A General Solution for Two-Dimensional Stress Distributions in Thin Films

[+] Author and Article Information
R. Krishnamurthy, D. J. Srolovitz

Princeton Institute for the Science and Technology of Materials, and Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08540

J. Appl. Mech 71(5), 691-696 (Nov 09, 2004) (6 pages) doi:10.1115/1.1782649 History: Received August 26, 2003; Revised April 22, 2004; Online November 09, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Timoshenko, S. P., and Goodier, J. N., 1970, Theory of Elasticity, McGraw-Hill, New York.
Larche,  F., and Cahn,  J. W., 1985, “The Interactions of Composition and Stress in Crystalline Solids,” Acta Metall., 33, pp. 333–357.
Downes,  J. R., and Faux,  D. A., 1997, “The Fourier-Series Method for Calculating Strain Distributions in Two Dimensions,” J. Phys.: Condens. Matter, 9, pp. 4509–4520.
Pickett,  G., 1944, “Application of the Fourier Method to the Solution of Certain Boundary Problems in the Theory of Elasticity,” ASME J. Appl. Mech., 66, pp. 176–182.
Faux,  D. A., 1994, “The Fourier-Series Method for the Calculation of Strain Relaxation in Strained-Layer Structures,” J. Appl. Phys., 75, pp. 186–192.
Faux,  D. A., and Haigh,  J., 1990, “Calculation of Strain Distributions at the Edge of Strained-Layer Structures,” J. Phys.: Condens. Matter, 2, pp. 10,289–10,302.
Glas,  F., 1987, “Elastic State and Thermodynamical Properties of Inhomogeneous Epitaxial Layers: Application to Immiscible III–V Alloys,” J. Appl. Phys., 62, pp. 3201–3208.
Glas,  F., 1991, “Coherent Stress Relaxation in a Half Space: Modulated Layers, Inclusions, Steps and a General Solution,” J. Appl. Phys., 70, pp. 3556–3571.
Fan,  Q. H., Fernandes,  A., and Periera,  E., 1998, “Stress-Relief Behavior in Chemical-Vapor-Deposited Diamond Films,” J. Appl. Phys., 84, pp. 3155–3158.
Dankov,  P. D., and Churaev,  P. V., 1950, Dokl. Akad. Nauk SSSR, 29, pp. 529–582.
Hou,  P. Y., and Cannon,  R. M., 1997, “The Stress State in Thermally Grown NiO Scales,” Mater. Sci. Forum, 251–254, pp. 325–332.
Eshelby,  J. D., 1957, “The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems,” Proc. R. Soc. London, Ser. A, 241, pp. 376–396.
Head,  A. K., 1953, “Edge Dislocations in Inhomogeneous Media,” Proc. R. Soc. London, Ser. B, 66, pp. 793–801.
Malvern, L. E., 1969, Introduction to the Mechanics of a Continuous Medium, Prentice-Hall, Englewood Cliffs, NJ.
Hu,  S. M., 1989, “Stress From a Parallelepipedic Thermal Inclusion in a Semispace,” J. Appl. Phys., 66, pp. 2741–2743.
Hu,  S. M., 1989, “Stress From Isolation Trenches in Silicon Substrates,” J. Appl. Phys., 67, pp. 1092–1101.
Churchill, R. V., 1963, Fourier Series and Boundary Value Problems, McGraw-Hill, New York.


Grahic Jump Location
Stresses due to a thermally mismatched inclusion; (a) shows contours of constant σxx in the film for a rectangular inclusion embedded in the center of the film and (b) is a comparison of the stresses obtained using Hu’s formulas and those obtained from our calculations for z=0.025
Grahic Jump Location
Exact and calculated results for the in-plane stress for a stress-free strain that is a function of z alone, i.e., εm=(z/H)3−z/H
Grahic Jump Location
Exact and calculated results for a stress-free strain that is sinusoidally modulated in x are shown at z=0.005
Grahic Jump Location
A schematic illustration of the steps involved in the Eshelby procedure
Grahic Jump Location
A schematic illustration of a thin film on a thick rigid substrate. The coordinate axes in film thickness H are labeled.



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In