Size-dependent And Surface-dependent Contact Mechanics Analysis Of Homogeneous Materials

With the rapid development of modern manufacturing technology,many mechanical products and devices are increasingly miniaturized and reduced to the scale of the micrometer or nanometer.When the mechanical system structure or material characteristic size is reduced to the order of micro-/nano-meter,the structures or materials will exhibit some special properties that are different from their macroscopic counterparts,and show the strong size effect and surface effect.At present,micro-/nano-scale contact mechanics have attracted extensive attention,and a lot of researches have been done in experiments and numerical simulations.The theoretical research is mainly based on some non-classical high-order continuum theories,such as couple stress theory and surface elasticity theory.By introducing the characteristic material length in the constitutive equations,the couple stress theory can be successfully used to predicate the size effect of microstructure materials;the surface elasticity theory introduces the surface material constants and non-classical boundary conditions to characterize the surface effect of materials.This dissertation focuses on the size-dependent and surface-dependent contact problems of the homogeneous material,including the two-dimensional sliding frictional and finite-friction contact problems of the homogeneous elastic materials based on the couple stress theory,and the two-dimensional and axisymmetric frictionless contact problems of piezoelectric materials based on the surface piezoelectricity theory.The main content and conclusions include:(1)Based on the couple stress theory,a size-dependent contact model of a homogeneous elastic half-plane is established,and the two-dimensional sliding frictional contact problem between the half-plane and a rigid flat,cylindrical and semi-circular punches is solved.By using the Fourier integral transformation,the fundamental solution under the normal and tangential concentrated lines loads can be transformed into the second kind of Cauchy singular integral equations,and then the solution will be solved numerically.The results show that with the increase of the characteristic material length,the normal contact stress of the flat punch initially departs from and then approach the classical elastic result,and the maximum normal contact stress of the cylindrical and semi-circular punches increases.In a sufficiently small contact region adjacent to both ends of the flat punch,there is a boundary layer effect,however,there is no boundary layer effect at both ends of the contact region of the cylindrical and the semi-circular punches.(2)Based on the couple stress theory,a size-dependent contact model of the homogeneous coated half-plane is established,and the two-dimensional sliding frictional and finite-friction contact problems between the homogeneous coated half-plane and the rigid punch are studied.The Fourier integral transformation is also used to obtain the singular integral governing equations under the normal and tangential line concentrated loads,and then the solution of this contact problem can be obtained by solving the integral equations numerically.For the finite-friction contact problem,the contact region is divided into an inner stick region and two outer slip regions,and the solution of this problem is obtained numerically by developing a complex iterative method.The results show that for the flat and cylindrical punches,the tensile stress appearing at the edge of the contact region increases with the increase of the shear modulus ratio and friction coefficient,which indicates that the shear modulus ratio and friction coefficient can be adjusted to improve micro-/nano-scale contact damage.(3)Based on the surface piezoelectric theory,a surface-dependent two-dimensional contact model of piezoelectric material is established.The two-dimensional frictionless contact problem between a homogeneous piezoelectric half-plane and the rigid flat and cylindrical punches is studied.The influence of residual surface stress,surface elastic constant,surface piezoelectric constant and surface dielectric constant on the contact behavior of piezoelectric materials is analyzed in detail.The results show that for the two-dimensional contact problem,the surface effect makes the normal contact stress of the cylindrical punch no longer zero at both ends of the contact region,and there is a non-zero compressive stress outside the contact region,which is different from the classical elastic results.The normal contact stress of the flat punch is only sensitive to the residual surface stress,while the normal contact stress of the cylindrical punch is not only sensitive to the residual surface stress,but also sensitive to the surface elastic constant and the surface dielectric constant.(4)Based on the surface piezoelectric theory,a surface-dependent axisymmetric contact model of piezoelectric material is established,and the axisymmetric frictionless contact problem between a homogeneous piezoelectric half space and the rigid flat-ended cylindrical and spherical punches is studied.By using the Hankel integral transformation,the integral governing equations of the surface-dependent axisymmetric contact problem are obtained,and then the solutions of the contact stresses and electric displacements of the half-space contact surface are solved numerically.The effects of residual surface stress,surface elastic constant,surface piezoelectric constant and surface dielectric constant on normal contact stress,radial stress and radial electric displacement are analyzed.The results show that for the axisymmetric contact problem,the surface effect makes the normal contact stress of the spherical punch no longer zero at the edge of the contact region,and there is a non-zero compressive stress outside the contact region,which is different from the classical elastic results.For the flat-ended cylindrical punch,the normal contact stress is mainly sensitive to residual surface stress.However,the normal contact stress of the spherical punch is not only sensitive to residual surface stress,but also sensitive to the surface elastic constant and dielectric constant.The systematic theoretical research on the size-dependent and surface-dependent contact problems have been studied in this dissertation.The research results have important theoretical significance for revealing micro-nano contact damage,and also have important application value in related to the optimal design of micro-nano mechanical systems and devices,and the performance characterization of micro-nanomaterials based on nano-indentation technology...