Seiya Hagihara

Elastic constant matrix required for thermal stress analysis of bulk single crystals during Czochralski growth

The elastic constant matrix of cubic single crystals such as GaAs and InP which are used in electronic and optical devices is required in the thermal stress analysis of their bulk single crystals during the Czochralski growth. In this paper, the components of this matrix are expressed in terms of an arbitrary Cartesian coordinate system and a cylindrical coordinate system. They depend on the azimuthal component of the cylindrical coordinate system and the terms containing the azimuthal coordinate cannot be neglected even in approximate sense. Strictly speaking, a three-dimensional thermal stress analysis may be required for those single crystals instead of an axisymmetric analysis.

Thermal stress analysis of bulk single crystal during Czochralski growth (comparison between anisotropic analysis and isotropic analysis)

Abstract A three-dimensional finite element program is developed for calculating the thermal stress in bulk single crystals during Czochralski growth. Elastic anisotropy is taken into account in this program. Thermal stress analyses of a GaAs bulk single crystal are performed in the cases of the [001] and [111] pulling directions, using its temperature distribution obtained from a heat conduction analysis and its material properties. The stress component and the dislocation density parameter are compared between the anisotropic analysis, taking account of elastic anisotropy, and the isotropic analysis, using Youngs modulus and the Poisson ratio in the {111} plane. Significant differences are found in their values and distribution patterns between both analyses.

Bifurcation creep buckling analysis of circular cylindrical shell under axial compression

Abstract In some experiments conducted by other authors, axially compressive cylindrical shells with a large ratio of radius to thickness were observed to buckle with circumferential waves. In this paper, the finite element method is used to study this buckling phenomenon. The bifurcation mode and the axisymmetric mode were considered in the analysis as the mode of creep buckling. The number of circumferential waves obtained from the present analysis agrees well with experimental results. This implies that the circumferential waves observed in the creep buckling experiments are due to bifurcation.

Finite Element Analysis for Local Creep of a Tube Coolant Piping System in Light Water Reactor Due to Local Heating Under Severe Accident Condition

During severe accident of a light water reactor (LWR), reactor coolant piping would be damaged when the piping is subjected to high internal pressure and very high temperature due to heat transfer from high-temperature gas and decay heat from wall-deposited fission product (FP), both from degraded core. In such a case, high-temperature fast creep deformation could be the main cause for the pipe failure. For the evaluation of piping integrity during severe accidents, a method to predict such high-temperature fast creep deformation should be developed, using a creep constitutive equation considering tertiary creep behavior which has not been considered well in the pipe failure analyses. In this paper, a creep constitutive equation was developed, which is based on the Kachanov-Ravotnov isotropic damage rule considered the tertiary creep behavior. Japan Atomic Energy Research Institute (JAERI) creep tensile test data for nuclear-grade cold-drawn SUS316 material was used to determine coefficients of the developed constitutive equation. Using the developed constitutive equation, finite element analyses were performed for local creep deformation of coolant piping under two temperature conditions; uniform temperature and temperature gradient. The analyses results indicated the damage variable being integrated following the evolution of creep damage can indicate pipe wall internal damage condition quantitatively. The damage variable was confirmed further to be able to reproduce the observation in JAERI piping failure tests; pipe failure from the wall outside.Copyright

Finite element creep buckling analysis of circular cylindrical shell under axial compression taking account of creep damage

Cylindrical shells are utilized as structural elements of nuclear power plants, heat exchangers or pressure vessels, which are operated under elevated temperature. Creep buckling is one of the failure modes of structures at elevated temperature. In some experiments conducted by other authors, axially compressive cylindrical shells with a large ratio of radius to thickness were observed to buckle with circumferential waves. It is observed that the circumferential waves occur due to bifurcation buckling. But, the critical time and the minimum loading for bifurcation buckling obtained from calculations of finite element analyses are not in very good agreement with those of the experiments. One of the reasons for the disagreement is considered to be that the creep constitutive equations employed in many previous analyses represent the steady creep. The creep phenomena usually have primary creep period, steady creep one and tertiary creep one. A creep strain - time relation through the three periods can be simulated by using a constitutive equation based on creep damage mechanics. In the present analysis, we analyzed the bifurcation creep buckling of circular cylindrical shells subjected to axial compression by the use of the finite element method taking account of the creep damage mechanics proposeol by of Kachanov-Rabotonov.

