Frictional Contact Analysis Of Functionally Graded Piezoelectric Materials

Piezoelectric materials possess superior mechanical performance and intrinsic electro-mechanical coupling effects.They have been widely used in various hi-tech smart structures and devices,such as transducers,actuators,piezoelectric ceramic transformers,piezoelectric ultrasonic motor and micro power generators.In practical engineering applications,because of the intrinsic brittleness of piezoelectric materials,the piezoelectric devices will easily suffer electro-mechanical contact damage at surface when subjected to the highly concentrated local electro-mechanical loading,which will result in the failure or destruction of the piezoelectric components and devices.In addition,the above novel smart structures and piezoelectric devices are not only subjected to the coupled highly concentrated electro-mechanical loads,but also often served in the vibration environment.Therefore,fretting contact damage and fatigue failure inevitably occurs in piezoelectric smart devices,which will lead to the failure of the smart devices.Theoretical and experimental investigations show that functionally graded materials(FGMs),used as coating,can efficiently adjust the distribution of the contact stress on material surface and improve the contact damage.These properties can hardly be approached for common homogeneous materials.This paper aims to use the functionally graded piezoelectric coating to adjust the distribution of the surface contact stress and electric displacement of the smart structures and devices,resist the surface contact damage.The two-dimensional sliding frictional contact,two-dimensional fretting contact,axisymmetric frictionless contact,axisymmetric partial slip contact and torsional fretting contact problem of functionally graded piezoelectric materials(FGPMs)are studied deeply in this paper.The main contents and conclusions of the paper include:(1)A new effective method is proposed to solve the two-dimensional sliding frictional contact between a rigid conducting cylindrical punch and an FGPM coated half-plane.The exponential model is used to simulate the electro-mechanical properties of the FGPMs.The Coulomb type friction is considered over the whole contact region.Using the Fourier integral transform,the fundamental solution with a concentrated line load and a concentrated line electric charge is reduced to a set of coupled Cauchy singular integral equations.By using the least squares method together with an iterative procedure,the present problem is effectively solved to obtain the optimal solution.The results indicate that the conventional method results in the spike of the distribution of the normal contact stress and electric displacement.The least squares method can provide smooth results for the sliding frictional contact problem.The reduction in the gradient index and friction coefficient of FGPM coating can lead to a decrease in the maximum tensile stress at the trailing end of the sliding region and maximum electric displacement at the edge of the contact region,and hence reducing and even preventing the electro-mechanical sliding frictional contact damage of smart devices.(2)The two-dimensional fretting contact between an FGPM coated half-plane and a rigid conducting cylindrical punch is considered.We will first solve the purely normal loading case,and then the cycled tangential loading case.The whole contact region is composed of an inner stick region and two outer slip regions in which Coulomb's friction law is assumed.The results indicate that the maximum value of the in-plane tensile stress and the electric displacement occurs at the edges of the contact region,which implies the possible site of the electro-mechanical contact damage and fretting crack initiation.The change in the gradient index of coating can adjust the distributions of the surface contact stress and electric displacement,and hence suppress the surface cracking and enhance the resistance of the fretting contact damage.(3)The axisymmetric frictionless contact of an FGPM coated half-space subjected to three typical rigid conducting punches(i.e.flat circular punch,spherical punch and conical punch)is investigated.By employing the Hankel integral transform technique,the fundamental solution of the axisymmetric contact problem is obtained,and then is transformed to a set of singular integral equations of the first kind.It is found that the distributions of the surface normal contact pressure,electric charge and radial stress can be changed by adjusting the gradient index of FGPMs,and thus resist the surface electro-mechanical contact damage.(4)The axisymmetric partial slip contact problem of an FGPM coated half-space indented by a rigid conducting spherical punch subjected to a monotonically increasing normal load is studied.The whole contact region consists of an inner circular stick region surrounded by an outer annular slip region.An iterative method is used to solve a set of coupled Cauchy singular integral equations of axisymmetric contact problem.It is observed that decreasing the gradient index of coating leads to the decrease of the maximum value of surface contact stress and electric displacement.This may have potential applications in the reduction of the surface electro-mechanical contact damage of the smart devices.(5)The axisymmetric torsional fretting contact between a rigid conducting spherical punch and an FGPM coated half-space is investigated.First,a monotonically increasing normal load is applied on the rigid spherical punch,and then normal load is fixed,and a cyclic torque applied to the rigid punch is further considered.The contact area consists of an outer annular slip area and an inner stick area.The fundamental solution with arbitrarily distributed circumferential shear traction is obtained,and then is transformed to singular integral equation.By using an iterative procedure,the present problem is efficiently solved.The results indicate that the distributions of the surface contact stress,principal stress and Mises stress can be changed by adjusting the gradient index of the FGPM coating,and hence suppress the surface crack initiation,enhance the fretting damage resistance and avoid the yield at the contact surface.The present investigation is a positive contribution to the theory of frictional contact and fretting of FGPMs,and also a significant to optimal design and practical applications of FGPM for the purpose of improving the frictional contact damage of piezoelectric devices.