Lattice models of polycrystalline microstructures: A quantitative approach

Abstract

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.

A multiscale quasicontinuum method for dissipative lattice models and discrete networks

“…Likewise, for investigating the mechanical responses of other materials, e.g. concrete and polymers, lattice models and discrete networks are often applied (Lilliu and Van Mier, 2003;Cusatis et al, 2003;Ostoja-Starzewski and Wang, 2006;Rinaldi et al, 2008;Kim and Buttlar, 2009;Zhao, 2012). The advantage of discrete models is that they naturally incorporate discrete phenomena occurring in meso-and microstructures of many materials.…”

A quasicontinuum methodology for multiscale analyses of discrete microstructural models

“…else → sum truss node by adding 1 to the weight factor of triangle t if no internal sampling node in triangle t is selected yet → select truss node i as internal sampling node -Partition f c,s and K c,s , solve system and update solution according to Equation (14) energy is exact, but accepting some error. However, for two-dimensional structural lattice models with only nearest neighbor interactions such as the example considered in this study, the computational cost of the exact method remains acceptable as will be shown in Section 3.…”

A three-dimensional cohesive-frictional grain-boundary micromechanical model for intergranular degradation and failure in polycrystalline materials

“…Das et al [41] coupled finite elements and cellular automata (CAFE) and showed the potential for microstructural and multiscale analysis of heterogeneous and polycrystalline materials. Also lattice models for quantitative estimates of the mechanical properties of polycrystalline microstructures and their damage have been reported [42]. The application and advantages of peridynamics for modelling crack initiation, propagation and fragmentation in polycrystalline ceramics are discussed in [36].…”