Numerical microstructure model of NiTi wire reconstructed from 3D-XRD data

Abstract

In this paper, the grain microstructure and strain partitioning in a polycrystalline NiTi wire subjected to tensile loading was reconstructed from an experimental 3D-XRD dataset. The reconstruction of a volume containing more than 8000 stressed grains involved optimization with respect to both the geometrical features and material elastic properties. The geometrical features of the microstructure were reconstructed using Laguerre tessellations based on the experimental 3D-XRD dataset. Two different algorithms fitting Laguerre tessellations were applied in order to assess the sensitivity of the reconstruction to the choice of the algorithm. The material properties in terms of elastic anisotropy were refined from an initial published value to minimize the mismatch between experiment and simulation using an optimization algorithm based on linear elasticity simulations. As a result of this, we constructed a numerical microstructure model that statistically matches the experimentally probed material in terms of positions and sizes of grains as well as partitioning of elastic strain and stress in the microstructure (average elastic properties and standard deviations of piecewise constant components of elastic strain and stress tensors in grains).

Statistical assessment of stress redistribution in loaded polycrystals

“…The method is tested on simulation data published in Heller et al (2020). The dataset is related to a single microstructure tessellation model approximating a real NiTi wire microstructure loaded by tension along the wire axis.…”

“…For example, the 3DXRD experimental method (Sedmák et al, 2016) providing information on microstructure features in terms of grain volumes, grains' centres of mass, and grain-wise averaged strains and stresses (Fig. 1 (b)) have been used to reconstruct a realistic microstructure model of a wire made from a NiTi shape memory alloy (Otsuka and Wayman, 1998;Heller et al, 2020) (Fig. 1 (a)) being used in biomedical applications.…”

“…The displacements at the elements' vertices are Fig. 1: Example of microstructure reconstruction and modelling used to simulate stress-strain fields in polycrystals subjected to external loads published in Heller et al (2020). The microstructure of a NiTi wire (a) was reconstructed from experimental data provided by the 3DXRD method (b) using tessellation modelling (Petrich et al, 2019) resulting in a set of convex polyhedra (c) that are further discretised by finite elements (d) for purposes of numerical simulations of stress-strain fields.…”