Homogenization and elastic-plastic transitions in random and FGM microstructures

Functionally Graded Materials (FGM);Fractals;Homogenization;Multiphase materials;Elasticity;Plasticity

Saharan, Ankit

关键词: Functionally Graded Materials (FGM);    Fractals;    Homogenization;    Multiphase materials;    Elasticity;    Plasticity;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/78772/SAHARAN-DISSERTATION-2015.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The research presented here uses homogenization as a tool to estimate the effective properties of heterogeneous materials with varying microstructures. Separation of scales (Micro (d), Meso(δ), Macro (L)), in these microstructures leads to the problem of determination of the Representative Volume Element (RVE) that corresponds to the effective properties of materials. Microstructural randomness is inherent in these materials and hence we study the scaling from Statistical Volume Element (SVE) to RVE. Using Hill condition, the RVE is achieved when the material response becomes independent of the two boundary conditions (kinematic and static boundary condition) setup on the SVE. Elastic responses of 2d microstructures such as two-phase random checkerboard are considered, and RVE of the same is also identified. This technique is consistent with the Hill-Mandel macrohomogenity condition. We propose to homogenize the elastic response of FGM (functionally graded materials) type microstructure in 3d using the same technique. Since the Hill condition is independent of the microstructure, hence it is counter-intuitive that FGM microstructure can- not be easily homogenized using the same approach. The inelastic response of FGM microstructures in 2d and 3d are also studied here. The elastic-plastic transition in multiphase materials is smooth (not sudden), suggesting fractal nature of the evolving plasticity in the material. An attempt is made to calculate the fractal dimension of these evolving plastic grains in the 2d and 3d FGM microstructure. In 3d, this results in massive simulations performed in parallel using commercially available FEM package called ABAQUS. The simulations were carried out using the computational resources available at the National Center for Supercomputing Applications (NCSA). This opens up the possibility of assessing plastic damage in material through fractals. Preliminary experimental study using viscoelastic materials for FGM microstructure is also presented here. Furthermore, we also present the scaling effect under finite mesoscale size quantified in the form of normalized scaling function. We propose to study the effect of this scaling function for the two-phase correlated microstructures of Gaussian type, formulation of which is also presented here. Comparison with existing experimental data shows our numerical model is well in agreement with the experimental data for various volume fractions of the constituent phases.