Stress-strain curve estimation from micropillar compression with transverse contraction effect

The Focused Ion Beam (FIB) technique and the associated compression testing capabilities provide versatile access to understanding the microstructural behaviour of materials. Among many objectives, determining the stress-strain relationship from experimental or numerical force-displacement data remains a fundamental challenge. However, for micropillers under compression, the inside deformation constraint is complex like in components and the transformation of a measured force-displacement curve into an accurate uniaxial stress-strain curve is not straightforward. In this context, in a previous numerical based analysis for perfect volume constancy or incompressibility the determination of reliable and accurate stress-strain curves from nonlinear load-deformation curves of micropillers was already verified. In the case of transverse contractions, however, numerical simulations of micropillers provide unexpected force-displacement behaviour, i.e. their force-displacement curves are almost superimposing and are very close to the force-displacements for incompressibility. This effect implies, that transverse contraction would have no contributions in micropillar compression. In contrast, independent simulations using a single finite element accurately explore the true uniaxial stress-strain behaviour for the whole range of transverse contractions. These are considered as the reference behaviour and are also treated by an analytical expression. With the presented new stress-strain estimation approach, including transverse contraction, any force-displacement curve from a micropillar under compression can be stepwise corrected. The first step of the new stress-strain curve estimation method, including transverse contraction, is carried out in the same way as in the preceding analysis for incompressibility, followed by further steps to obtain the final true stress-strain curve. Although the presented numerical analysis is exemplarily performed for the behaviour of fused silica, but the stress-strain approach is in the same manner generally applicable for a material behaviour with other stress-strain curves. The assumption behind is isotropic and nonlinear material behaviour. • Numerical analysis of nonlinear deformation behaviour of FIB micropillars with transverse contraction. • Uniaxial stress-strain curves with transverse contraction by single finite element simulations. • Triaxiality affects force-displacement curves of micropillers preventing systematic influence of transverse contraction. • Verification of an extended procedure for estimating stress-strain curves from micropillars with transverse contraction.