Abstract
The coupled nonlinear theory of diffusion in elastic media is considered. It is shown that the classical result of I.M. Lifschitz and V.V. Slezov (1990) for the critical size of an equilibrium void is also valid for coupled nonlinear diffusion in elastic media. Analytical solutions to some model problems are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Belova, I.V. and Murch, G.E. (1995). Thermal and diffusion-induced stresses in crystalline solids. Journal of Applied Physics 77(1), 127–134.
Bower, A.F. and Freund, L.B. (1994). Analysis of stress-induced void nucleation and growth in passivated interconnect lines, American Institute of Physics, Stress-induced phenomena in metallization, II International Workshop, Austin, 137–152.
Cheremski, P.G., Slezov, V.V. and Betekhtin, V.I. (1990). Voids in solid body, M., 375p. (in Russian).
Eshelby, J.D. (1956). The continuum theory of lattice defects. Solid State Physics, N.Y., Academic Press, 3, 79–144.
Goldstein, R.V. and Balueva, A.V. (1996). The influence of kinetic processes and medium degassing on crack growth. Proc. ECF 11-Mechanisms and Mechanics of Damage and Failure (Edited by J. Petit), Vol. II, 1549–1555.
Kachanov, L.M. (1964). On the fracture at the effect of liquid-metal media. Research of the elasticity and plasticity, LGU, 3, 225–232 (in Russian).
Lubov, V.Ja. (1981). Diffusion processes in non-homogeneous media, M., Science, 295p. (in Russian).
Lufrano, J. and Sofronis, P. (1996). Numerical analysis of the interaction of solute hydrogen atoms with the stress field of a crack. International Journal of Solids and Stuctures 33(12), 1709–1723.
Lufrano, J., Sofronis, P. and Birnbaum, H.K. (1996). Modeling of hydrogen transport and elastically accommodated hydride formation near a crack tip. Journal of the Mechanics and Physics of Solids 44(2), 179–205.
Markenscoff, X. and Paukshto, M. (1998). The cosserat spectrum in the theory of elasticity and applications. Proceedings of the Royal Society London 454, 631–643.
Mikhlin, S.G., Morozov, N.F. and Paukshto, M.V. (1995). The integral equations of the theory of elasticity, Stuttgart-Leipzig, 375p.
Mikhlin, S.G. (1996). On the Cosserat functions. Problems of Mathematical Analysis, LGU, 59–69 (in Russian).
Nowacki, W. and Olesiak, Z.S. (1991). Termodyfuzia w cialach stalych, PWN, Warszawa, 272p. (in Polish).
Romanov, A.E. and Samsonidze, G.G. (1988). Diffusion in elastic field wedge disclination. Letter in JTP 14, 1339–1342 (in Russian).
Sullivan, T.D. (1989). Thermal dependence of voiding in narrow aluminum microelectronic interconnects. Applied Physics-Letters 55(23), 2399–2401.
Timoshenko, S.P. and Goodier, J.N. (1970). Theory of elasticity, McGraw-Hill, N.Y.
Yokobori, Jr., A.T., Nemoto, T., Satoh, K. and Yamada, T. (1996). Numerical analysis on hydrogen diffusion and concentration in solid with emission around the crack tip. Engineering Fracture Mechanics 55(1), 47–60.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Paukshto, M. Diffusion-induced stresses in solids. International Journal of Fracture 97, 227–236 (1999). https://doi.org/10.1023/A:1018618918888
Issue Date:
DOI: https://doi.org/10.1023/A:1018618918888