Simulations of micro- and nanoindentation of pentaerythritol tetranitrate including size effects

Abstract

Nanoindentation with a Knoop indenter tip can reveal the plastic response of brittle materials, which is contained in the measured Knoop hardness anisotropy and force–displacement curves. Due to short length scales, details of the local dislocation distribution and dislocation stresses cannot be ignored in the analysis of experimental measurements. Inclusion of such effects leads to a non-local theory of plasticity, where gradients of strain fields are present in the expressions for stress. In this work, a non-local plasticity model is developed and implemented in the Abaqus finite element software. The geometrically necessary dislocations (GND) are quantified via the Nye tensor, and the backstress tensor is found from gradients of the Nye tensor by summation of dislocation stresses. Micro- and nanoindentation experiments on pentaerythritol tetranitrate (PETN) are simulated with the developed model. The average errors between simulated and measured micro- and nanohardness are around 13% and 25%, respectively, while the maximum errors are around 20% and 30%, respectively. The set of active slip systems for PETN that can match the experimental hardness anisotropy trends is {110}⟨11¯1⟩, {100}⟨011⟩, and {101}⟨101¯⟩. The GND hardening, the backstress, and the indenter shape are investigated in relation to the indentation size effects. The model predicts a weak effect of backstress on hardness, while the coupled effects of indenter shape and GND hardening are predominantly responsible for predicted size effects.