Buckling of fuel rods under inertia loading

Abstract

The buckling analysis of fuel rods during an end drop impact of a spent fuel transportation cask has traditionally been performed to demonstrate the structural integrity of the fuel rod cladding or the integrity of the fuel geometry in criticality evaluations for a cask drop event. The actual calculation of the fuel rod buckling load, however, has been the subject of some controversy, with estimates of the critical buckling load differing by as much as a factor of 5. Typically, in the buckling analysis of a fuel rod, assumptions are made regarding the percentage of fuel mass that is bonded to or that participates with the cladding during the buckling process, with estimates ranging from 0 to 100%. The greater the percentage of fuel mass that is assumed to be bonded to the cladding, the higher the inertia loads on the cladding, and, therefore, the lower the 'g' value at which buckling occurs. However, these solutions do not consider displacement compatibility between the fuel and the cladding during the buckling process. By invoking displacement compatibility between the fuel column and the cladding column, this paper presents an exact solution for the buckling of fuel rods under inertia loading. The results show that the critical inertia load magnitude for the buckling of a fuel rod depends on the weight of the cladding and the total weight of the fuel, regardless of the percentage of fuel mass that is assumed to be attached to or participate with the cladding in the buckling process. Therefore, 100% of the fuel always participates in the buckling of a fuel rod under inertia loading.     

A semi-analytical solution for deformation of elasto-viscoplastic circular thin plates under axisymmetric loading

For a circular plate under axisymmetric loading a semi-analytical solution is derived. It is supposed that the total strain tensor can be decomposed additively into a purely elastic and an inelastic part. The evolution of the inelastic strain is governed by a constitutive model with internal state variables. The inelastic boundary value problem is solved analytically. The initial value problem posed by the inelastic constitutive model is integrated numerically. Numerical results are presented for a full, clamped plate under uniform, but time dependent pressure where the inelastic deformation is governed by Hart's constitutive model.     

Ductile fracture of cracked steel plates

A simple relationship between loading for crack initiation, or onset of ductile tear, and crack length is presented for center-cracked plates of mild steel. Formulation of the nonlinear boundary-value problem is based on incremental theory of plasticity for Prandtl-Reuss materials. Quasi-static solutions corresponding to a series of incremental loading conditions are obtained by the mothod of finite elements. Tests conducted on plates of two types of mild steel agree with numerical results.     

Lower bound limit load of a circumferentially cracked pipe under combined mechanical loading

In a study on extension of the reference stress method, for J simplified assessment, to a three dimensional (3D) configuration under combined loading, lower bound limit analysis has been developed by J. Desquines. In the present paper the limit load for cracked pipe, with a 3D circumferential flaw, under pressure, tension and bending is detailed. The limit load is explicitly defined as a yield surface is the 3D space loading. A simple algorithm is proposed to solve the non linear problem associated to the reference stress calculation. Moreover, the lower bound solution is compared with Elastic Compensation Method (ECM) results computed on a 3D finite element mesh of the cracked pipe. The lower bound yield surface underestimates the numerical limit loads with a discrepancy lower than 20%.     

A transient creep solution for uniaxial tension rectangular thin plates with central circular holes

A general method for the solution of non-linear creep problems is presented. This method reduces the creep problem to a sequence of elastic problems with initial strains. The solution of the elastic problem with initial strains is determined using four displacement functions together with the point-matching method. The method is based on the extension of Goodier's concept of reducing a thermoelastic problem to one at constant temperature with no body force. Using this method, creep behaviour in the vicinity of a circular hole in a uniaxial tension thin rectangular plate has been investigated for a time-hardening material law. The results show how stress concentration factors vary with time for various combinations of geometrical shape and stress index.     

