Title: Indentation of Multi-Layered Materials Using Spherical Indentation
Description: In the field of indentation there is a subset of study that examines indentation of thin films on substrate materials. Early work in this area primarily focused on the properties of the film, neglecting the substrate. However, there are a great many instances where understanding the substrate may be as important if not more important than understanding the film properties. The primary focus of this research and associated thesis is to extend the level of knowledge of the moderately deep spherical indentation of film-substrate systems, investigating both film and substrate. By choosing to use a spherical indenter the effects of damaging the test material at these moderate depths is reduced. It also allows for the incorporation of the innovative technique of invoking the non-self-similarity characteristics of this type of indenter. This thesis is focused on this phenomenon and furthers the present knowledge that exists today of thin film-substrate elastic indentation. The beginning of this thesis reviews the historical path that indentation has followed from the early work of Hertz to present day research in thin film on substrate materials.

The next section focuses on thin films on substrates under spherical indentation in a fully elastic condition, investigating both film and substrate. A forward analysis incorporating Dimensional Analysis will be performed that will determine two relationships that can be used to solve for material properties of both film and substrate. Moderate indentation depths are chosen that will allow for the addition of the substrate effect while directly avoiding problems related to shallow indentation. A full numerical reverse analysis is performed using simulations that will check the applicability and accuracy of the relationships developed from the forward analysis. In the reverse analysis, different input values are used providing for a unique and unbiased review of the work performed. The next section will extend this research into the area of fully elastic film affixed on substrate systems with the film under an applied equi-biaxial steady-state stress. A forward analysis is performed incorporating dimensional analysis to help reduce the number of variables.

A set of relationships are established that are then tested by an independent numerical reverse analysis using a full set of discreet and arbitrary input values. Finally a general examination of multi-layered systems is performed. This is done by first examining a specific problem that exists in industry today, water filtration, then extending this to a general relationship as a proof-of-principal investigation of a multi-layered system. Throughout this work an independent and rigorous error analyses is performed in order to identify potential instabilities in the proposed solutions. Finally an examination and proposal is made of how this work can be used to further extend specific areas of both research and commercial applications of indention of materials to moderate depth, incorporating the substrate effect.