Critical impact energies for scabbing and perforation of concrete target

In this paper, the influences of the relative target thickness (H/d) on those critical impact energies, at which local damage of various forms in concrete targets are initiated, are explored. The empirical formulae developed in the R3 Impact Assessment Procedure [BNFL, 2003. Reinforced Concrete Slab Local Damage Assessment, R3 Impact Assessment Procedure, vol. 3, Appendix H. Magnox Electric plc & Nuclear Electric Limited] are rationalized by different methods. A dimensional analysis was conducted to identify influential non-dimensional numbers, which were subsequently employed in the analyses of the experimental results relevant to scabbing and perforation by flat nosed missiles.The relationships between the non-dimensional impact energy at failure and the non-dimensional target thickness H/d are presented for all of the relevant experimental data in the “World Impact Data” collection [Bainbridge, P., 1988. World Impact Data—S.R.D. Impact Database Version Pre 3i, CCSD/CIWP(88)107(P)]. This collated hundreds of experimental data on local damage in concrete targets due to missile impact from various sources of nuclear industries, as well as experimental data from the UK electrical power industry used to develop empirical formulae in the R3 Impact Assessment Procedure [BNFL, 2003. Reinforced concrete slab local damage assessment, R3 Impact Assessment Procedure, vol. 3, Appendix H. Magnox Electric plc & Nuclear Electric Limited]. The experimental data in Bainbridge [Bainbridge, P., 1988. World Impact Data—S.R.D. Impact Database Version Pre 3i, CCSD/CIWP(88)107(P)] are compared with empirical and semi-empirical formulae for scabbing and perforation in order to examine the effects of H/d on the critical non-dimensional impact energy for these two local failures. An analytical formula based on a penetration-plugging model is employed to give the relationship between the critical impact energy and target thickness for perforation by a flat-ended projectile. Comparisons between these formulae and experimental data are presented.     

Impact load for tornado-generated missiles

Nuclear power plant structures are designed to resist impact loads from tornado-generated missiles. The paper gives a method to determine the contact pressure at the interface of the missile and the target, and the velocity and deceleration time-histories of the missile. It also gives a method to obtain the design load due to impact by tornado-generated missiles. The calculated design load compares very well with the total support reaction from a full-scale dynamic test. The comparison between the predicted deceleration and the deceleration recorded in a test is excellent. The method of determining the deceleration has also been used with very good results for earth-penetrating missiles.     

Load combination by partial safety factors

The Load and Resistance Factor Design (LRFD) format, which is a generic form of most current mechanical and structural design criteria, is accepted to be appropriate for load combination purposes. The meaning of the load factors in the framework of a LRFD format is discussed from a theoretical point of view. These load factors can be obtained by suitable calibration procedures. The problems that arise in the application of these procedures are analysed.A new calibration methodology is formulated and its operative aspects are dicussed. In this approach, the structure is designed to have a high reliability under permanent and quasi-permanent loads. Consistent degrees of safety for different design situations are achieved by calibrating the combination factors to be applied to the short-duration loads. Some numerical examples of this new calibration procedure are presented.The applications in reactor technology may be of some interest. The structural components of a nuclear power plant are generally subjected to several actions of different nature. By adopting the approach discussed in this paper, the reliability of every sub-structure has to be assessed only when the sub-structure is subjected to a set of few actions in combination. Moreover the safety analyses can be conducted in a deterministic context, all probabilistic calculations being limited to a preliminary investigation on the loads.     

Characterization of plastic collapse load determination in circumferentially through-wall cracked elbows

The solutions of cracked elbow are shown to be excessively conservative and on occasion, non-applicable to the cases for which they are intended. The objective of the work described in this paper is to use the 3D non-linear finite element method (FEM) backed up with experimental results to determine the collapse limit load. Non-linear finite element analyses were performed considering both material and geometrical non-linearity using the advanced fracture analysis code WARP3D. Various alternative methods are used to determine plastic collapse loads based on the FEM calculated load–displacement curves. The predicted collapse loads are compared to collapse loads determined by available solutions and finally these are compared to experimental results. The work can be considered as the source of the benchmark data that helped to shape the engineering treatment of piping elbows in design codes.     

