| This dissertation presents theoretical investigations to estimate the graded properties of a hard thin layer on a soft substrate. For this purpose, theoretical approaches have been made to explain experimental phenomena that can be observed in the surface-modified layer of PDMS.; A general strategy is presented, which can be used to determine the critical strain and the corresponding wave number for the wrinkling instability of a half space or thick layer loaded in compression, when the elastic properties vary with depth. Results exhibit dependence on modulus ratios similar to those observed when a homogeneous stiff surface layer is bonded to a more flexible substrate (i.e. where the elastic properties are piecewise constant).; Indentation theories are explored to explain the linear force-indentation depth relationships obtained from nanoindentation experiments. The plate theory and bi-layer system are considered as a theoretical model for the indentation problem at first. After examining the theory using the finite-element simulation, we conclude that the theory may not an adequate model for the indentation by a rigid indenter. A theoretical model is suggested, which considers the indentation into a half space with graded modulus by a rigid indenter. The force-indentation depth relationships very close to linear is obtained when the error function is used as a modulus function. Based on these results, we suggested an iterative method to determine the modulus of a surface-modified PDMS. The effect of residual strains is considered in the iterative method. With the residual strain, the method gives reasonable order of the modulus values.; We did two types of experiments to produce wrinkling in a modified-surface of PDMS. In each experiment, a discrepancy in the wavelengths is observed between the loading methods. To reveal this discrepancy, analytical models to describe the stress field in the system is suggested. The effect of Poisson's ratio mismatch, crack opening, and graded modulus is considered. While qualitative estimations for the discrepancy can be obtained with the effect of crack opening and graded modulus, quantitative estimations are not made in this research. |
