The mechanics of size-dependent indentation

Indentation tests at scales on the order of one micron have shown that measured hardness increases significantly with decreasing indent size, a trend at odds with the size-independence implied by conventional plasticity theory. In this paper, strain gradient plasticity theory is used to model materials undergoing small-scale indentations. Finite element implementation of the theory as it pertains to indentation modeling is briefly reviewed. Results are presented for frictionless conical indentations. A strong effect of including strain gradients in the constitutive description is found with hardness increasing by a factor of two or more over the relevant range of behavior. The results are used to investigate the role of the two primary constitutive length parameters in the strain gradient theory. The study indicates that indentation may be the most effective test for measuring one of the length parameters.