Changes in shape of internally pressurized tubes caused by operating temperatures and pressures are enhanced by fast neutron irradiation. Lengths and diameters of Zr-2.5Nb pressure tubes in CANada Deuterium Uranium-Pressurized Heavy Water (CANDU-PHW) power reactors and test reactors have been monitored periodically over the past 20 years. Axial and transverse strain rates have been evaluated in terms of operating variables and the crystallographic texture and anisotropic microstructure of the extruded and cold-drawn tubes. The anisotropic deformation occurring during steady-state irradiation creep and growth is described by a self-consistent model that takes into account the presence of intergranular stresses without building up any discontinuities of strain and stress at the grain boundaries. In this model, it is assumed that climb-assisted glide of dislocations on prismatic, basal, and pyramidal planes is the dominant creep mode and that growth occurs by net fluxes of interstitials and vacancies to a non-random distribution of dislocations and grain boundaries. The predictions from a deformation equation based on data from the Pickering and Point Lepreau Nuclear Generating Stations and the WR1, Osiris, DIDO, and NRU test reactors are in good agreement with measurements of pressure tubes in Bruce units. The equation has been employed as a material subroutine in the 3-D finite element code H3DMAP for predicting the detailed shape change of pressure tubes. The prediction from H3DMAP is a more complete description of shape change than that obtained from the closed-form expression.

Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented.

No abstract

The occurrence of flow-induced vibration fretting wear in process equipment such as heat exchangers and steam generators accounts for the majority of the failures due to vibration. One of the parameters which plays a vital role in the prediction of tube wear rate is the impact force which occurs when the free displacements of the tube exceed the clearance in the support plates, resulting in a collision. To date the determination of these impact forces reported in the literature has been restricted to simplified mathematical models which consider only straight spans of tube with gaps. The need to consider more generalized configurations has led to the development of an analytical method which simulates the nonlinear dynamic-impact response of multi-supported tubes including U-bends and the effect of nonuniform gap clearances at the supports. The approach is incorporated into a computer code based on the finite element and displacement methods using an unconditionally stable numerical integration scheme to solve the nonlinear equations of motion. The algorithm developed includes equilibrium iteration and variable time stepping based on convergence criteria, which ensures that temporal solution errors are minimized. The direct integration of the equations enables all the frequencies (subject to the finite element mesh) to be included. This is necessary since the high-frequency response at impacting may be significant. At present, the method is being used to simulate impact between tubes and support plates in steam generators and heat exchangers in order to determine tube bundle susceptibility to fretting wear failure at the design stage or operational phase. The paper describes the analytical development of the method, verification cases, and applications to the problem of tube/support plate impacting.

In a number of applications, the hydrodynamic effect of a fluid must be included in the structural evaluation of liquid-filled vessels undergoing transient loading. Prime examples are liquid radioactive waste transportation packages. These packages must demonstrate the ability to withstand severe accidental impact scenarios. A hydrodynamic model of the fluid is developed using a finite element discretization of the momentum equations for a three-dimensional continuum. An inviscid fluid model with an isotropic stress state is considered. A barotropic equation of state, relating volumetric strain to pressure, is used to characterize the fluid behavior. The formulation considers the continuum as a compressible medium only, so that no tension fields are permitted. The numerical technique is incorporated into the existing general-purpose three-dimensional structural computer code H3DMAP. Part 1 of the paper describes the theory and implementation along with comparisons with classical theory. Part 2 describes the experimental validation of the theoretical approach. Excellent correlation between predicted and experimental results is obtained.