Material properties for reactor pressure vessels and containment shells under dynamic loading

The effects of high strain rate, dynamic biaxial loading and deformation mode (tension, shear) on the mechanical properties of AISI 316 austenitic stainless steel in as-received and pre-damaged (creep, LCF) conditions are reported. This research was conducted to assess the performances of the containment shell of fast breeder reactors. The results of this research have been utilized to prepare similar investigations for SA 537 Class 1 ferritic steel used for the containment shell of LWR. The first results of these investigations are reported. A programme to study the mechanical properties of plain concrete with real size aggregate at high strain rate is described.     

Steel containment resistance under dynamic pressure

Loadings to cause severe accidents on containment buildings can include combinations of uniform internal pressure, dynamic pressure, and seismic. Most studies that have been conducted to predict containment building capacity have focused on the effect of overpressurization on containment performance. A simple methodology that permits rapid and reasonably accurate analysis for assessing the capacity of steel containment buildings due to global or local uniform or spatially varying dynamic loading was developed. An axisymmetric model was used and the circumferential variation of the pressure, displacements, and stress resultants were represented by Fourier series. Shell vibration and buckling analysis were performed using modified versions of BOSOR4 and BOSOR5 finite difference codes. The modified version of BOSOR5 allows the input of pressures that vary along the meridianal direction. These pressures were increased until failure of the containment occurred. Failure was defined to occur when membrane strains reached twice the yield strain or the bifurcation point was introduced. The applicability of this analysis method was verified by analyzing several problems as well as a simplified containment building. The axisymmetric analysis demonstrated a powerful tool to access the capacity of steel containment buildings.     

Assessment of CDFR primary containment capability under HCDA loading

The paper reviews UK studies of fast reactor containment response under hypothetical core disruptive accident (HCDA) loading, describing the evolution of complementary programmes of model experiments, numerical methods development and code validation. Results are presented from studies of the CDFR primary vessel, roof and core support structure, with particular emphasis on recent experimental work: these examples illustrate the level of detail required in the assessment of containment structures. The status of the work is critically reviewed, drawing attention to problems associated with the extrapolation of data from model experiments to the reactor situation. The likely direction of future work is indicated, focussing on more detailed assessment of particular structural features, the performance of seals and the study of leakage.     

Non-linear response of reinforced concrete containment structure under blast loading

The paper demonstrates the effect of an external explosion on the outer reinforced concrete shell of a typical nuclear containment structure. The analysis has been made using appropriate non-linear material models till the ultimate stages. The generation and the propagation of blast wave and its effect on a cylindrical structure are discussed. Parametric studies have also been performed for surface detonations of different amount of blast charges at a distance of 100 m from a nuclear containment shell. Critical distances have been evaluated for different amount of blast charges for nuclear containment shell.     

Investigation of steel containment buckling under dynamic loads

Buckling of freestanding nuclear steel containment buildings from dynamic base excitation was investigated in a combined experimental/numerical program. A polycarbonate scale model of a containment building was excited with scaled earthquake transients and single-frequency harmonic transients to determine the peak base acceleration levels required to induce buckling. Buckling was identified using recorded signals from strain gages and accelerometers, with high-speed video records, and by audibility. Experimental results are compared with numerical results obtained by using a freezing-in-time technique. The results are preliminary, since several more tests are to be performed. However, the limited data obtained indicate that the freezing-in-time technique approximates the required acceleration levels reasonably well, although not conservatively. Additional experiments are described that will take containment asymmetries into account, as well as use instrumentation that will provide more accurate measures of the occurrence of buckling.     

