There are many sources for the internal stresses (i.e., better to say internal strain) in coated material such as thermal expansion coefficient difference between the coated material and the substrate, which results residual stresses at the ambient or operation temperatures. Similarly for the  hetero epitaxially grown thin films,  the main source for internal stress  is the lattice spacİng miss matched.  Or the possible phase transition  taking place in the coated material during the processing period may be also the source for the residual stresses.

No matter what is the cause for internal strains,  there three main mechanism for the internal  stress relieve; 1) micro plasticity which involves movement s of point  and line defects (dislocations and disinclination)  into minimum internal energy configurations (polygonization) .2) Stored energy relieve by the formation of surface undulation and roughness. 3) the recrystallization by the formation of stress free new grain structure at elevated annealing temperatures. 

The onset of the plastic deformation is characterized by the yield strength. The higher the yield strength  of a given material lower would be the initiation of the micro plasticity by activation of dislocation mechanism (slip, climb and glide etc.) by thermal fluctuations at the given annealing temperature. Therefore, if the substrate would be more stiff then the coating material,  the internal stresses  of  the coating material would have tough time to relieve through the strain relaxation of the substrate material.

BUT NOW ANOTHER MECHANİSM ENTERS INTO SCENARİO WHICH IS THE FORMATION   OF THE SURFACE ROUGHNESS THAT DECREASES  THE BULK ELASTIC STORED ENERGY OF THE COATING MATERİALS.

IN THE CASE OF HETERO-EPITAXIAL GROWN FILM, THE FORMATION OF DISLOCATION TANGLES AND TREADS AT THE INTERFACE BETWEEN FILM AND THE SUBSTRATE  WOULD BE THE MAIN MECHANISM FOR THE STRAIN RELAXATION DURING THE ANNEALING. 

I think,  I  would prefer  a substrate having higher yield strength than the coating material if ı don't worry about the surface roughness on the coating otherwise visa verse    I would select a coating material having high rigidity compared to substrate to relive the strain through the plastic deformation of the underlying substrate.  But this structure would be susceptible for the surface flaws, which enhances the   initiation of fracture mechanisms. 

dear

read this link

file:///C:/Users/ssc/Downloads/JMMCE20120200003_51246919.pdf

best regard

Thank you for you all dear colleagues and I do appreciate you valuable answers and are very helpful.