Structural damping values as a function of dynamic response stress and deformation levels

The development of extreme load design criteria both as to rate and depth within any national jurisdiction as applied to nuclear power plant design is a function of several factors. The prime factor is the number of nuclear power plant facilities which are operating, under construction or planned in a given country. The second most important factor seems to be the degree of development of a domestic independent nuclear steam system supplier, NSSS vendor. Finally, countries whose domestic NSSS firms are active in the export market appear to have more active criteria development programs or at least they appear more visible to the foreign observer.For the purposes of this paper, extreme loads are defined as those loads having probability of occurrence less than 10⁻¹/yr and whose occurrence could result in radiological consequences in excess of those permitted by national health standards. The specific loads considered include earthquake, extreme wind (tornado), airplane crash, detonation, and high energy system rupture. The paper identifies five national centers for extreme load criteria development; Canada, Great Britian, USA, USSR, and West Germany with both France and Japan also about to appear as independent centers of criteria development. Criteria under development by each national center are discussed in detail.     

Critical impact energy for the perforation of metallic plates

This paper investigates the empirical formulae used in engineering practice to predict the critical perforation energy of metallic plates struck by rigid projectiles in the sub-ordnance regime. Main factors affecting the critical perforation energy are identified and valid conditions for each empirical formula are compared. Dimensional analysis is conducted to show the dependence of the non-dimensional critical impact energy on other influential non-dimensional numbers. Available empirical formulae are re-expressed in non-dimensional forms. A modified Jowett/AEA equation is proposed to predict the critical perforation energy of a flat-ended short projectile. The present work increases the confidence of using these empirical formulae and can be regarded as a quick guide for ballistic protection design of metallic shields and steel armour plates.     

An energy approach study of the penetration of concrete by rigid missiles

This paper presents an energy approach for investigating the penetration of concrete by rigid missiles and the associated phenomena. However, the principal assumptions made here must be validated experimentally before giving the proposed subject further considerations. In the following, a new measure for concrete resistance to penetration by hard missiles is presented. The suggested term for this measure is “the Volumetric Crushing Energy Density” of concrete which can be described as the energy required for converting a unit volume of concrete to separate particles under compressive loading so that the particles of the crushed volume meet certain gradation criteria. Using this quantity, an explanation of the scale effect is postulated. Moreover, a dimensionless semi-analytical formula for the penetration depth of a rigid missile in a concrete target is proposed which includes a large number of the variables of the problem. The formula assumes that the penetration incident may include several successive phases where the set of variables that governs the impact is different during each phase, and the variables that characterize the impact during each phase correlate in a different manner as well. Furthermore, many of the penetration depth formulae available in the literature are rewritten according to the formula proposed here where the concrete penetration resistance of any incident is estimated by modifying the resistance of “reference impact incidents.” The rewritten formulae show the wide variation of the values of concrete resistance which are implicitly included in the original formulae. Finally, the proposed formula is applied using data of penetration experiments presented by Forrestal et al. [Forrestal, M.J., Altman, B.S., Cargile, J.D., Hanchak, S.J., 1994. An empirical equation for penetration depth of ogive-nose projectiles into concrete targets. Int. J. Impact Eng. 15(4), 395-405; Forrestal, M.J., Frew, D.J., Hickerson, J.P., Rohwer, T.A., 2003. Penetration of concrete targets with deceleration-time measurements. Int. J. Impact Eng. 28, 479-497] to estimate the values of penetration resistance of the concrete targets.     

Thermal–structural analysis of ITER triangular support for dominant load verification

The triangular support is located on the lower inner shell of vacuum vessel of ITER, which should be designed to withstand various loads such as nuclear heat, coolant pressure and so on. The appropriateness of its design is evaluated under the dominant load that could represent the most conservative condition among the design loads. In order to decide the dominant load, a valid method for thermal–structural analysis is firstly verified considering contradictory behaviors between heat and structural loads.In this paper, two approaches; one-way coupling and load combination, are introduced for thermal–structural analysis. The one-way coupling is a method generally used but has a limit to apply on contradictory conditions. The load combination could give a proper solution since it evaluates each load independently and then adds up each result linearly. Based on the results of each case, structural analysis for another load case, baking condition with incident, is conducted to find out which load is dominant for triangular support.Consequently, it is found that the baking condition is the dominant load for triangular support bracket. The proposed load combination method gives a physically reasonable solution which can be used as a reference for checking the validity of other thermal–structural analysis. It is expected that these results could be applied for manufacturing design of the triangular support under various load conditions.     

