The residual stresses in thin films are explained using elementary mechanics. In particular, the range of validity of the well-known Stoney’s formula is examined using a strength of materials approach. An improved formula is obtained. The results of these analyses can also be used to compute energy release rates for cracks in thin film systems. Some simple examples of such applications are given. [S1043-7398(00)01603-0]
Issue Section:
Technical Papers
1.
Frank
, F. C.
, and Van Der Merwe
, J. H.
, 1949
, “One Dimensional Dislocation II. Misfitting Monolayers and Oriented Overgrowth
,” Proc. R. Soc. London Series A
, 198
, pp. 216
–225
.2.
Doerner
, F. M.
, and Nix
, D. W.
, 1988
, “Stresses and Deformation Processes in Thin Films on Substrates
,” CRC Crit. Rev. Solid State Mater. Sci.
, 14
, No. 13
, pp. 225
–268
.3.
Nix
, W. D.
, 1989
, “Mechanical Properties of Thin Films
,” Metall. Trans.
, 20A
, pp. 2217
–2245
.4.
Thouless
, M. D.
, Olsson
, E.
, and Gupta
, A.
, 1992
, “Cracking of Brittle Films on Elastic Substrates
,” Acta Metall. Mater.
, 40
, No. 6
, pp. 1287
–1292
.5.
Thouless
, M. D.
, Hutchinson
, J. W.
, and Liniger
, E. G.
, 1992
, “Plane-Strain, Buckling-Driven Delamination of Thin Films: Model Experiments and Mode II Fracture
,” Acta Metall. Mater.
, 40
, No. 10
, pp. 2639
–2649
.6.
Evans
, A. G.
, and Hutchinson
, J. W.
, 1994
, “On the Mechanics of Delamination and Spalling in Compressed Films
,” Int. J. Solids Struct.
, 20
, No. 5
, pp. 455
–466
.7.
Drory
, D. M.
, and Evan
, A. G.
, 1990
, “Experimental Observations of Substrate Fracture Caused by Residual Stressed Films
,” J. Am. Ceram. Soc.
, 73
, No. 3
, pp. 634
–638
.8.
Evans
, A. G.
, and Hu
, M. S.
, 1989
, “The Cracking and Decohesion of Thin Films on Ductile Substrates
,” Acta Metall.
, 37
, No. 3
, pp. 917
–925
.9.
Hu
, M. S.
, Thouless
, M. D.
, and Evans
, A. G.
, 1988
, “The Decohesion of Thin Films from Brittle Substrates
,” Acta Metall.
, 36
, No. 5
, pp. 1301
–1307
.10.
Hutchinson
, J. W.
, and Suo
, Z.
, 1992
, “Mixed Mode Cracking in Layered Materials
,” Adv. Appl. Mech.
, 29
, pp. 63
–191
.11.
Jiao
, J.
, Gurumurthy
, C. K.
, Kramer
, E. J.
, Sha
, Y.
, Hui
, C. Y.
, and Borgesen
, P.
, 1998
, “Measurement of Interfacial Fracture Toughness under Combined Mechanical and Thermal Stresses
,” ASME J. Electron. Packag.
, 120
, pp. 349
–353
.12.
Doerner
, F. M.
, Gardner
, D. S.
, and Nix
, D. W.
, 1986
, “Plastic Properties of Thin Films on Substrates as Measured by Submicron and Substrate Curvature Techniques
,” J. Mater. Res.
, 1
, No. 6
, pp. 845
–851
.13.
Thouless
, M. D.
, Gupta
, J.
, and Harper
, J. M. E.
, 1993
, “Stress Development and Relaxation in Copper Films During Thermal Cycling
,” J. Mater. Res.
, 8
, No. 6
, pp. 1845
–1852
.14.
Dempsey
, J. P.
, and Sinclair
, G. B.
, 1979
, “On the Stress Singularities in the Plane Elasticity of the Composite Wedge
,” J. Elast.
, 9
, pp. 373
–391
.15.
Bogy
, D. B.
, 1971
, “Two Edge-Bonded Elastic Wedges of Different Materials and Wedge Angles Under Surface Tractions
,” ASME J. Appl. Mech.
, 94
, pp. 377
–386
.16.
Stoney
, G. G.
, 1909
, “The Tension of Metallic Films Deposited by Electrolysis
,” Proc. Roy. Soc. London A Math.
, 82
, pp. 172
–175
.17.
Liu
, X. H.
, Suo
, Z.
, and Ma
, Q.
, 1998
, “Split Singularities: Stress Field Near the Edge of Silicon Die on Polymer Substrate
,” Acta Metall.
, 47
, No. 1
, pp. 67
–76
.18.
Suo
, Z.
, and Hutchinson
, J. W.
, 1990
, “Interface Cracks Between Two Elastic Layers
,” Int. J. Fract.
, 43
, pp. 1
–18
.19.
Suo
, Z.
, and Hutchinson
, J. W.
, 1989
, “Steady-State Cracking in Brittle Substrate Beneath Adherent Films
,” Int. J. Solids Struct.
, 25
, No. 11
, pp. 1337
–1353
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