Research On The Contact Problem For Multilayer Graded Piezoelectric Coating Under The Conducting Indenter

Piezoelectric materials(PM)are widely used in sensors,transformers,micro motors and other precision instruments due to their unique electro-mechanical coupling characteristics.In practical engineering applications,brittle piezoelectric materials subjected to high strength loads are easy to experience the electrodynamic contact damage,resulting in failure and destruction of piezoelectric elements.In order to improve the mechanical properties of piezoelectric materials,the concept of functionally graded material(FGM)was introduced into piezoelectric materials.The functionally graded piezoelectric material(FGPM)which was obtained have the electro-mechanical coupling properties of piezoelectric materials and the properties of functionally graded materials.A large number of studies have shown that the functionally graded piezoelectric materials using as coatings can alter the contact mechanical properties of piezoelectric materials and suppress contact damage and achieve the designability.Due to the complexity of the governing equation which describe the functionally graded piezoelectric materials,previous studies mainly focus on the material parameters of FGPM varies as exponential function,and lack of researches on the other kinds of functionally graded piezoelectric materials.In this paper,a multilayer gradient piezoelectric coating model is established to solve the frictionless contact and sliding contact problems of functionally gradient piezoelectric material(FGPM)coatings with different kinds of varying form of material parameters under the conducting indenter.The influence of the gradient variation of material parameters on the force-electric response in functionally gradient piezoelectric coatings for two-dimensional frictionless and sliding friction contact mechanics are considered.The main contents of this paper are as follows:(1)The mechanical model of the multilayer functionally graded piezoelectric material coating is established.The basic solutions of the coating under concentrated linear load,concentrated linear charge and tangential linear load are obtained by using Fourier integral transformation and transfer matrix method.(2)Using the fundamental solution,the frictionless contact problem of multilayer functionally graded piezoelectric coatings with different kinds of materials parameters under the conducting indenter is solved.The effect of parameter gradient variation on the electromechanical response of gradient piezoelectric coating was analyzed.(3)Based on the fundamental solutions which has been obtained,the singular integral equation for the friction contact problem of multilayer functionally gradient piezoelectric coating under the action of rigid conducting cylindrical indenter is derived.The effects of materials parameter with gradient variation,applied load and friction coefficient on the electro-mechanical response of the gradient piezoelectric coating were obtained by numerical method.By studying the frictionless and frictional contact problems of functionally gradient piezoelectric coatings with different material parameter variations under the action of conducting indenter,the following conclusions are obtained:(1)The multilayer piezoelectric materials model in this paper can be used to simulate the functional gradient piezoelectric coatings with different material parameters varying in different functional forms.The results obtained by choosing 13 sub-layers to calculate the mechanical response of the functional gradient piezoelectric coating under the action of the conducting indenter are in good agreement with the previous results.(2)The curve of load vs.generalized displacement(indentation,potential),contact stress and charge distribution in the two-dimensional frictionless contact problem of functionally gradient piezoelectric coatings can be improved by adjusting the gradient parameters.When the functionally gradient piezoelectric coating indented by the rigid flat conducting indenter,the indentation,electrical potential,maximum surface stress,maximum surface electrical charge,maximum stress at the interface and maximum electrical displacement at the interface increase with the gradient index increases for hard coating.When the functionally gradient piezoelectric coating indented by the rigid flat rigid conducting cylindrical indenter,the indentation and potential increase with the gradient index value increases for hard coating,while the contact radius becomes larger,the maximum surface stress,surface maximum charge,maximum stress at the interface and maximum electrical displacement will decrease.The results for soft coatings.is reversed(3)The two-dimensional sliding friction contact problem for functionally gradient piezoelectric coating under conducting cylindrical indenter was considered.when the materials parameters of the functionally gradient piezoelectric coating varying as the power function.The maximum contact stress and surface charge in the contact region and the maximum tensile stress in the edge of the contact region decreases with the increase of gradient index for hard coating while the indentation and potential increase under the same external load.The results are completely reversed for soft coating.The electric displacement of the normal stress in the contact area have little change and the in-plane stress and electric displacement have great changes with the friction coefficient change.The internal maximum compressive stress and tensile stress increase with the friction coefficient increases in both hard and soft coatings.The research results in this paper are of great significance for the improvement of contact failure and damage by using the gradient piezoelectric coating.The results can be used as a basis for the design of gradient piezoelectric coating.