Selected mechanical problems in load- and depth-sensing indentation testing
Pharr, George M.
Doctor of Philosophy
Indentation techniques are used extensively in mechanical property testing. In this dissertation, selected mechanical problems in load and depth sensing indentation testing are presented. One commonly used technique for determining a material's elastic modulus and hardness from indentation load-displacement data is the Oliver-Pharr method. In this method, radial displacements, pile-up and film-substrate interactions are not explicitly considered. Models to address the importance of these issues are developed and compared with the finite element analyses. Good agreement is achieved in many cases. An elastic solution for indentation of a monolithic material was developed by Sneddon in the 1950s. Analytical and finite element results are presented which show that modifications to Sneddon's solution are needed to describe elastic indentation accurately. Since most indentation methods for measuring mechanical properties are based on Sneddon's solution, these modifications have important consequences for making accurate measurements. A general modified formula is developed for an indenter whose shape can be described as a body of revolution of a power function. During the indentation process, samples plastically deformed by the indenter tend to pile up around the edge of contact. Pile-up can be a significant factor affecting the accuracy of indentation measurement. A new elastic-plastic model for conical indentation is presented which can increase the accuracy of the Oliver-Pharr method by accounting for this pile-up. The model is in good agreement with an empirical model proposed by Hainsworth and Page. Film/substrate interactions pose a particularly formidable problem in making indentation property measurements. In order to properly interpret experimental indentation data, an elastic solution for the film/substrate problem is highly desirable. However, an exact elastic solution is not available. In lieu of an exact solution, numerical methods and approximate methods are useful. A first order perturbation solution for the indentation of an elastic film on an elastic substrate is presented, the results of which are in good agreement with physical limits as well as with finite element results. Finite element analysis is a useful tool for studying elastic plastic indentation. With it, details of the indentation process which may be difficult to observe experimentally can be examined to gain insight into the mechanisms of contact. The finite element method has been used to examine the elastic-plastic behavior of a hard NiP film on a soft Cu substrate. The finite element results provide physical insight into unusual experimental behavior reported for this system.
Mechanical engineering; Engineering; Materials science