Search

We review the recently developed models for load fluctuations in the displacement controlled mode and displacement jumps in the load controlled mode of indentation. To do this, we devise a method for calculating plastic contribution to load drops and displacement jumps by setting-up a system of coupled nonlinear time evolution equations for the mobile and forest dislocation densities by including relevant dislocation mechanisms. These equations are then coupled to the equation defining constant displacement rate or load rate. The model for the displacement controlled mode using a spherical indenter predicts all the generic features of nanoindentation such as the elastic branch followed by several force drops of decreasing magnitudes and residual indentation depth after unloading. The stress corresponding to the elastic force maximum is close to the yield stress of an ideal solid. The predicted numbers for all the quantities match experiments on single crystals of Au using a spherical indenter. We extend the approach to model the load controlled nanoindentation experiments that employ a Berkovich indenter. We first identify the dislocation mechanisms contributing to different regions of the F − z curve as a first step for obtaining a good fit to a given experimental F − z curve. This is done by studying the influence of the parameters associated with various dislocation mechanisms on the model F − z curves. The study also demonstrates that the model predicts all the generic features of nanoindentation such as the existence of an initial elastic branch followed by several displacement jumps of decreasing magnitudes and residual plasticity after unloading for a range of model parameter values. Furthermore, an optimized set of parameter values can be easily determined that give a good fit to the experimental load–displacement curves for Al single crystals of ( 110 ) and ( 133 ) orientations. Our model also predicts the indentation size effect in a region where the displacement jumps disappear. The good agreement of the results of the models with experiments supports our view that the present approach can be used as an alternate method to simulations. The approach also provides insights into several open questions.

One of the most interesting phenomena that occur in ductile materials strained in the proximity of absolute zero are the adiabatic shear bands. In the stainless steels, massively used to construct superconducting magnets, their occurrence can be detected by various techniques, including magnetometric methods (feritscope). Formation of adiabatic shear bands is strictly correlated to the occurrence of the intermittent plastic flow (IPF), characteristic of stainless steels strained in liquid or superfluid helium. Evidence for the occurrence of the phase transformation during nucleation and formation of the shear bands in the proximity of absolute zero is for the first time given. The rate of shear bands propagation along the sample as well as the amount of secondary phase is measured. In order to describe the intermittent plastic flow, novel double surface model has been developed. It includes type Huber-Mises-Hencky yield surface, and new recovery surface reflecting the lower bound for the stress oscillations. The yield surface can move and expand due to nonlinear mixed (kinematic and isotropic) hardening, resulting from the phase transformation, whereas, the recovery surface remains constant. The serrations occur between the yield surface and the recovery surface, with the yield surface coming back to its initial position after each serration. Each serration corresponds to formation of single shear band there, where the easy slip planes are available, and the mechanism of anchoring the shear bands by the secondary phase is explained. New double surface model has been correlated to the experimental data and applied to explain stress oscillations during the regular stage of the intermittent plastic flow, when the shear bands gradually cover the gauge length of the sample. [Display omitted] • The shear bands formation in the context of intermittent plastic flow in the proximity of absolute zero is investigated. • For the first time evidence is given for occurrence of the fcc-bcc phase transformation during formation of the shear bands. • Unique set-up for 4.2 K, complemented by the SEM with EBSDand the feritscope for secondary phase measurements, is applied. • The rate of shear bands propagation is estimated, and the profiles of the volume fraction of secondary phase are measured. • Novel double surface constitutive model of intermittent plastic flow is implemented for the regular stage of serrations. • The stress, strain components and Odqvist parameter in the shear bands are computed and compared with the experimental data. [ABSTRACT FROM AUTHOR]

We review the recently developed models for load fluctuations in the displacement controlled mode and displacement jumps in the load controlled mode of indentation. To do this, we devise a method for calculating plastic contribution to load drops and displacement jumps by setting-up a system of coupled nonlinear time evolution equations for the mobile and forest dislocation densities by including relevant dislocation mechanisms. These equations are then coupled to the equation defining constant displacement rate or load rate. The model for the displacement controlled mode using a spherical indenter predicts all the generic features of nanoindentation such as the elastic branch followed by several force drops of decreasing magnitudes and residual indentation depth after unloading. The stress corresponding to the elastic force maximum is close to the yield stress of an ideal solid. The predicted numbers for all the quantities match experiments on single crystals of Au using a spherical indenter. We extend the approach to model the load controlled nanoindentation experiments that employ a Berkovich indenter. We first identify the dislocation mechanisms contributing to different regions of the F − z curve as a first step for obtaining a good fit to a given experimental F − z curve. This is done by studying the influence of the parameters associated with various dislocation mechanisms on the model F − z curves. The study also demonstrates that the model predicts all the generic features of nanoindentation such as the existence of an initial elastic branch followed by several displacement jumps of decreasing magnitudes and residual plasticity after unloading for a range of model parameter values. Furthermore, an optimized set of parameter values can be easily determined that give a good fit to the experimental load–displacement curves for Al single crystals of ( 110 ) and ( 133 ) orientations. Our model also predicts the indentation size effect in a region where the displacement jumps disappear. The good agreement of the results of the models with experiments supports our view that the present approach can be used as an alternate method to simulations. The approach also provides insights into several open questions. [ABSTRACT FROM AUTHOR]