Simplified J estimation methods for cracked cylinders under combined thermal and mechanical loading

In the field of non-linear fracture mechanics, a lot of work has been done on structures submitted to mechanical loadings. However, for thermal loadings and particularly for thermal shocks, only few results are available. The aim of this paper is to present the main results of a complete set of finite element (FE) computations, conducted by CEA, EDF and FRAMATOME, on cracked cylinders submitted to combined mechanical and thermal loads. The interaction between these two types of loads is analysed in the cases of austenitic and ferritic structures. Moreover, these results are compared to the predictions obtained by simplified engineering methods (R6 procedure and two French approaches) in order to improve them. Their domain of validity is also discussed.     

Device for testing concrete under impact tensile loading and lateral compression

At the Delft University of Technology the dynamic material response of concrete is being investigated, using the split Hopkinson bar technique (SHB). To gain more insight into the influence of the initial stress conditions on the dynamic response, the SHB has been combined with a static compression loading device perpendicular to the SHB. This paper describes the test set-up, the monitoring techniques and the tests performed during the development of the biaxial loading device. Special attention is paid to the interaction of both loading devices in the biaxial set-up.     

On the creep deformation of a thin tube under combined loading

Approximate analyses are briefly described for the creep curvature of a thin constant thickness, circular cross-section cylindrical shell under various loading. The loads are bending moment, internal pressure, and torsion, which may be applied in any combination. It is shown that the results have a certain common feature which allows their presentation in a rather simple but useful form.     

Buckling analysis of a cylindrical shell,under neutron radiation environment

This research investigates the buckling of a cylindrical shell in the neutron radiation environment, subjected to combined static and periodic axial forces. Radiation induced porosity in elastic materials affects the thermal, electrical and mechanical properties of the materials. In this study, the data based technique was used to determine the volume fraction porosity, P, of shell material. A least-squares fit of the Young's module data yielded the estimated Young's modulus. The shell assumed made of iron irradiated in the range of 2–15e?7 dPa/s at 345–650 °C and theoretical formulations are presented based on the classical shell theory (CST). The research deals with the problem theoretically; keeping in mind that one means of generating relevant design data is to investigate prototype structures. A parametric study is followed and the stability of shell is discussed. It is concluded that both temperature and neutron induced swelling have significant effects on the buckling load.     

Elasto-plastic analysis of thin shells under thermal transients

The objective of this paper is to use a thermal-elasto-plastic algorithm developed by the authors in order to find the temperatures and thermal stresses that are produced by time-dependent thermal loads, such as the ambient temperatures and prescribed surface heat fluxes. These loads must be given as functions of time. With the thermal conductivities and surface film coefficients given for heat conduction, and the elastic and plastic material properties for stress analysis, the outcome is the temperature, displacement, and stress distributions that are produced by the thermal transients. We apply the analysis to thin shells; that is, objects that have one dimension, wall thickness, smaller than any other length. Even though the ideas given here appy to shells of general shape, we limit the analysis in this paper to cylindrical shells and consider axisymmetric thermal loads only. For verification, the results of a simple problem are compared with those of an established finite element code, and the agreement is noted. The algorithm presented here is well suited for the calculation of residual stresses that are produced by cyclic thermal loads. It is applied to the induction heating stress improvement (IHSI) in pipes. The general features of the IHSI are reproduced.     

Transient analysis of thick-walled piping under polynomial thermal loading

The transient response of a thick-walled pipe subjected to a generalized excitation of temperature on the internal surface was derived using Duhamel’s relationship. Generalization of the temperature excitation was achieved by using a polynomial composed of integral- and half-order terms. In order to avoid the evaluation of recurring functions in the complex domain, Laplace transformation and a 10-term Gaver–Stehfest inversion formula were used to perform part of the necessary integrations. Excellent agreement between the derived relationships and existing analytical and finite-element solutions was seen for a thick-walled cylinder subjected to an asymptotic temperature rise on the exposed surface. As intended, the use of a smoothed polynomial allows the incorporation of empirical date not easily represented by standard functions. Moreover, the resulting relationships are easily programmed and can be used for a wide range of nuclear, piping, and cylindrical vessel applications.     

