On the methodologies for determining the elastic and plastic material properties of small scale structures using indentation testing

Phadikar, Jayanta Kumar
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University of Delaware
Instrumented indentation is a popular technique used to determine the elastic and plastic material properties of small scale structures. In this dissertation, an attempt is made to advance the indentation research in three areas: i) Indentation of non-flat substrates; ii) Uniqueness and sensitivity of indentation testing; iii) Indentation of anisotropic materials. Regarding indentation of non-flat substrates, conical indentation of a sphere made of isotropic, linear-elastic, perfectly-plastic material and viscoelastic material is investigated. For the sphere with time-independent properties, a semi-analytical method and a finite element based reverse analysis technique are proposed to determine the material properties. It is shown that the methods can predict the material properties quite accurately. For the viscoelastic sphere, a semi-analytical method is developed to obtain the force-displacement relationship of the sphere. The method can be used to obtain the force-displacement relationship of a viscoelastic sphere much faster than the finite element simulation, thus saving computational cost for a possible reverse analysis. The methodologies proposed for the sphere can inspire similar methodologies for other non-flat substrates. Regarding the non-uniqueness and sensitivity due to experimental error of indentation testing, it is shown comprehensively that the two phenomena are not independent, rather non-uniqueness is an extreme case of sensitivity. A methodology is developed to systematically identify the materials which will result in identical force-displacement relationship. The concept of condition number is employed to quantify and rank the sensitivity of different indentation methodologies due to experimental error. Thus, guidelines are provided regarding the selection of test conditions to improve the sensitivity. The guidelines obtained from the condition number are verified by explicit sensitivity analysis. It appears that, in general, indentation tests need to be very accurate to determine the material properties accurately. Regarding indentation of anisotropic materials, various possible dual indentation methodologies have been considered for indentation of a transversely isotropic, linear-elastic, perfectly-plastic material. The methodologies developed for uniqueness and sensitivity analysis are applied to the material. It appears that the sensitivity for transversely isotropic materials is higher compared to the isotropic materials.