Effect of Texture on Plastic Flow Localization of FCC Polycrystals Using Homogenization-Based Polycrystalline Plasticity

In this study, a framework to predict the onset of plastic flow localization is introduced. The Marciniak-Kuczyński type approach, which is a classical method to predict the strain localization, and a crystal plasticity model with a homogenization-based finite element method are combined, and forming limit strains that are defined as the onset of plastic flow localization for FCC polycrystals are computed. The forming limit strains with several kinds of textures are evaluated with the present approach, and the results are compared with those obtained by the Taylor model, which is a widely used conventional polycrystalline model. Within the present application, the present method and the classical Taylor model give similar forming limit strains for FCC polycrystal sheets. According to the present results, the use of the Taylor model in the sheet necking analysis might be justified, at least for FCC polycrystal sheets with various textures.

Calculation of Dynamic Fracture Mechanics Parameter Using the Element-Free Galerkin Method

The objective of this study is to present a procedure based on the element-free Galerkin method (EFGM) for evaluating dynamic fracture parameters. The EFGM is one of the famous meshless methods. By using the EFGM, the first derivatives i.e. strain and stress for a structural analysis have continuity because of moving least square method (MLSM). When contours used for evaluating path independent integrals, such as the J-integral, are chosen, it can be regardless of the analyzed mesh. In fracture mechanic problems, the EFGM may be useful to calculate fracture mechanics parameters for crack propagation problems. In this study, half-round contours are applied to evaluate dynamic fracture parameter J-integrals. The center cracked plate subjected to tension with a Heaviside function which depends on time has been successfully analyzed and dynamic stress intensity factors have been evaluated by calculating the dynamic fracture mechanics parameter J-integrals. We have found that the EFGM can evaluate the fracture mechanics parameters appropriately and that fracture mechanics analyses of the EFGM using arbitrary contours was much easier than that of the FEM.

Finite element dynamic bifurcation buckling analysis of torispherical head of BWR containment vessel subjected to internal pressure

Abstract In this paper the bifurcation buckling pressure for the torispherical head of the Mark II type BWR containment vessel subjected to dynamically applied internal pressure is calculated, using a finite element program for a dynamic analysis. Three kinds of dynamic loadings, that is, step loading, ramp loading and pulse loading are considered in the present analysis. The minimum bifurcation buckling pressure is predicted for the respective loadings. The minimum bifurcation buckling pressure for dynamic loading is much lower than the bifurcation buckling pressure for static loading.

Effect of Lattice Rotation on Hardening Behavior of HCP Metals

Strain hardening behavior is known to strongly affect the formability of metallic sheets. The effect of lattice rotation on the hardening behavior of hexagonal close-packed (HCP) metals is numerically investigated using a homogenization-based crystal plasticity model to represent the polycrystalline behavior. The effect of lattice rotation on strain hardening behavior evaluated using different initial textures, and the geometrical hardening effect of HCP metals is investigated. In addition, the critical resolved shear stress of each slip system is varied and is shown to affects the strain hardening in HCP metals. In this study, we further discuss the possibility to improve the formability of HCP metals.

Quantitative Evaluation of Deformation Twinning Behavior in Polycrystalline Pure Magnesium

A crystal plasticity analysis of polycrystalline pure magnesium is conducted to investigate deformation twinning behavior at the crystal grain scale. A dominant factor in the onset of deformation twinning is the resolved shear stress on a twinning system. More than one twin system may simultaneously be activated in a crystal grain, resulting from inhomogeneous stress distribution caused by constraints imposed by neighboring grains. In this study, a pure magnesium polycrystal is modeled using a fine finite element mesh and analyzed using the crystal plasticity model involving deformation twinning. The evolution of deformation twinning at the crystalline scale is numerically investigated, and the present approach demonstrates that two or more twinning systems are be activated in a single crystal grain because of the strong inhomogeneity in the grain.