure-property interactions in composite materials (Pyrz, R., ed.), pp. 235-246. Dordrecht: Kluwer Academic Publishers 1995.
24. Moulinec, H., Suquet, P.: A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comp. Meth. Appl. Mech. Engng. 157, 69-94 (1998).
25. Tien, K., Copley, S. M.: The effect of orientation and sense of applied uniaxial stress on the morphology of coherent gamma prime precipitates in stress annealed Nickel-base superalloy crystal. Metall. Trans. 2, 543-553 (1970).
26. Pineau, A.: Influence of uniaxial stress on the morphology of coherent precipitates during coarsening - elastic energy considerations. Acta Metall. 24, 559-564 (1975).
27. Khachaturyan, A. G., Shatalov, G. A.: Elastic-interaction potential of defects in a crystal. Soviet Physics - Solid State 11, 118-123 (1969).
28. Khachaturyan, A. G.: Theory of structural transformations in solids. New York: Wiley 1983.
29. Dreyer, W., Olschewski, J.: Order-disorder transitions under load in single crystal superalloys: theory. In: Solid - solid phase transformations (Johnson, W. C., Howe, J. M., Laughlin, D. E., Soffa, W. A., eds.), pp. 419-424. Warrendale: The Minerals, Metals & Materials Society 1994.
30. Jury, E. I.: Theory and application of the Z-transform method. Huntington: Krieger 1973.
31. Rosenfeld, A., Kak, A. C.: Digital picture processing, vol. 1., 2nd ed., New York: Academic Press 1982.
32. Henrici, P.: Applied and computational complex analysis, vol. 3. Discrete Fourier analysis-Cauchy integrals-construction of conformal maps-univalent functions. New York: Wiley 1986.
33. Davis, P. J., Polonsky, I.: Numerical interpolation, differentiation, and integration. In: Handbook of mathematical functions (Abramowitz, M., Stegun, I. A., eds.), Sect. 25. Washington: Applied Mathematics Series 1964.
34. Kittel, C.: Introduction to solid state physics, 4th ed., New York: Wiley 1971.
35. Gradshteyn, I. S., Ryzhik, I. M.: Table of integrals, series, and products. New York: Academic Press 1980.