Efficient model for the elastic load of film-substrate system involving imperfect interface effects

In this paper,an efficient calculation method based on discrete Fourier transformation is developed for evaluating elastic load induced elastic deformation fields of film-substrate system.Making use of 2 D discrete Fourier transformation,the elastic fields induced by Hertz load is harvested in frequency domain,and the displacement and stress fields across the interface are enforced to satisfy the elasticity conditions for each Fourier modes.Given arbitrary distributed stress field at free surface plane of the three types of film-substrate systems,unique resultant elastic field within the can be harvested.Hertz load of half space,elastic film on elastic substrate,elastic film on rigid substrate system and elastic film-substrate system with three types of imperfect interface models are investigated:(1)the spring-like imperfect interface model which can be described as:u^fk|zf=-h-u^sk|z^s=0=KTσKZ and u^fz|zf=-h-u^sz|z^s=0=KNσZZ;(2)the dislocation-like interface model,where interface displacement and stress components relation can be described as:u^fi|zf=0=k^uiju^si|z^s=0 andσ^fiz|z^f=0=σ^siz|zf=0=σ^siz|z^s=0;(3)the force-like interface model,where interface displacement and stress components relation can be described as:u^fi|z^f=0=u^si|z^s=0 andσ^fiz|z^f=0=k^tijσ^siz|z^s=0 respectively.Finally,several simulation examples are performed for verification of the reliability and efficiency of the proposed semi-analytical methods.