Study On The Micro/nanoscopic Adhesive Contact Mechanical Models

In the micro/nano scale, the surface profile and surface interaction play an important role in the contact behavior of materials. The normal adhesive contact problem of arbitrary axisymmetric elastic objects with an arbitrary surface adhesive interaction is studied in this thesis. The continuum models for mechanical contacts are extended and supplemented to enhance the practicability of the full self-consistent model (FSCM) and the validity of the Maugis model.For the arbitrary axisymmetric elastic objects with an arbitrary surface adhesive interaction, the surface deformation-interaction consistent relation and the load-displacement relation are derived and the FSCM is established under the frictionless or non-slipping condition. For convenience in numerical calculation, we rewrite the consistent relation with the surface central gap, instead of the displacement, as the control parameter. The two dimensionless relations under the non-slipping condition are found to be same as those under the frictionless condition, respectively, except the definition of a dimensionless parameterÏ…, which characterizes the material properties and surface shape. This parameter under the non-slipping condition is 1—β² times as that under the frictionless condition, whereβis the Dundurs constant. The two-dimensional FSCM is also studied, but unfortunately the displacement can't be determined.The full self-consistent numerical calculation based on a specific interaction model is further improved in several aspects. First, a variable-spacing technology is designed to improve the computational efficiency and accuracy. Second, a surface central gap control, which is the simplest one without the necessity of dealing with the solution bifurcation, is used to derive the full load-displacement curve as firstly used by Greenwood. Third, a Riemann-Stieltjes integral is employed to avoid the singularity pointed out by Greenwood. Fourth, the relaxation method that may lead to errors is replaced by a Newton-Raphson method to accelerate convergence and improve the efficiency of iterations. Through these improvements, the FSCM will be applied more effectively.The FSCM is applied to the case of a power-law shape function and the Lennard-Jones (L-J) potential. The numerical results show that the jumping-on and jumping-off are due to the displacement control in practice. It is shown that the surface friction restrains the deformation. An extended Tabor numberμ, is defined and a transition from the extended Johnson-Kendall-Roberts (JKR) model to the extended Bradley model, named as an extended Muller-Yushchenko-Derjaguin (MYD) transition, is found.The Maugis model is extended to that of arbitrary effective axisymmetric elastic objects with an arbitrary surface adhesive interaction. Based on the Dug-dale model, a generalized Maugis-Dugdale (M-D) model is derived. Under two limit conditions, it is simplified to the generalized JKR model and the generalized Derjaguin-Muller-Toporov (DMT) model, respectively. The generalized M-D model is applied to the case of a power-law shape function and a continuous transition from the extended JKR model to the extended DMT model is found in this extended M-D model for an arbitrary shape index n. Based on the extended M-D model, a three-dimensional Johnson-Greenwood adhesion map is constructed with coordinates of the transition parameter A, the dimensionless load P| and the shape index n.In the original M-D model, the step cohesive stressσ₀ is arbitrarily chosen to be the theoretical stressσ_th to match that of the L-J potential. An alternative and more reasonable one is proposed in this thesis. Using the Dugdale approximation to match the L-J potential in the adhesive contact of axisymmetric elastic objects in power-law is first discussed. A relation of the identical pull-off force at the rigid limit is required for the approximate and exact models. With this requirement, the stressσ₀ is found to be k(n)Δγ/z₀, where k(n) is a coefficient, n shape index,Δγthe work of adhesion and z₀ the equilibrium separation. Hence we haveσ₀ = 0.588Δγ/z₀ (= 0.573σ_th), especially for n = 2. The prediction of the pull-off forces using this new value shows surprisingly better agreement with the MYD transition than that usingσ_th = 1.026Δγ/z₀ and this is true for other values of shape index n. And then, for a more general relationship of the L-J potential, the step cohesive stressσ₀ is also presented. Finally, a similar discussion is carried out in the adhesive contact between an ideal sphere and a half-space.