Dislocation Mechanism Based Model for Portevin Le-Chatelier Like Instability in Microindentation of Dilute Alloys

Abstract

While the topic of intermittent plastic flow manifesting as load fluctuations or displacement jumps in nanoindentation (depths less than 100 nm) has attracted considerable attention, the existence of steps on load-indentation (F-z) curves reported in microindentation (depths of several microns) of samples of dilute alloys has received little attention from a modeling point of view. There are no simulations either. Following our earlier approaches to nanoindentation instabilities and indentation size effect, we develop a model that predicts all the reported characteristic experimental features. We develop time evolution equations for the mobile, the forest, dislocations with solute atmosphere and the geometrically necessary dislocation densities. The model includes all the relevant dislocation mechanisms such as collective pinning and unpinning of dislocations from solute atmosphere, dislocation-solute interaction resulting in strengthening of the alloy samples in addition to multiplication, storage and recovery mechanisms. We model the growth of the geometrically necessary dislocation density by the number of loops that can be activated under the contact area and the mean strain gradient based on recent experimental observations that show small misorientation at small depths suggesting limited geometrically necessary dislocation density. The equations are then coupled to the load rate equation. The model predicts all the characteristic features of experiments such as (a) the stepped response of the F-z curves, (b) the existence of a critical load and critical indentation depth for the onset of the instability, (c) the decreasing dependence of the maximum indentation depth of the F-z curves with increasing concentration of the alloying element, (d) the mean critical indentation depth z* for the onset of the instability increases with decreasing concentration with a concomitant increase in levels of fluctuations, (e) the decreasing power law dependence of critical indentation depth with concentration, (f) the manifestation of intermittent stepped response in a window of load rates, and (g) The magnitude of the load steps scales linearly with the load.