Dislocation-based model for predicting size-scale effects on the micro and nano indentation hardness of metallic materials

Abstract

In micro- and nano-indentation tests for evaluating strength and stiffness properties of engineering materials, a commonly observed phenomenon is the dependence of material properties on the indent size, also known as indentation size effect (ISE). The objective of the present work is to formulate a micro-mechanical based model based on dislocation mechanics for predicting ISE from conical or pyramidal (Berkovich and Vickers) indenters and to compare it with the most widely used Nix-Gao model. The key idea proposed here while deriving the model is a non-linear coupling between the geometrically necessary dislocations (GNDs) and the statistically stored dislocations (SSDs) that eventually allows it to simultaneously predict ISE from both micro- and nano-indentations tests on a wide range of metallic materials while the Nix-Gao model fails to do so. The work also presents a method for identifying the length scale parameter from micro- and nano-indentation experiments and also correlates it with the spacing between dislocations and thus gives a physical interpretation of the material intrinsic length scale.