The Micro/Nanoscopic Self-consistent Elastic Adhesive Contact Model And Interface Strengthening/Weakening Mechanisms

With the rapid development of nanotechnology,the mechanical behavior of materials at the micro/nano scale has attracted great attention.At this scale,the specific surface area of material is large,and the adhesion behavior between interfaces has a significant effect on the overall mechanical property.The adhesive contact behavior of micro/nano solids is affected by many factors,such as surface topography,surface internal stress,surface elasticity,material gradient,etc.These factors are coupled with the nonlinear interface interaction,which brings great challenges to theoretical modeling and numerical calculation.The adhesive contact model based on the framework of continuum mechanics is one of the most powerful tools to characterize and predict the interface properties of micro/nano material.Thanks to the efforts of generations of mechanics researchers,great progress has been made in the study considering the scale effect and the surface effect under this framework.However,there are still some key scientific problems to be solved,such as the mechanical mechanisms of surface roughness affecting the interfacial adhesion,the coupling influence mechanisms of residual surface stress and surface elasticity on the interfacial adhesion,and the accurate characterization on the adhesive contact behavior of graded material.Faced with these scientific problems,we intend to expand the self-consistent adhesive contact model in this dissertation.Based on this model,we discussed the adhesive contact behavior and interface strengthening mechanisms of micro/nano elastic solids,and carry out the following research.A full self-consistent model(FSCM)for the adhesion of elastic wavy surface is established.By combining the arc-length control method,Riemann-Stieltjes integral method,adaptive mesh technique and Newton-Raphson iterative method,a high-precision and high-efficiency numerical calculation method is developed.The full force-displacement curve is obtained,and it is found that the pull-off force increases first and then decreases with the increase of roughness.There are two adhesive contact modes for rough surfaces,namely the simple contact mode under small roughness and the multiple contact mode under large roughness.The ratio of the roughness amplitude to the wavelength is an important parameter controlling the adhesion mode transition.An adhesion map with amplitude and wavelength as two axes is constructed.The optimal roughness corresponds to the boundary of the two modes in the adhesion map.The mechanical mechanism of interface strengthening/weakening under different roughness is revealed.The surface pressure is corrugated under small roughness.and some of the repulsive zone is transformed into the attractive zone,which increases the interface adhesion.The interface cavitation occurs and develops under large roughness,and the tensile stress is limited by the theoretical stress,which weakens the interface adhesion.Based on the Gurtin-Murdoch theory of surface elasticity and the full self-consistent theory,a unified mechanical framework considering residual surface stress and surface elasticity is established.The governing equations coupling material intrinsic surface effect and adhesion effect between solids are given.In order to deal with the integral oscillation in the self-consistent equations,a regularization strategy is proposed.By means of integral decomposition,integral transformation,and singularity treatment,the difficulty in numerical calculation is solved.Four dimensionless parameters,i.e.,the Tabor number μ,the residual surface stress Sr,the surface elastic parameter Se and Poisson’s ratio v,are obtained by scaling the self-consistent equation.The effects of dimensionless parameters on force-displacement curve,the pull-off force,the surface deformation,and the contact stiffness are studied.It is found that the residual surface stress parameter inhibits the surface normal deformation and adhesion hysteresis,and the surface elastic parameter increases the contact stiffness of materials.The effect of Se on the adhesive contact behavior of materials with negative Poisson’s ratio is greater than that with positive Poisson’s ratio.The reduced forms of the self-consistent equation are given.The asymptotic adhesion behavior is analyzed when the residual surface stress and the surface elastic parameter tend to infinity.A full self-consistent model for power-law graded elastic material is established by using the surface displacement solution of half-space under an annular loading and combining with the Derjaguin approximation.By using the Riemann-Stieltjes integral and Gauss hypergeometric function,the integral singularity in the self-consistent equation is strictly eliminated.A new dimensionless parameter(the generalized Tabor number)is defined to reflect the coupling effects of surface shape,material gradient and molecular force range on the interface adhesion.A power-law relation between the jumping displacement of power-law graded elastic material and the generalized Tabor number is obtained through asymptotic analysis.The pull-off force transition from soft material/strong adhesion to hard material/weak adhesion is given for power-law graded elastic material,and the sensitivity of interface strength on the modulus gradient under different surface shapes is obtained.The full self-consistent model is used to verify the extended Maugis-Dugdale(M-D)model,and the rigid limit consistent condition is introduced to improve the extended M-D model,which improves the prediction accuracy on the force-displacement curve and the pull-off force.A full self-consistent model for the adhesive contact problem of Gibson solid(incompressible linear gradient elastic material)is established through two theoretical approaches.The self-consistent equation is a high-order polynomial equation with respect to the surface gap.By taking the surface gap as an independent variable,the first explicit form of an FSCM is given.It is found that the Gibson solid exhibits unusual adhesion behavior when the Tabor number exceeds the critical value.The critical Tabor number is determined theoretically.The bifurcation of the force-displacement curve,the jumping-in instability,the adhesion hysteresis,and the surface folding deformation are found.The evolution behavior of the interface folding deformation during loading and unloading is studied.Due to the folding deformation,the contact and cohesive zones in the extended Johnson-Kendall-Roberts(JKR)and M-D models cannot be defined accurately,and thus the two models fail at large Tabor numbers.The soft limit for the adhesion of Gibson solid is given by numerical and asymptotic analysis.Aiming at the adhesive contact problems of micro/nano elastic solids,this dissertation extends the full self-consistent model in several important directions,which improves the practicability of the FSCM and systematically reveals the influence mechanisms of surface roughness,surface effect,and material gradient on the interface adhesion.This study provides an effective mechanical tool for the high performance design of micro/nano material interface.