Mechanics Of Micro-scale Adhesive Contact On Advanced Functional Materials

With the rapid advance of materials science and nanotechnology, advanced functional materials represented by functionally graded materials and piezoelectric materials have found wide applications in many microscale physical and biological systems. It is desirable to understand the adhesive contact mechanism of functionally graded materials and piezoelectric materials, which has presented both challenges and new opportunities to the classical adhesive contact theories. The present dissertation focuses on adhesive contact behaviors of power-law graded elastic solids and transversely isotropic piezoelectric materials within the framework of continuum mechanics. By developing a few successful theotetical models, some general solutions are derived which provide analytical expressions for the surface stress, deformation fields and equilibrium equations of the system. Based on these results, we then examine the normal/tangential coupling effect, the role of a substrate strain, the effect of mode-mixity, the punch shape effect, the role of surface roughness, the adhesion hysteresis phenomenon and the energy dissipation mechanisms.This dissertation begins by building up non-splipping JKR adhesive contact models for power-law graded solids in a plane strain case as well as in an axisymmetric one, respectively. By introducing the substrate strain and the effect of mode-mixity, we proceed further to consider more complex conditions, including reversible adhesion with a mismatch strain, mode-mixity-dependent adhesion and irreversible adhesion involving a substrate strain. With use of the Jacobi polynominal method and the principle of energy balance, a series of closed-form analytical solutions are obtained, which include the frictionless and homogenesous solutions as special cases. The normal/tangential coupling effect is identified to be an important factor in the adhesive contact problems. Our results indicate that the frictionless solutions are limited within tranditional materials with positive Poisson’s ratio and not applicable for solids with negative Poisson’s ratio.Based on an axisymmetric frictionless adhesive contact model for power-law graded solids, we then develop two equivalent sets of general solutions involving an arbitrary punch profile, that is, Betti’s reciprocity theorem and the generalized Abel transform, the cumulative superposition and equivalent energy release rate approaches. By using these methods, the adhesive behaviors under some typical punch profiles are quantified, including a power-law profile, an exactly spherical profile, an optimal profile and two general concave profiles. Some classical results for homogenesous solids are extened to power-law graded materials. The solution also suggests stragegies to improve the adhesion strength by designing optimal surface topographies and material properties.By establishing two JKR-type adhevie contact models for power-law graded solids with smaller and larger surface roughness, the effect of surface roughness and adhesion hysteresis are found to exert significant influence on adhesive contacts. For the smaller surface roughness, the effective macroscopic response of systems is represented by envelops on the asymptotic form of equilibrium curves, and the associated energy dissipation due to adhesion hysteresis is estimated to increase with roughness. For the larger surface roughness, the multiple asperity contact model for rough surface is employed, where the rough surface is simulated by asperities of the same radius curvature and with heights following a Gaussian distribution. Results show that the rough-adhesion hysteresis mechanism and the resulting energy dissipation are expected to be fairly general for both functionally graded and homogeneous elastic solids, for both smaller and larger surface roughness.In addition, a cohesive zone model of axisymetric adhesive contact between a rigid sphere and a power-law graded elastic half-space is established by extending the classical double-Hertz model. This model incorporates the interaction forces outside the contact area and can be applied to general material properties. A series of analytical solutions have been derived in closed form, such as the interfacial stress, surface displacement and equilibrium equations. By defining a generalized Tabor parameter for power-law graded materials, our results include the JKR and DMT type solutions as special cases and capture a continuous transition transition between these two limiting situations. Based on these results, the pull-off force for power-law graded materials is predicted to vary from (3+k)nRAy/2to2πR△γ. We have also highlighted that the pull-off force for the Gibson solid is identically equal to2πR△γ independent of the Tabor parameter.Finally, a generalized non-slipping JKR adhesive model is developed for the plane strain contact on a transversely isotropic piezoelectric half-space. This model is not only able to capture the normal/tangential coupling effect, but also can account for the roles of the inclined mechanical force and the substrate strain. Surface Green’s function is established on a basis of the Stroh formalism for piezoelectric materials. With use of the analytical function theory, analytical solutions are then proposed to predict the adhesive responces of six piezoelectric materials under different loading conditions.Our analysis shows that the adhesive contact behaviors for different types of piezoelectric materials may be quite different.The results obtained in this dissertation expand the literature on classical adhesive contact mechanics by including the corresponding solutions for homogeneous isotropic materials as special cases, and hence can serve as benchmarcks for computational simulation and experiment. On the other hand, these results provide a theoretical foundation for the novel applications of functionally graded solids and piezoelectric materials in artificial adhesion systems. Since these advanced matericals not only show similar adhesive behaviors to the homogeneous isotropic materials, but also possess more designable material parameters to optimize the adhevion strength and toughness of the systems.