Adhesive Contact Of Elastic Cylinders And Randomly Rough Surfaces Based On The Double-Hertz Model

With the rapid development of micro-and nano-technology, the small scale components and devices have been widely used in many physical and biological systems. As adhesive forces that act between contacting bodies play a key role in determining the mechanical behavior of micro-scale contact systems, it is imperative for us to make a better understanding of the adhesive contact mechanism, which has brought both challenges and new opportunities to the classical adhesive contact theories. Based on the classical Double-Hertz theory, the present dissertation develops two cohesive zone models for adhesive contact of elastic cylinders and rough surfaces, respectively, and some general solutions are derived, including the interfacial traction, deformation field and the equilibrium equations of the system. Based on these results, we further examine the effect of materials, surface roughness and the adhesion hysteresis on adhesion behavior of the contact system.This dissertation first develops a cohesive zone model for two-dimensional adhesive contact by extending the double-Hertz theory to the contact between elastic cylinders. In this model, the adhesive force within the cohesive zone is described by the difference between two Hertzian pressure distributions of different contact widths, and closed-form analytical solutions are obtained for the interfacial traction, deformation field and the equilibrium equations of the system. Based on these results, a complete transition between the JKR and the Hertz type contact models is captured by defining a dimensionless transition parameter, which governs the range of applicability of different models. Compared with the two-dimensional Maugis-Dugdale model, the present model serving as an alternative cohesive zone solution turns to be more analytically tractable.By establishing a cohesive zone model for rough surface adhesion, the effect of surface roughness and adhesion hysteresis are found to play a significant role on adhesion strength and adhesion toughness. Based on the Greenwood-Williamson contact model, the rough surface is modeled as an ensemble of asperities with identical radius of curvature and Gaussian distributed heights. By applying the double-Hertz theory to each individual asperity of the rough surface, the total normal forces for the rough surface are derived for loading and unloading stages, respectively, and a prominent adhesion hysteresis associated with dissipation energy is revealed. Our analysis results show that both the total pull-off force and the energy dissipation due to adhesive hysteresis are influenced by the surface roughness only through a single adhesion parameter, which measures statistically a competition between compressive and adhesive forces exerted by asperities with different heights. It is also found that rough surfaces with a large adhesion parameter result in lower energy dissipation and pull-off force, i.e. increasing surface roughness can effectively reduce the adhesion strength and toughness of the contact system.The cohesive zone models proposed in this dissertation enrich the literature of classical adhesive contact mechanics by providing general solutions for arbitrary homogeneous material, and it can serve as benchmarks for computational simulation and experiment.