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We have studied the buckling behavior of rectangular bellows under pressure loads. Our final objective is to establish the design guidelines for the rectangular bellows of an experimental fusion reactor, the ITER, the International Thermonuclear Experimental Reactor. Based on the numerical investigation by the FEM, we proposed a simplified method to evaluate the buckling pressure. The evaluation method of the buckling pressure for circular bellows can be found, for example, in the standards of the expansion joint manufacturers association in the U.S.A. (EJMA Standards). For rectangular bellows, however, investigation of the buckling behavior is limited, and EJMA does not provide a method for evaluating the buckling pressure. Therefore, we investigated the buckling behavior of rectangular bellows by the FEM and proposed a simplified evaluation method based on the half-pitch model.

Experimental and theoretical investigations were carried out on heat transfer tubes of an intermediate heat exchanger (IHX). The IHX is a helium;helium heat exchanger of the high-temperature engineering test reactor (HTTR), which is a high-temperature gas-cooled reactor being under construction in Japan. In the IHX, if the secondary gas was lost in an accident, the tubes would be subjected to an external primary gas of 4 MPa at high temperature and the possibility of the creep collapse would occur. Thus, it is indispensable to evaluate the collapse time of the tubes and confirm a calculated method to predict the creep collapse behavior of the tubes under external pressure. Here, the effect of the initial ovality, wall thickness, and pressure level on the collapse time of a heat transfer tube subjected to both constant and cycled external pressure at elevated temperature was examined experimentally and analytically. The creep deformation of the tube obtained by FEM code and the simplified method was a good approximation. The simplified method proposed by Nishiguchi et al. is an effectual method in the estimation of the creep buckling deformation and the collapse time of the tube under external pressure at elevated temperature as compared with themore » experimental results and the FEM. Though many cracks initiated by creep collapse were observed on the outer surface of a few test tubes, the cracks did not pass through the tube thickness, and leak tightness was maintained despite a collapse for all tubes tested.« less

The effects of the initial ovality, wall thickness and pressure level on the collapse time of a heat transfer tube subjected to external pressure at high temperatures were examined experimentally and analytically. The creep deformation of the tube obtained by the ABAQUS code was a good approximation. The predictions of the creep collapse time were in fairly good agreement with the experimental results. Though many cracks initiated by creep collapse were observed on the outer surface of a few test tubes, the cracks did not pass through the tube thickness and the leak tightness was maintained regardless of a collapse for all tubes tested.

The viscoplasticity theory based on overstress (VBO) is extended to finite deformation (FVBO). Yield surfaces and loading/unloading conditions are not part of this theory which represents creep, relaxation, and rate sensitivity in a “unified” way. Additive decomposition of the rate of deformation into the elastic and the inelastic parts is assumed. For the elastic part, the hypoelastic relation is used. For the inelastic part, the flow law of VBO is augmented by a term quadratic in the overstress together with a modified Jaumann stress rate which jointly or separately allow the modeling of second-order effects.

A one-step time integration method is developed for the finite deformation theory of viscoplasticity based on overstress (FVBO) described in Part I. This time integration method is based on a forward gradient approximation and it leads to explicit expressions of the tangent operators suitable for finite element implementation. Numerical experiments and closed-form solutions for a hypoelastic material in homogeneous deformation states are presented. The FVBO is applied to the modeling of second-order effects in torsion. The numerical results show that a modification of the Jaumann rate and second-order terms of the inelastic rate of deformation are necessary to model the observed effects.

A simplified method is proposed to predict the creep collapse behavior of a long tube subjected to external pressure. The shape of the cross section of a tube is assumed to be quasi-elliptical characterized by a single variable, often called as shape factor in the literature. The growth of the displacement field is represented by the change of shape factor which is governed by an ordinary differential equation. A general class of creep constitutive equations can be employed with an accompanying elasticity whose effect is crucial under higher external pressure. Plane strain condition is assumed. Nonlinearity of stress distribution through the wall of the tube is allowed according to the creep constitutive equation in general, while the strain distribution is assumed to be linear. The method is applied to the analyses of heat tubes, which are typical for heat exchangers of high-temperature gas-cooled reactors, and is compared with the computer solution by the finite element method based on a finite deformation theory, as well as solutions by other simplified methods.

General parametric elements adopt different functions for the expression of unknown field variables and the mapping of geometric configurations. By introducing the concept, paper shows that useful singularity and infinite elements can be produced in a unified manner. In the derivation of these especial elements, a technique is incorporated for imposing respective constraint conditions in the analysis. In the second part of paper, the technique is generalized so that a variety of constraint conditions are implemented in the standard finite element analysis routine at the level of element stiffness formations. It is pointed out that the joint or interface element is also an interesting application of the proposed method.