Multiscale analysis of piezoelectric material by using EBSD-measured realistic model

Material properties of a polycrystal piezoelectric ceramic, a barium titanate BaTiO3, were analyzed by the two-scale crystallographic homogenization method. Threedimensional (3-D) micro-finite element (FE) model was constructed based on the electron backscatter diffraction (EBSD) measured crystal orientation distribution images. The images are piled up to a 3-D voxel data of crystal orientation distribution by repeating mechanically and chemically polishing, and EBSD measurement of the ceramic. We obtained 13 EBSD images of 128×100 pixels, which measurement interval was 0.635μm in-plane and the average amount of polishing was 1.66μm in thickness (normal) direction of specimen. Each voxel of EBSD was assigned into 8-node solid FE in-plane with maintaining resolution of EBSD measurement, and was divided into three FEs along thickness direction with same crystal orientation, because of improvement of aspect ratio of FE. The total number of FEs was 499,200 (=128×100×13×3) which corresponded to over two millions degrees of freedom. In order to realize a large-scale micro-analysis using EBSD-measured voxel FE model, the coupled problem of the piezoelectric material was solved by parallel conjugate gradient (CG) method combined with the block Gauss-Seidel (BGS) method. The coupled micro-FE equation to obtain characteristic function vectors was separated into two linear equations, such as the elastic deformation and electrostatic analyses, by employing the BGS method, and then the equations were solved by the parallel CG solver while substituting coupling terms each other. Therefore, nested iterative scheme was constructed on a PC cluster. In addition, the representative volume element (RVE) size was determined based on the orientation distribution function analyses of EBSD voxel data. The least RVE size was 25,000μm3, which corresponded to include 150 crystal grains

A new crystal plasticity constitutive equation based on crystallographic misorientation theory

Since plastic deformation of polycrystal sheet metal is greatly affected by its initial and plastic deformed textures, multi-scale finite element (FE) analysis based on homogenization with considering micro-polycrystal morphology is required [1]. We formulated a new crystal plasticity constitutive equation to introduce not only the effect of crystal orientation distribution, but also the size of crystal grain and/or the effect of crystal grain boundary for the micro-FE analysis. The hardening evolution equation based on strain gradient theory [2], [3] was modified to introduce curvature of crystal orientation based on crystallographic misorientation theory. We employed two-scale structure, such as a microscopic polycrystal structure and a macroscopic elastic/plastic continuum. Our analysis code predicts the plastic deformation of polycrystal metal in the macro-scale, and simultaneously the crystal texture and misorientation evolutions in the micro-scale. In this study, we try to reveal the relationship between the plastic deformation and the microscopic crystal misorientation evolution by using the homogenized FE procedure with the proposed crystal plasticity constitutive equation. The crystallographic misorientation evolution, which affects on the plastic deformation of FCC polycrystal metal, was investigated by using the multi-scale FE analysis. We confirmed the availability of our analysis code employing the new constitutive equation through the comparison of a uniaxial tensile problem with the numerical result and the experimental one

Microscale electrical contact resistance analysis for resistance spot welding

Electrical contact resistance is an important parameter for resistance spot welding. In this study, a microscale electrical contact resistance analysis method is pro- posed for resistance spot welding. The microscale electrical contact resistance analysis method is combination of an elasto–plastic large deformation contact analysis and an electric current analysis. The electric current analysis is performed for deformed shape of asperity. The tendency of the electrical contact resistance on contact pressure and tem- perature for the electrical contact resistance analysis agrees with that for Babu’s electrical contact resistance model. A multiscale coupled analysis method is also proposed for resistance spot welding. The multiscale analysis consists of macroscale elasto–plastic large deformation contact, electric current and thermal conduction triply coupled analysis and microscale electrical contact resistance analysis. It is confirmed that the resistance spot welding analysis without measurement of electrical contact resistance can be performed by using the microscale electrical contact resistance analysis

