0
BRIEF NOTES

An Alternative Method of Solving Multilayer Bending Problems

[+] Author and Article Information
C. H. Hsueh

Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6068

S. Lee

Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu, Taiwan

T. J. Chuang

Ceramics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899-8521

J. Appl. Mech 70(1), 151-154 (Jan 23, 2003) (4 pages) doi:10.1115/1.1526123 History: Received March 17, 2002; Revised July 26, 2002; Online January 23, 2003
Copyright © 2003 by ASME
Your Session has timed out. Please sign back in to continue.

References

Rosse,  1908, “Bimetallic Mirrors made by Electro-Deposition,” Nature (London), 78(2025), pp. 366–367.
Hu,  S. M., 1991, “Stress-Related Problems in Silicon Technology,” J. Appl. Phys., 70(6), pp. R53–R80.
Stoney,  G. G., 1909, “The Tension of Metallic Films Deposited by Electrolysis,” Proc. Phys. Soc. London, 82, pp. 172–175.
Timoshenko,  S., 1925, “Analysis of Bi-Metal Thermostats,” J. Opt. Soc. Am., 11, pp. 233–255.
Saul,  R. H., 1969, “Effect of a GaAsxP1−x Transition Zone on the Perfection of GaP Crystals Grown by Deposition onto GaAs Substrates,” J. Appl. Phys., 40(8), pp. 3273–3279.
Olsen,  G. H., and Ettenberg,  M., 1977, “Calculated Stresses in Multilayered Heteroepitaxial Structures,” J. Appl. Phys., 48(6), pp. 2543–2547.
Feng,  Z. C., and Liu,  H. D., 1983, “Generalized Formula for Curvature Radius and Layer Stresses Caused by Thermal Strain in Semiconductor Multilayer Structures,” J. Appl. Phys., 54(1), pp. 83–85.
Iancu,  O. T., Munz,  D., Eigenman,  B., Scholtes,  B., and Macherauch,  E., 1990, “Residual Stress State of Braze Ceramic/Metal Compounds, Determined by Analytical Methods and X-Ray Residual Stress Measurements,” J. Am. Ceram. Soc., 73(5), pp. 1144–1149.
Jou,  J. H., and Hsu,  L., 1992, “Bending-Beam Measurement of Solvent Diffusions in Polyimides: Theoretical and Experimental,” J. Appl. Polym. Sci., 44, pp. 191–198.
Liu,  H. C., and Murarka,  S. P., 1992, “Elastic and Viscoelastic Analysis of Stress in Thin Films,” J. Appl. Phys., 72(8), pp. 3458–3463.
Chuang,  T. J., and Lee,  S., 2000, “Elastic Flexure of Bilayered Beams Subjected to Strain Differentials,” J. Mater. Res., 15(12), pp. 2780–2788.
Timoshenko, S., 1955, Strength of Materials, Part I: Elementary Theory and Problems, D. Van Norstrand Company, New York.
Hearn, E. J., 1977, Mechanics of Materials, Pergamon Press, Oxford, UK.
Beer, F. P., and Johnston, E. R. Jr., 1981, Mechanics of Materials, McGraw-Hill, New York.
Hsueh,  C. H., and Evans,  A. G., 1985, “Residual Stresses in Metal/Ceramic Bonded Strips,” J. Am. Ceram. Soc., 68(5), pp. 241–248.
Townsend,  P. H., Barnett,  D. M., and Brunner,  T. A., 1987, “Elastic Relationships in Layered Composite Media With Approximation for the case of Thin Films on a Thick Substrate,” J. Appl. Phys., 62(11), pp. 4438–4444.

Figures

Grahic Jump Location
Schematics showing bending of a multilayer strip due to residual stresses and external bending: (a) stress-free condition, (b) unconstrained strains due to temperature change ΔT, (c) constrained strain to maintain displacement compatibility, (d) bending induced by asymmetric stresses, and (e) external bending
Grahic Jump Location
Schematics showing (a) equivalent cross section of the bilayer to account for different Young’s moduli between the two layers when the bilayer is subjected to only external bending and (b) the bending axis in the cross section of the bilayer is located at the same position as the neutral axis in the equivalent cross section
Grahic Jump Location
Normalized position of neutral axis as a function of normalized applied bending moment, M/Ests2f−αs)ΔT, for GaAs/Si bilayer systems with tf/ts=0.2

Tables

Errata

Discussions

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