Wave propagation effects in dynamic loading

The problem of the maximum credible accident (MCA), and more recently that of the design basis accident (DMA) for LMFBR, has up to now been studied under conditions of symmetry with respect to the source of the dynamic loading. Calculation codes have been developed to take into account the events generated in the centre of the core, with respect to which the vessel is in position of symmetry. Thus, even experiments on models have been carried out taking similar loading conditions into account. Under these conditions, no waves propagate in the vessel inasmuch as it is deformed symmetrically with respect to its central axis. In reality, however, asymmetries are found. In fact, the sodium-fuel reaction, the event judged today to be the most probable for the DBA, can be generated in any subassembly. Moreover, rupture of the thermal shields at one point inside the vessel could provoke the concentration of a pressure pulse in a restricted area of the vessel. This would lead to a asymmetric loading on the vessel which might be very dangerous insofar as it has not been foreseen in the calculations of pressurized vessels. In addition, this pulse, localized in a restricted area of the vessel, will propagate elastoplastic waves along the wall until they collide at a point symmetrically opposite to the one at which the pulse was generated. These reflections can therefore give rise to pressure peaks in the material which are capable of becoming considerably higher than the original ones. Yet another complication is caused by the presence of penetrations, nozzles, etc. which create stress concentration points and give rise to further reflections.We have performed dynamic tensile tests using the Hopkinson bar system on short test-pieces of AISI 304L and AISI 316L and various carbon steels, both at room and working temperatures, and for strain rates of between 10⁻² and 10³ sec⁻¹. Mild steels present, as expected, a sharp increase of stress-strain curve and a reduction of elongation to rupture with increasing strain rate, and a sharp peak for yield stress. Austenitic stainless steels show a rise of stress-strain curve and a reduction of elongation to rupture at increasing strain rate; at strain rates higher than 800 sec⁻¹ the flow stress tends to oscillate. These instabilities would lead one to expect a variation in the propagation velocity of the plastic waves during the deformation. If this hypothesis is proved to be correct, it would add yet another complication to the laws of the trans-mission of deformation waves in the vessel, and of their reflections. We are therefore preparing some experiments on wave propagation in long test-pieces which will also contribute to determine the constitutive equations of materials.     

Conservative estimates for dynamic containment loads from hydrogen combustions

For the design of severe accident resistant reactor containments estimates are needed for limiting dynamic loads from hydrogen combustion processes. This paper presents some first exploratory results.The approach for a systematic study of dynamic loads from large scale hydrogen detonations is described. The parameter range of H₂-steam-air detonations is defined and then narrowed down to the region which seems accessible in severe reactor accidents. Maximum possible hydrogen masses, unfavorable hydrogen distributions and limiting detonation cases are discussed. The effect of gas composition, geometry, and scale on detonation pressurs and impulses was investigated with one-dimensional calculations. An accident scenario which combines many conservative parameters was analyzed. The one-dimensional modeling, which contains a high degree of conservatism, resulted in 10.5 MPa peak pressure and 60 kPa s reflected impulse (at 30 ms) over approx. 1400 m² containment surface.     

Analytical study on dynamic buckling of reactor containment vessel

The dynamic buckling of a reactor containment vessel under earthquake conditions is evaluated using a nonlinear finite element method. It is based on the four-node MITC (mixed interpolated tensorial components) shell element originally proposed by K.J. Bathe, which has been modified by the authors to include the effect of large rotational increments. At first, the buckling modes for a thin cylindrical shell under a simplified base excitation were classified, then the dynamic buckling analysis of a typical PWR steel containment vessel was carried out, considering both geometrical and material nonlinearities, to compare the results with those of a conventional static analysis. It was found that the global shear buckling of a steel containment vessel occurred under a load level several times greater than the design earthquake, and the buckling load estimated by the conventional analysis was smaller than the buckling load estimated by the dynamic analysis.     

Nonlinear dynamic response of cracked reinforced concrete nuclear containment vessels

In the design of reinforced concrete nuclear vessels horizontal cracks are assumed to exist as a result of pressurization. Seismic shear forces must be transmitted across these cracks. The nonlinear dynamic response of cracked vessels is studied. The force-displacement relationship across the cracks are taken from the experimental investigation that included the shear transferred by the concrete but not by dowel action of the vertical steel. The stiffness is highly nonlinear, hysteretic, and degrading. A modal analysis technique, based on an eigenvalue reanalysis procedure, is developed and it is compared with a direct numerical integration solution. Only typical response values are given for particular values of the variables and for one particular earthquake input.     

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.     

Constitutive laws of materials in dynamics—outline of a programme of testing on small and large specimens for containment of extreme dynamic loading conditions

A sound foundation of stress and/or strain criteria for the mechanical design of fast breeder reactor structures capable of bearing extreme dynamic loading conditions, passes through the experimental determination of dynamic mechanical properties of materials in end-of-life conditions with respect to the damaging processes to which the structures are submitted.Calculation codes must be implemented by constitutive equations describing the dynamic mechanical response of the materials, without the knowledge of which any calculation code is liable to important inaccuracies which provoke the use of high safety coefficients and, often, the uncertainty as to the effective capability of the structures to withstand the accidental loads.The results of a screening programme of dynamic tensile tests performed on AISI 304 and AISI 316 austenitic stainless steels using small specimens (7 mm²) showed that the dynamic response of such steels at temperatures of 400 and 550°C is not univocal, passing from a substantial dynamic hardening behaviour to a dynamic softening behaviour, probably due to residual microstructural differences caused by the transformation processes.From the discussion of the results obtained, follows the development of a testing programme on small (up to 20 mm² cross section) and large specimens (up to 5000 mm² cross section) focused on: (i) developing and calibrating dynamic constitutive equations founded on basic physical aspects, for uniaxial and multiaxial loading conditions under particular deformation and loading histories; (ii) verifying in dynamics the existing yielding criteria, hardening rules and failure theories; (iii) investigating by means of a high-load apparatus (5 MN) the influence of near real-size thickness, welding, defects and notches, on dynamic strength and deformation capability of large reactor structures.     

