A closed-form analytical solution to thermoelastic bending problems of multilayered beams is obtained by an alternative two-variable method. There are only two unknowns to be solved and two equilibrium conditions to be satisfied in the present analysis. Differences among zero-strain axis, zero-stress axis, bending axis and centroidal axis are compared.
Issue Section:
Technical Briefs
1.
Rosse
, 1908, “Bimetallic Mirrors Made by Electro-Depositions
,” Nature (London)
0028-0836, 78
(2025
), pp. 366
–367
.2.
Stoney
, G. G.
, 1909, “The Tension of Metallic Films Deposited by Electrolysis
,” Proc. Phys. Soc. London
0370-1328, 82
, pp. 172
–175
.3.
Timoshenko
, S.
, 1925, “Analysis of Bi-Metal Thermostats
,” J. Opt. Soc. Am.
0030-3941, 11
, pp. 233
–255
.4.
Sun
, C. T.
, Achenbach
, J. D.
, and Hermann
, G.
, 1968, “Continuum Theory for a Laminated Medium
,” ASME J. Appl. Mech.
0021-8936, 28
, pp. 467
–475
.5.
Timoshenko
, S.
, 1955, Strength of Materials, Part I: Elementary Theory and Problems
, Van Nostrand
, New York
.6.
Hearn
, E. J.
, 1977, Mechanics of Materials
, Pergamon
, Oxford, UK
.7.
Beer
, F. P.
, and Johnston
, Jr., E. R.
, 1981, Mechanics of Materials
, McGraw-Hill
, New York
.8.
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.
0021-8979, 40
(8
), pp. 3273
–3279
.9.
Olsen
, G. H.
, and Ettenberg
, M.
, 1977, “Calculated Stresses in Multilayered Heteroepitaxial Structures
,” J. Appl. Phys.
0021-8979, 48
(6
), pp. 2543
–2547
.10.
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.
0021-8979, 54
(1
), pp. 83
–85
.11.
Liu
, H. C.
, and Murarka
, S. P.
, 1992, “Elastic and Viscoelastic Analysis of Stress in Thin Films
,” J. Appl. Phys.
0021-8979, 72
(8
), pp. 3458
–3463
.12.
Freund
, L. B.
, 1993, “The Stress Distribution and Curvature of a General Compositionally Graded Semiconductor Layer
,” J. Cryst. Growth
0022-0248, 132
(1–2
), pp. 341
–344
.13.
Freund
, L. B.
, 1996, “Some Elementary Connections Between Curvature and Mismatch Strain in Compositionally Graded Thin Films
,” J. Mech. Phys. Solids
0022-5096, 44
(5
), pp. 723
–736
.14.
Sorensen
, B. F.
, Sarraute
, S.
, Jorgensen
, O.
, and Horsewell
, A.
, 1998, “Thermally Induced Delamination of Multilayers
,” Acta Mater.
1359-6454, 46
(8
), 2603
–2615
.15.
Pitakthapanaphong
, S.
, and Busso
, E. P.
, 2002, “Self-Consistent Elastoplastic Stress Solutions for Functionally Graded Material Systems Subjected to Thermal Transients
,” J. Mech. Phys. Solids
0022-5096, 50
(4
), 695
–716
.16.
Hsueh
, C. H.
, and Evans
, A. G.
, 1985, “Residual Stresses in Metal∕Ceramic Bonded Strips
,” J. Am. Ceram. Soc.
0002-7820, 68
(5
), pp. 241
–248
.17.
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.
0021-8979, 62
(11
), pp. 4438
–4444
.18.
Chu
, S. N. G.
, 1998, “Elastic Bending of Semiconductor Wafer Revisited and Comments on Stoney’s Equation
,” J. Electrochem. Soc.
0013-4651, 145
(10
), pp. 3621
–3627
.19.
Chuang
, T. J.
, and Lee
, S.
, 2000, “Elastic Flexure of Bilayered Beams Subjected to Strain Differentials
,” J. Mater. Res.
0884-2914, 15
(12
), pp. 2780
–2788
.20.
Hsueh
, C. H.
, 2002, “Modeling of Elastic Deformation of Multilayers Due to Residual Stresses and External Bending
,” J. Appl. Phys.
0021-8979, 91
(12
), pp. 9652
–9656
.21.
Hsueh
, C. H.
, 2002, “Thermal Stresses in Elastic Multilayer Systems
,” Thin Solid Films
0040-6090, 418
(2
), pp. 182
–188
.22.
Hsueh
, C. H.
, Lee
, S.
, and Chuang
, T. J.
, 2003, “An Alternative Method of Solving Multilayered Bending Problems
,” ASME J. Appl. Mech.
0021-8936, 70
(1
), pp. 151
–154
.23.
Hsueh
, C. H.
, and Lee
, S.
, 2003, “Modeling of Elastic Thermal Stresses in Two Materials Joined by a Graded Layer
,” Composites, Part B
1359-8368, 34
(8
), pp. 747
–752
.24.
Hsueh
, C. H.
, 2003, “Stress Distribution and Curvature in Graded Semiconductor Layers
,” J. Cryst. Growth
0022-0248, 258
(3–4
), pp. 302
–309
.25.
Zhang
, N. H.
, and Xing
, J. J.
, 2006, “An Alternative Model for Elastic Bending Deformation of Multilayered Beams
,” J. Appl. Phys.
0021-8979, 100
, pp. 103519
.Copyright © 2008
by American Society of Mechanical Engineers
You do not currently have access to this content.