Numerical design of a 20 MW lead–bismuth spallation target for an accelerator-driven system

A spallation target system is a key component to be developed for an accelerator-driven system (ADS). It is known that a 15–25 MW spallation target is required for the practical size of an ADS. Although there have been some design studies for small power spallation targets, that is, less than 10 MW, designs of high power target systems for ADS are relatively rare. The design of a 20 MW spallation target is very challenging because more than 60% of the beam power is deposited as heat in a small volume of the target system. In the present work, a numerical design study was performed to get optimal design parameters for a 20 MW spallation target for a 1000 MW ADS. The cylindrical beam tube and the hemispherical beam window were adopted in the basic target design concept with 1 GeV proton energy, and the thermal-hydraulic and the structural analyses were performed with the CFX and ANSYS codes. The beam window diameter and thickness were varied to find the optimal parameter set based on the design criteria: maximum lead–bismuth eutectic (LBE) temperature <500 °C, maximum beam window temperature <600 °C, maximum LBE velocity <2 m/s, and the maximum beam window stress <160 MPa. The results of the present study show that a 40 cm wide proton beam with a uniform beam profile should be adopted for the spallation target of 20 MW power. It was found that a 2.5 mm thick beam window is needed to sustain the mechanical load.     

Effective-lenght factors for buckling of cable-tray supports

Cable tray systems at many nuclear power facilities are supported by structural steel supports. These supports are safety related and therefore must be evaluated for seismic loads. Because vertical and horizontal earthquake motion may induce compressive loads on some supports, these supports must be design verified to meet compressive load (buckling) allowables. Although trapeze supports suspended from the ceiling are inherently more stable than floor-mounted supports, they must be evaluated for compressive loads as well as the floor-mounted supports. Many ceiling-suspended supports are attached to flexible concrete slabs which may induce vertical accelerations which exceed gravity. For this reason, such supports must be designed to withstand compressive loads in the vertical posts regardless of the cyclic nature of such loads and of the stabilizing effect of gravity.Many industry-accepted design procedures evaluate the stability of individual elements of a frame rather than the stability of the entire frame. In many cases, these industry-accepted design procedures may be overly conservative due to the simplifying assumptions that must be made ragarding the end restraints of each element of the frame.For this study, effective-length factors were developed for the buckling of cable-tray supports typically used at nuclear power facilities. The buckling response of the entire cable-tray support was considered. Nonlinear finite element analyses were performed to obtain the effective-length factors. Sensitivity studies were performed to assess influences of (a) vertical load distribution, (b) transverse loads, (c) longitudinal restraint, and (d) rotational restraint at support anchorages. These influences were important in obtaining effective-length factors. All were accounted for in developing the effective-length factors except the influence of transverse load which was conservatively neglected.     

Extended applications of LBB piping evaluation diagrams for a new plant design

Plant specific data, such as pipe geometry, material properties and pipe loads, are required to apply leak-before-break (LBB) to a piping system. Thus, LBB evaluation cannot be done until piping design and routing are completed. A simple method for evaluating LBB for piping systems during design process considering the effects of nozzle and the change in local and global compliance in cracked piping system is developed in this paper. This method produces piping evaluation diagrams for intermediate pipe locations and pipe-nozzle interface locations which defines the LBB requirements to the piping designer for use during the design process and is independent of pipe routing. Piping evaluation diagrams can be used for the LBB evaluation for a new plant design.     

