Accounting for Localized Deformation: A Simple Computation of True Stress in Micropillar Compression Experiments

Compression experiments are widely used to study the mechanical properties of materials at micro- and nanoscale. However, the conventional engineering stress measurement method used in these experiments neglects to account for the alterations in the material’s shape during loading. This can lead to inaccurate stress values and potentially misleading conclusions about the material’s mechanical behavior, especially in the case of localized deformation.

Our goal is to calculate true stress in cases of localized plastic deformation from standard experimental data (displacement-force curve, aspect ratio, shear band angle and elastic strain limit).

We use a simple mechanical-geometrical approach based on reasonable physical assumptions to get analytic formulas of true stress and eliminating the need for finite element computations. Furthermore, in numerical simulations of pillar compression, the formula-based true stress demonstrates strong alignment with the theoretical true stress.

We propose analytic formulas for calculating true stress in cases of localized plastic deformation commonly encountered in experimental settings for a single band oriented in arbitrary directions with respect to the vertical axis of the pillar.

The true stress computed with the proposed formulas provides a more precise interpretation of experimental results and can serve as a valuable and simple tool in material design and characterization.