1 - Erich Schmid Institute

E
Mechanics of Residually Stressed Coated
Systems: Derivation of Basic Equations
S. Massl a , J. Keckes b and R. Pippan a
a Erich Schmid Institute of Materials Science, Austrian Academy of Sciences, A–8700
Leoben, Austria
b Department Materials Physics, University of Leoben, A–8700 Leoben, Austria
Abstract
The basic mechanical equations necessary for the description of depth profiles of residual
stresses in coated systems and for the calculation procedure of the ion beam layer
removal method developed are derived. Here, the stresses are assumed to originate from
the difference of the coefficients of thermal expansion of the substrate and the thin film
subjected to a temperature difference ∆T = 0. A sign convention is introduced in order
to assure a uniform description of residually stressed systems. Finally, the stress profile
of an arbitrary model system subjected to a temperature difference of ∆T = 300K is
calculated and compared with Stoney’s equation. The most important equations are
highlighted.
E–1
E