Systematics for (n,p) excitation functions in the neutron energy between 13.3 and 15.0 MeV

Systematics of (n,p) excitation functions in the neutron energy between 13.3 and 15.0 MeV were studied on the basis of experimental data measured by the Nagoya and Fusion Neutronics Source groups. The empirical formulae of a cross section (σ₁₄) at 14.0 MeV and a relative slope (S) of excitation functions were deduced. These formulae covered the mass range between 19 and 188. The empirical formula of S was expressed as a function of (N—Z)/A and threshold energy, where N, Z and A are the mass, proton and neutron numbers numbers for the target nuclei, respectively. The empirical formula of σ₁₄ was expressed by a simple formula with two fitting parameters. By using the proposed empirical formulae, the partial excitation functions between 13 and 15 MeV were reproduced. Comparing the experimental data with the calculated excitation functions, we concluded that the accuracy of the proposed empirical formulae was ± 20%.     

Transient thermo-mechanical behavior of a direct-drive target during injection in an inertial fusion energy chamber

During injection in an inertial fusion energy (IFE) chamber, a direct-drive target is subject to heat loads from chamber wall radiation and energy exchange from the chamber gas constituents. These heat loads can lead to the deuterium-tritium (DT) reaching its triple point temperature and even undergoing phase change, leading to unacceptable non-uniformity based on target physics requirements for compression and ignition of the DT fuel pellets using multiple laser beams. A two-dimensional bubble nucleation mode was added to the previously presented thermo-mechanical model to help better define the design margin for direct-drive IFE targets. The new model was validated by comparison with analytical results for controlled cases. It was then used to simulate heating experiments on DT targets conducted at the Los Alamos National Laboratory (LANL), where the ³He present in the DT due to tritium decay was found to affect the nucleation process.The previous requirement for target survival was for the temperature of the DT to remain below triple point of DT (19.79 K). If the existence of a melt layer does not violate the symmetry requirements on the target for successful implosion, the constraint could be relaxed by assuming a limit based on the avoidance of bubble nucleation. This study shows that the thresholds for melting and bubble nucleation are significantly different, allowing for extra margin in target survival under this assumption.     

Methods for reliability of structures under multiple time varying loads

Current probabilistic studies on load combination have been concentrating on the modeling and linear combination of loads and load effects. Herein, a methodology for the assessment of life-time reliability of structural systems under multiple time varying loads is proposed. The method is based on considerations of load occurrences (including coincidence) and conditional probability of failure given occurrence whereby current methods of structural reliability and random vibration analysis can be incorporated. It has a wide range of applications. The emphasis is on the time domain load behavior, structural capacity uncertainty and non-linear dynamic load effects. The accuracy and computational advantage of this method as compared with other methods are examined by a numerical example of a simple frame under loads modeled as Poisson renewal pulse processes. Also, the errors implied in the widely used ‘Turkstra’ rule, a recently proposed modification of this rule, the load reduction factor method, and a SRSS (square root of sum of squares) rule for load combinations are quantified for linear combination and the implications in risk evaluation mentioned.     

Numerical Assessment of Spent Fuel Casks Impacting on Real Targets

Abstract

A reference container of high capacity was analysed for loads beyond those it has to withstand during a 9 m IAEA drop test onto an unyielding target. In doing this a lid-end drop with shock absorber onto a real target was simulated. This is a possible accident for the rail transport of such casks. In this case the most critical components of the containment system are the primary lid bolts. The behaviour of the lid system and its sealing function were investigated with finite element (FE) analysis. To correlate the findings with a corresponding impact velocity onto real targets an analytical method was used. Despite the conservative assumptions made in this study a two-fold safety factor compared to the 9 m drop tests onto the unyielding target could be shown. The quantification of the additional safety the cask might provide requires further basic investigations on the behaviour of the real targets considered as well as the reduction of the conservatism included in the assumptions made up to now.     

Model tests of turbine missile impact on reinforced concrete

The results of 25 impact tests on 1/11-scale models of reinforced concrete nuclear plant walls are presented. These tests determined experimentally the maximum velocity at which postulated turbine missiles are contained by typical reinforced concrete walls. The parameters varied were missile weight, velocity, orientation, and impact angle, as well as target design and thickness. The results showed that the NDRC perforation formula used extensively in current practice is overly conservative, whereas a newer empirical formula (CEA-EDF) gave reasonably conservative predictions of the test results. All but the most energetic postulated missiles are stopped by containment wall models, and steel liners on these walls are effective in suppressing backface concrete scabbing.     