Thermal Fluid Coupled Analysis of Hydrothermal Destruction Reactor

Multi-regionally coupled analysis of thermal fluid flow and heat conduction of solid using OpenFOAM is carried out to clarify the behavior of hydrothermal oxidative destruction reactor of polychlorinated biphenyls (PCBs). Internal fluid of the reactor assumes a single-phase hot water without chemical reactions considering temperature dependence of thermophysical properties. Compressible Navier-Stokes equation with buoyancy force and energy equation with gravity term are alternately solved for the thermal fluid analysis. In order to consider conjugate heat transfer between the internal fluid and the reactor vessel, two-regionally coupled analysis of the fluid and vessel was executed by chtMultiRegionFoam solver in the OpenFOAM. To verify coupling effect, the multi-regionally coupled analyses results were compared with thermal fluid analysis of the internal fluid or heat conduction analysis of the vessel

Multi-Region and Multi-Component Thermal Fluid Analysis of Hydrothermal Oxidative Decomposition Reactor

To elucidate the corrosion mechanism of a hydrothermal oxidation decomposition reactor for the treatment of polychlorinated biphenyls (PCBs), a coupled thermal fluid analysis of the heat transfer between two mixtures of fluids with different physical properties and the reactor body was executed using OpenFOAM. Based on the analysis results, we propose a method to evaluate the corrosion risk at the solid-liquid interface by focusing on three factors: (1) the corrosion temperature of reactor vessel, (2) the amount of fluid deposition that causes corrosion, and (3) the wall shear stress on the solid-liquid interface. Variation of corrosion risk with operating conditions of the reactor is discussed

Multiscale analysis of piezoelectric material by using EBSD-measured realistic model

Material properties of a polycrystal piezoelectric ceramic, a barium titanate BaTiO3, were analyzed by the two-scale crystallographic homogenization method. Threedimensional (3-D) micro-finite element (FE) model was constructed based on the electron backscatter diffraction (EBSD) measured crystal orientation distribution images. The images are piled up to a 3-D voxel data of crystal orientation distribution by repeating mechanically and chemically polishing, and EBSD measurement of the ceramic. We obtained 13 EBSD images of 128×100 pixels, which measurement interval was 0.635μm in-plane and the average amount of polishing was 1.66μm in thickness (normal) direction of specimen. Each voxel of EBSD was assigned into 8-node solid FE in-plane with maintaining resolution of EBSD measurement, and was divided into three FEs along thickness direction with same crystal orientation, because of improvement of aspect ratio of FE. The total number of FEs was 499,200 (=128×100×13×3) which corresponded to over two millions degrees of freedom. In order to realize a large-scale micro-analysis using EBSD-measured voxel FE model, the coupled problem of the piezoelectric material was solved by parallel conjugate gradient (CG) method combined with the block Gauss-Seidel (BGS) method. The coupled micro-FE equation to obtain characteristic function vectors was separated into two linear equations, such as the elastic deformation and electrostatic analyses, by employing the BGS method, and then the equations were solved by the parallel CG solver while substituting coupling terms each other. Therefore, nested iterative scheme was constructed on a PC cluster. In addition, the representative volume element (RVE) size was determined based on the orientation distribution function analyses of EBSD voxel data. The least RVE size was 25,000μm3, which corresponded to include 150 crystal grains

Microscale electrical contact resistance analysis for resistance spot welding

Electrical contact resistance is an important parameter for resistance spot welding. In this study, a microscale electrical contact resistance analysis method is pro- posed for resistance spot welding. The microscale electrical contact resistance analysis method is combination of an elasto–plastic large deformation contact analysis and an electric current analysis. The electric current analysis is performed for deformed shape of asperity. The tendency of the electrical contact resistance on contact pressure and tem- perature for the electrical contact resistance analysis agrees with that for Babu’s electrical contact resistance model. A multiscale coupled analysis method is also proposed for resistance spot welding. The multiscale analysis consists of macroscale elasto–plastic large deformation contact, electric current and thermal conduction triply coupled analysis and microscale electrical contact resistance analysis. It is confirmed that the resistance spot welding analysis without measurement of electrical contact resistance can be performed by using the microscale electrical contact resistance analysis