On the Stoney Formula for a Thin Film/Substrate System With Nonuniform Substrate Thickness

2007 ◽  
Vol 74 (6) ◽  
pp. 1276-1281 ◽  
Author(s):  
X. Feng ◽  
Y. Huang ◽  
A. J. Rosakis
Keyword(s):  
Thin Film ◽  
Misfit Strain ◽  
Film Stress ◽  
Substrate Thickness ◽  
Full Field ◽  
Temperature Changes ◽  
Thin Film Stress ◽  
Curvature Measurements ◽  
Film Substrate ◽  
Stoney Formula

Current methodologies used for the inference of thin film stress through system curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis, and co-workers [Acta Mech. Sinica, 21, pp. 362–370 (2005); J. Mech. Phys. Solids, 53, 2483–2500 (2005); Thin Solid Films, 515, pp. 2220–2229 (2006); J. Appl. Mech., in press; J. Mech. Mater. Struct., in press] established methods for the film/substrate system subject to nonuniform misfit strain and temperature changes. The film stresses were found to depend nonlocally on system curvatures (i.e., depend on the full-field curvatures). These methods, however, all assume uniform substrate thickness, which is sometimes violated in the thin film/substrate system. Using the perturbation analysis, we extend the methods to nonuniform substrate thickness for the thin film/substrate system subject to nonuniform misfit strain.

Stresses in a Multilayer Thin Film/Substrate System Subjected to Nonuniform Temperature

2008 ◽  
Vol 75 (2) ◽  
Author(s):  
X. Feng ◽  
Y. Huang ◽  
A. J. Rosakis
Keyword(s):  
Thin Film ◽  
Field Measurements ◽  
Film Stress ◽  
Effect Of Temperature ◽  
Multilayer Thin Film ◽  
Nonuniform Temperature ◽  
Curvature Invariant ◽  
Full Field ◽  
Curvature Measurements ◽  
Film Substrate

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to uniform film stress and system curvature states over the entire system of a single thin film on a substrate. By considering a circular multilayer thin film/substrate system subjected to nonuniform temperature distributions, we derive relations between the stresses in each film and temperature, and between the system curvatures and temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “nonlocal” part, which reflects the effect of temperature of other points on the location of scrutiny. We also derive relations between the film stresses in each film and the system curvatures, which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a “nonlocal” dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. The interfacial shear tractions between the films and between the film and substrate are proportional to the gradient of the first curvature invariant, and can also be inferred experimentally.

Extension of Stoney’s Formula to Arbitrary Temperature Distributions in Thin Film/Substrate Systems

2006 ◽  
Vol 74 (6) ◽  
pp. 1225-1233 ◽  
Author(s):  
Y. Huang ◽  
A. J. Rosakis
Keyword(s):  
Thin Film ◽  
Field Measurements ◽  
Film Stress ◽  
Effect Of Temperature ◽  
Curvature Invariant ◽  
Full Field ◽  
Polar Components ◽  
Temperature Distributions ◽  
Curvature Measurements ◽  
Film Substrate

Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states that are assumed to remain uniform over the entire film/substrate system. By considering a circular thin film/substrate system subject to nonuniform and nonaxisymmetric temperature distributions, we derive relations between the film stresses and temperature, and between the plate system’s curvatures and the temperature. These relations featured a “local” part that involves a direct dependence of the stress or curvature components on the temperature at the same point, and a “nonlocal” part that reflects the effect of temperature of other points on the location of scrutiny. Most notably, we also derive relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary nonuniformities. These relations also feature a “nonlocal” dependence on curvatures making full-field measurements of curvature a necessity for the correct inference of stress. Finally, it is shown that the interfacial shear tractions between the film and the substrate are related to the gradients of the first curvature invariant and can also be inferred experimentally.

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