Crack opening behavior of penetrated crack under cyclic or monotonic loading

Crack opening displacements (CODs) were examined experimentally at room temperature for both plate and pipe specimens containing a surface crack. Application of COD solutions from plate specimens, as proposed by the present authors, to pipe specimens were investigated. COD after penetration could be satisfactorily determined regardless of a type of load using the COD, solutions proposed by the authors.     

Simplified creep analysis of perforated plates under steady creep condition

A study is performed on the creep analysis of perforated plates based on the equivalent solid plate concept.A series of creep analyses by FEM for various materials, ligament efficiencies and loading conditions is performed on a perforated plate with a triangular penetration pattern of circular holes. Based on the results of the analysis, prediction methods for both the equivalent solid plate property and the stress-strain concentration around the hole are proposed.The prediction method for the equivalent solid plate property is compatible with the elastic property shown in the ASME B&PV Code Sec. III A-8000. The prediction method for the stress—strain concentration is based on Neuber's rule together with Hoff's analogy, and is compatible with the elastic peak stress multiplier in the ASME B&PV Code Sec. III A-8000.     

Seismic analysis of cracked reactor vessels

This paper deals with the dynamic response of a thin finite, elastic circular cylindrical shell representing a reactor vessel to time-dependent loadings symmetrical with respect to the axis of the cylinder. The shell contains an axial through-crack of length 2c. The dynamic counterpart of Donnell's shell equations are used in this investigation. Extensive numerical results are presented for stress intensity factors in aluminum and steel vessels and results are discussed.     

A statistical based circumferentially cracked pipe fracture mechanics analysis for design or code implementation

This paper discusses a simple engineering approach to evaluate surface flaws in carbon steel or stainless steel piping and their weldments. It is based on statistical data from a large number of pipe fracture experiments. To ensure a reasonably conservative approach, a 95-percent confidence level was established. Toughness and pipe size effects are accounted for in one correction factor, while ovalization and flow stress effects are accounted for in two other factors. The limitations and possible improvements to such an approach are also discussed.     

Buckling of a stud-supported thin cylindrical liner shell encased in concrete

The problem of a point-supported liner shell encased in a rigid cylindrical cavity is studied. The large displacement equations are developed, and the resulting non-linear equations are solved in closed form for an assumed buckling wave. The analytical model is specialized to the case of the ring or infinite cylinder under circumferential strain, and is compared to published results. Complete load displacement curves are presented for the ring or cylinder with a predominate circumferential strain, and for the axisymmetric response or cylindrical shells under an axial load. The results of this study can be used to determine the spacings of point supports for cylindrical liner shells.     

Numerical analysis of circular elastic-plastic plates under cycles of pressure and temperature

A numerical approach is considered to compute neutral domains (ND) of elastic response for the so-called load control-program (LCP), i.e. for the relation ƒ(p,T) = 0, where p and T are pressure and temperature parameters, respectively. Elastic-plastic material with combined isotropic-kinematic strain-hardening is adopted. Material characteristics are assumed to be functions of temperature in incremental equations of the theory of plastic flow. Small strains are assumed but geometrical and equilibrium equations are derived for moderately large deflections. Distribution of temperature in the plate is assumed to be known in every point of the plate ξ, as the function (ξ, T). The method of solution lies in computation of a sequence of boundary-value problems, first along the LCP curve, then along the ND curve. The BV problem is solved by means of forward numerical integration. Coordinates of points on the ND curve are computed by use of an iterative procedure which bases on a directed search approach. Computations have been carried out for a sandwich annular plate for linear and piecewise LCP.     

Structural analysis of a Japanese BWR MARK-I containment under internal pressure loading

This paper describes the elastic-plastic analysis of the Japanese BWR MARK-I steel containment vessel under pressure loadings by a general purpose finite element method code ADINA. The present study is focused on the entire deformation of the vessel rather than the stress or strain concentrations around the structural singularities such as penetrations. Elastic deformation limits, displacements and equivalent stress distributions are discussed.