A unified statistical model for indentation pop-in: Effects of indenter radius and microstructure density on the transition from homogeneous nucleation to heterogeneous nucleation to bulk plasticity

Indentation pop-in, i.e. a sudden displacement burst on the measured load-penetration depth curves, has been known as the onset of elastic-plastic deformation for crystalline materials. Depending on the indenter radius or density of pre-existing dislocation nucleation sources, the evolution of pop-in shear stress can generally be categorized into three deformation stages, i.e. the homogeneous dislocation nucleation stage, heterogeneous dislocation nucleation stage and bulk plasticity stage. For the former, the fluctuation of pop-in stress is dominated by the thermally activated nucleation process. For the middle, a size-dependent pop-in behavior with stress fluctuation is informed over a wide range of indenter radius and microstructure density. For the later, the materials strength is determined by the critical resolved shear stress for the motion of existing dislocations. Here, we find two additional transition stages between the adjacent deformation stages that can be effectively addressed by a novel competition mechanism, and the transition points are affected by the density of dislocation nucleation sites. All these critical features are well characterized by a unified statistical model proposed in this work. Moreover, a mechanistic model with closed-form formulas is developed for the size-dependent pop-in behavior during the heterogeneous dislocation nucleation stage. By comparing both the calibrated and predicted theoretical results with different sets of experimental data, good agreements are achieved that can rationally verify the proposed model. This work presents a theoretical framework to characterize the fundamental pop-in mechanisms, and provides an avenue towards the prediction of transition points distinguishing different plasticity deformation regimes. •A unified statistic model is proposed for the indentation pop-in behavior.•A novel competition mechanism is developed to characterize the transition between adjacent deformation stages.•Indentation pop-in size effect is addressed by a mechanistic model with closed-form formulas.•Theoretical results can match well with annealed, pre-strained and ion-irradiated experimental data.