Pipe rupture and steam/water hammer design loads for dynamic analysis of piping systems

The design of restraints and protection devices for nuclear Class I and Class II piping systems must consider severe pipe rupture and steam/water hammer loadings. Limited stress margins require that an accurate prediction of these loads be obtained with a minimum of conservatism in the loads. Methods are available currently for such fluid transient load development, but each method is severely restricted as to the complexity and/or the range of fluid state excursions which can be simulated. This paper presents a general technique for generation of pipe rupture and steam/water hammer design loads for dynamic analysis of nuclear piping systems which does not have the limitations of existing methods. Blowdown thrust loadings and unbalanced piping acceleration loads for restraint design of all nuclear piping systems may be found using this method. The technique allows the effects of two-phase distributed friction, liquid flashing and condensation, and the surrounding thermal and mechanical equipment to be modeled. A new form of the fluid momentum equation is presented which incorporates computer generated fluid acceleration histories by inclusion of a geometry integral termed the “force equivalent area” (FEA). The FEA values permit the coupling of versatile thermal-hydraulic programs to piping dynamics programs. Typical applications of the method to pipe rupture problems are presented and the resultant load histories compared with existing techniques.     

Experience in the application of a finite element system to the analysis of complex prestressed concrete pressure vessels

The increasing geometric complexity of prestressed concrete pressure vessels (PCPVs) requires an accurate mathematical idealization of the shape of the structure. Finite elements of the isoparametric type provide one answer to this problem. The commercial availability of finite element analysis packages requires the designer to make a careful selection of a suitable package and adapt and extent that system to suit his particular needs. This paper discusses the application by Taywood Engineering Ltd, of the Atkins Stress Analysis System (ASAS) to the analysis of complex, multi-podded PCPVs.

Details are given of the modelling process and the choice of grid fineness to be used. The preparation of data and the associated comprehensive checking procedures are described. The selection of material properties is of prime importance in finite element analysis and the dependence of the properties on temperature and creep is discussed together with the way in which results from only three analyses can be combined to provide the designer with the required information. Considerable emphasis is laid on the provision of small pre- and post-processing programs designed to remove the tedium of such large analyses and to leave the designer free to concentrate on the important engineering aspects of his design.

The significance of the work lies in the fact that a suite of programs has been built around a general finite element system to satisfy the precise needs of a vessel designer. A design office tool has been produced which is economic in terms of the time and effort required in data preparation and assessment of results.     

Abstracts on Packaging,Transport, Storage and Security of Radioactive Material

Abstract

The design testing of packages for radioactive materials considers normal operating conditions and accident conditions. A mechanical test, especially under accident conditions, must include the safety assessment of possibly undetected material defects. BAM has developed improved assessment methods, using fracture mechanics, for cracks in the most highly stressed regions of cubic containers made of ductile cast iron. Postulated surface cracks in the centre of the container walls and grooves are investigated numerically. In the static case relations between the crack tip parameters (stress intensity factor or the J integral, respectively), stress load, crack depth, container geometry and material behaviour are derived. In the dynamic case it can be shown by numerical simulations of the drop test of containers onto different targets, even without shock absorbers, that the dynamic crack tip parameter may be estimated by static formulae with the dynamic stress inserted in the intact component. This somewhat surprising result can be explained by the fact that the drop event happens over milliseconds. That is slow enough for the crack to behave quasistatically although the crack is loaded with a dynamic, i.e. time-dependent, stress. Based on these calculations, the critical crack depth is given as a function of the stress, the material quality (defined by the fracture toughness) and the wall thickness for surface cracks in the centre of walls as well as in grooves of a cubic container.     

A Study on the New Empirical Cross Section Formulae for (γ, p) Reactions at 20 ± 1 MeV Incident Energy

In this study, we have investigated theoretical cross sections of (γ, p) reactions at 20?±?1 MeV for the photon incident energy and then we have obtained two new empirical formulae for 40?≤?A?≤?108 and for the even Z-even N target nuclei including new fitting parameters. These new empirical formulae depending on the asymmetry parameters (s?=?(N???Z)/A) were determined by using the least squares approximation fitting method to the available experimental cross section data taken from EXFOR. The results have been compared with the experimental data and found to be well in agreement.