I guess it should not be too complicated...
I have found an equation to calculate the residual stress in the coating on the substrate.
It is given in some papers considering Thermal barriere Coatings:
sigma(ox)= - (E(ox)*del_T*(alpha(met)-alpha(ox)))/((E(ox)/E(met))*(d(ox)/d(met))*(1-v(met))+(1-v(ox)))
(ox- oxide, met-metal)
E - Youngs module
v - Poisson contraction number
alpha - coeff. of thermal expansion
d - thickness
Nevertheless, I can not find the similar equation for the calculation of the residual stress for rough surface (surface with curvature radius R for instance). One I found considered the oxide growth, but I don't have an oxide growth, just two laminae, with strong adhesion between them (no delamination occurs). Since the both materials are brittle, I assume no plastic deformation. I also assume no initial cracks.
(it is supposed to be a simple proof that the cracks are favorized on some positions within the surface of the coating).
So, does anybody knows some valuable literature where one could simply find such relation?
I have found an equation to calculate the residual stress in the coating on the substrate.
It is given in some papers considering Thermal barriere Coatings:
sigma(ox)= - (E(ox)*del_T*(alpha(met)-alpha(ox)))/((E(ox)/E(met))*(d(ox)/d(met))*(1-v(met))+(1-v(ox)))
(ox- oxide, met-metal)
E - Youngs module
v - Poisson contraction number
alpha - coeff. of thermal expansion
d - thickness
Nevertheless, I can not find the similar equation for the calculation of the residual stress for rough surface (surface with curvature radius R for instance). One I found considered the oxide growth, but I don't have an oxide growth, just two laminae, with strong adhesion between them (no delamination occurs). Since the both materials are brittle, I assume no plastic deformation. I also assume no initial cracks.
(it is supposed to be a simple proof that the cracks are favorized on some positions within the surface of the coating).
So, does anybody knows some valuable literature where one could simply find such relation?