Evaluation of flawed piping under dynamic loading

This paper describes analytical studies of several of the large-scale flawed pipe experiments conducted for the International Piping Integrity Research Group (IPIRG), including detailed discussion of the test with the longest loading duration. Dynamic excitation with increasing load amplitude leads to failure of the piping at a predesignated test section containing a large manufactured flaw. Here, elastic analysis is shown to describe the system dynamic response reasonably well, provided that an appropriate value of structural damping can be selected. A simplified two degree-of-freedom model displays sensitivity to damping and is used to help select the optimal damping value for use in subsequent finite element calculations. The total damping for the IPIRG piping system is caused by a combination of structural damping from the support conditions and from plastic deformation at highly-stressed locations, such as at the degraded cross section itself or at the long-radius elbows. Effective, calculated damping values for the IPIRG tests varied by an order of magnitude, with low values of 0.5 to 1% associated with short-duration dynamic response and 5% or more for the long-duration test. The discussion includes comparisons of the calculated IPIRG results with ASME Code-suggested analysis damping values.     

Stresses and strains in the steel containment resulting from transient pressure and temperature loading during loss-of-coolant accident

Posttest calculations of stresses and strains in the steel containment of the German research reactor HDR were performed for a simulated LOCA. The results of the theoretical investigations will be presented and compared to experimental findings. The pressure and temperature loading of the shell was determined with the thermodynamic code COFLOW on the basis of a multi-compartment model. Using a three-dimensional finite element model the temporal behaviour of the containment was calculated employing the structural mechanics code ASKA. Global bending deformations and local negative straining of the steel shell is discussed. Theoretical and experimental results agree in most cases rather well. Reasons for deviations will be discussed. The specific behaviour of strains found in the vicinity of locally heated areas will be explained by means of analytical considerations.     

Coolant boiling noise in LMFBRs

The noise that may arise due to boiling of Na in LMFBRs is investigated. The study deals specifically with investigations of the likely frequency range of Na boiling and its dependence on local parameters like coolant flow velocity, cavity size and contact angle.     

Nuclear containment in France

An outline of the two types of containment buildings as employed in the power reactors of France are discussed. The behavior of the containment structures for specific accident assumptions are studied.The response of the two types of containment employed is observed to be quite distinct.     

Dynamic loading of containment during blowdown: review of experimental data from marviken and brunsbüttel

This paper deals with the problem of the dynamic loading of the pressure suppression type containment due to pressure fluctuations which are induced during blowdown as a result of steam condensation in the suppression pool. It reviews the experimental data on pressure fluctuations and on the corresponding dynamic response of the structures submerged in the water charge. Two series of containment response experiments were performed on real pressure suppression systems. One series of measurements was performed within the framework of relief valve vent tests in the Brunsbüttel Power Plant (Federal Republic of Germany) in 1974. Another series of measurements was carried out within the framework of the blowdown tests performed at the Marviken Power Plant (Sweden) in 1972–1973.For the measurements of pressure fluctuations in the suppression pool strain gage-based pressure transducers were used. The dynamic response of the loaded structure was measured by strain gages or by piezoresistive (in some cases piezoelectric) accelerometers. The signal was amplified by carrier-frequency amplifiers (or loading amplifiers). The amplified signals were recorded on magnetic tape (FM recording). A two-step evaluation procedure was used. In the first step the time history plots of the variables directly measured (such as pressure, bending strain and acceleration) were plotted and interpreted. In the second evaluation step the cross-power spectral density function of different signal pairs was calculated, plotted and interpreted. For evaluation of the fluctuating pressure field in the suppression pool the combination was chosen of a reference pressure signal (measured at a fixed position called ‘reference position’) with a second pressure signal (measured at a different, arbitrary position) in most cases to perform the cross-spectra analysis. The set of cross-spectral density functions obtained by analyzing all signal combinations chosen was used to determine the power spectra, RMS amplitudes and phases of the corresponding pressure waves impinging on the structure submerged in the suppression pool. For the evaluation of pressure field—structural response relations one pressure signal was combined with one response signal (bending strain or acceleration) to give the input for cross-spectral analysis. By the combination of two response signals (bending strain—bending strain or acceleration—acceleration) for cross-spectral analysis the modal shapes of the responding structure was determined.