TY - JOUR
T1 - On the Use of Laguerre Tessellations for Representations of 3D Grain Structures
AU - Lyckegaard, Allan
AU - Lauridsen, Erik Mejdal
AU - Ludwig, Wolfgang
AU - Fonda, Richard Warren
AU - Poulsen, Henning Friis
PY - 2011
Y1 - 2011
N2 - Accurate descriptions of 3D grain structures in polycrystalline materials are of key interest as the grain structure is closely correlated to the macroscopic properties of the material. In the present study, we investigate the accuracy of using Laguerre tessellations to represent 3D grain structures from only the spatial center of mass location and the volume of the grains. The ability of Laguerre tessellations to describe accurate grain shapes and topologies of real 3D grain structures are revealed by direct comparison to 3D reconstructions of an un-deformed meta-stable β -titanium alloy obtained by phase-contrast micro-tomography. This study reveals that (volume weighted) Laguerre tessellations are superior to classical Voronoi tessellations when it comes to providing accurate representations of real 3D grain structures. Furthermore, although the Laguerre tessellations were only able to correctly describe the local arrangements of grains (i.e., the grain neighbors and number of grain facets) for 31.8% of the investigated grains, the Laguerre tessellations were able to accurately describe statistical grain characteristics such as grain size distributions and grain neighbor distributions.
AB - Accurate descriptions of 3D grain structures in polycrystalline materials are of key interest as the grain structure is closely correlated to the macroscopic properties of the material. In the present study, we investigate the accuracy of using Laguerre tessellations to represent 3D grain structures from only the spatial center of mass location and the volume of the grains. The ability of Laguerre tessellations to describe accurate grain shapes and topologies of real 3D grain structures are revealed by direct comparison to 3D reconstructions of an un-deformed meta-stable β -titanium alloy obtained by phase-contrast micro-tomography. This study reveals that (volume weighted) Laguerre tessellations are superior to classical Voronoi tessellations when it comes to providing accurate representations of real 3D grain structures. Furthermore, although the Laguerre tessellations were only able to correctly describe the local arrangements of grains (i.e., the grain neighbors and number of grain facets) for 31.8% of the investigated grains, the Laguerre tessellations were able to accurately describe statistical grain characteristics such as grain size distributions and grain neighbor distributions.
KW - Materials characterization and modelling
KW - Materials and energy storage
KW - Materialekarakterisering og materialemodellering
KW - Materialer og energilagring
U2 - 10.1002/adem.201000258
DO - 10.1002/adem.201000258
M3 - Journal article
SN - 1438-1656
VL - 13
SP - 165
EP - 170
JO - Advanced Engineering Materials
JF - Advanced Engineering Materials
IS - 3
ER -