TY - JOUR
T1 - Lattice models of polycrystalline microstructures
T2 - A quantitative approach
AU - Rinaldi, Antonio
AU - Krajcinovic, Dusan
AU - Peralta, Pedro
AU - Lai, Ying-Cheng
N1 - Funding Information:
This research is sponsored by the Mathematical, Information and Computational Science Division, Office of advanced Scientific Computing Research, US Department of Energy under contract number DE-AC05-00OR22725 with UT-Battelle, LLC. The authors desire to address a special thank to Dr. S. Simunovics for valuable support. Antonio Rinaldi expresses his gratitude to Prof. G. Farin at ASU for the kind help on the generation of the Voronoi’s froth.
PY - 2008/1
Y1 - 2008/1
N2 - This paper addresses the issue of creating a lattice model suitable for design purposes and capable of quantitative estimates of the mechanical properties of a disordered microstructure. The lack of resemblance between idealized lattice models and real materials has limited these models to the realm of qualitative analysis. Two procedures based on the same methodology are presented in the two-dimensional case to achieve the rigorous mapping of the geometrical and the elastic properties of a disordered polycrystalline microstructure into a spring lattice. The theory is validated against finite elements models and literature data of NiAl. The statistical analysis of 900 models provided the effective Young's modulus and Poisson ratio as function of the lattice size. The lattice models that were created have in average the same Young's modulus of the real microstructure. However, the Poisson's ratio could not be matched in the two-dimensional case. The spring constants of the lattices from this technique follow a Gaussian distribution, which intrinsically reflects the mechanical and geometrical disorder of the microscale. The detailed knowledge of the microstructure and the Voronoi tessellation necessary to implement this technique are supplied by modern laboratory equipments and software. As an illustrative example of lattice application, damage simulations of several biaxial loading schemes are briefly reported to show the effectiveness of discrete models towards elastic anisotropy induced by damage and damage localization.
AB - This paper addresses the issue of creating a lattice model suitable for design purposes and capable of quantitative estimates of the mechanical properties of a disordered microstructure. The lack of resemblance between idealized lattice models and real materials has limited these models to the realm of qualitative analysis. Two procedures based on the same methodology are presented in the two-dimensional case to achieve the rigorous mapping of the geometrical and the elastic properties of a disordered polycrystalline microstructure into a spring lattice. The theory is validated against finite elements models and literature data of NiAl. The statistical analysis of 900 models provided the effective Young's modulus and Poisson ratio as function of the lattice size. The lattice models that were created have in average the same Young's modulus of the real microstructure. However, the Poisson's ratio could not be matched in the two-dimensional case. The spring constants of the lattices from this technique follow a Gaussian distribution, which intrinsically reflects the mechanical and geometrical disorder of the microscale. The detailed knowledge of the microstructure and the Voronoi tessellation necessary to implement this technique are supplied by modern laboratory equipments and software. As an illustrative example of lattice application, damage simulations of several biaxial loading schemes are briefly reported to show the effectiveness of discrete models towards elastic anisotropy induced by damage and damage localization.
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U2 - 10.1016/j.mechmat.2007.02.005
DO - 10.1016/j.mechmat.2007.02.005
M3 - Article
AN - SCOPUS:34548561708
SN - 0167-6636
VL - 40
SP - 17
EP - 36
JO - Mechanics of Materials
JF - Mechanics of Materials
IS - 1-2
ER -