Fracture behavior of recrystallized and stress-relieved Zircaloy-4 cladding under biaxial stress conditions

Pellet-cladding mechanical interaction (PCMI) under reactivity-initiated accident conditions may lead to failure of high-burnup fuel rods. The biaxial stress states of Zircaloy cladding tubes induced by PCMI loading presumably makes the tubes more susceptible to failure. To clarify the influence of the anisotropic mechanical properties of Zircaloy cladding tubes on their fracture behavior under biaxial stress conditions, biaxial tensile tests were performed, and the measured stresses and strains were converted to reduced parameters such as equivalent strain, equivalent stress, and stress triaxiality by using the anisotropic constants of the Hill yield function derived in our previous study. The minimum fracture strains of recrystallized (RX) and stress-relieved (SR) specimens were located where the stress ratio of axial to circumferential is 0.75. The equivalent plastic fracture strains tended to decrease monotonously with increasing stress triaxiality, which is a typical trend observed in ductile fracture, in the range of 0.65–0.78 for both specimens. In the case of SR specimens, however, the analysis with stress triaxiality did not reduce the fracture strains well to a single trend curve, showing that another influential factor is required such as an anisotropic fracture behavior or a plastic behavior deviated from that predicted by the yield function.     

Fracture assessment of a brittle RPV under cold loading

The oldest Swedish reactor is a boiling water reactor (BWR) with a vessel made of A302 Grade B with rather high Cu and Ni content. These elements have intensified the irradiation embrittlement in the beltline region so that RT_NDT of certain welds may exceed 100 °C at the end-of-life condition. A preliminary study of the fracture risk for the beltline region showed that the limiting loading case would be the cold over-pressurization of the reactor. The objective of this study was to develop a reliable methodology for fracture assessment of the aged reactor vessel under cold loading scenarios. The test program covered experiments on standard SEN(B) specimens and clad beams under uniaxial and biaxial loading. The test material was a reactor vessel steel prepared with a special heat treatment to simulate fracture toughness properties of the aged reactor. No significant effects of shallow crack and biaxial loading were observed on cleavage fracture toughness in different clad specimens. While the ASME K_Ic reference curve was shown to be overly conservative, the Master Curve methodology satisfactorily predicted the experimental outcomes of the test program. The Master Curve methodology indicated that a 20-mm deep surface crack was acceptable in the beltline region under a cold over-pressurization scenario. This value was three times greater than what a methodology based on the ASME K_Ic reference curve yielded.     

Fracture mechanical assessment of cracks under cyclic thermal shock and operational conditions

For different deep nozzle corner cracks under cyclic thermal loading the problem of crack initiation and fatigue crack growth is described. In consideration of elastic-plastic material behavior the influence of local constraint is discussed when determining crack initiation with material constants and correlating possible fatigue crack growth by crack growth laws.     

Fatigue strength in polymer-reinforced concrete beams under cyclic loading

This research focuses on producing an inexpensive polymer, and also on experiments for producing various colors of the high strength polymer concrete in concrete structures. At present, only a few tests on the shear behavior of polymer-reinforced concrete (PRC) beams have been reported. Even fewer experiments on fatigue loading have been carried out to date. In the current experiments, reinforced concrete beams with a polymer fraction are investigated. The beams in this study are reinforced with conventional stirrups at appropriate intervals, and are designed to take static and fatigue loads. The strength of the beams is measured and the behavior of the beams under each loading are observed to determine the advantages of adding a polymer to reinforced concrete beams. Since the shear-fatigue behavior of PRC beams is not well understood, the appropriate limit state model of PRC beams subjected to shear-fatigue loading is developed in this research by incorporating the uncertainties which are assessed based on fatigue test results. Using specimens of reinforced concrete or PRC beams with and without stirrups, compression and split cylinder tests, as well as fatigue tests, were performed. The static test data consist of load, displacement and strain measurements at specified reinforcement locations. In this study, mean regression S---N curves are obtained to investigate the shear-fatigue characteristics that the test results are distributed over a wide fatigue life range at the same fatigue load level but, in general, the mean shear-fatigue strength of PRC beams with stirrups is higher than for PRC beams without stirrups. In the static tests, it has been observed that the beams have the same fracture modes as those of reinforced concrete. In the fatigue tests, the PRC beams were observed to perform rather poorly with regard to impact load, but it can be said that the increase in strength and excellent repair performance of the beams were verified. Consequently, this work strongly suggests that steam curing or air curing must be used to increase the strength.     

Dynamic uniaxial and biaxial stress-strain relationships for austenitic stainless steels

The question of reliability technology using quantified techniques is considered for systems and structures. Systems reliability analysis has progressed to a viable and proven methodology whereas this has yet to be fully achieved for large scale structures.Structural loading variants over the life-time of the plant are considered to be more difficult to analyse than for systems, even though a relatively crude model may be a necessary starting point. Various reliability characteristics and environmental conditions are considered which enter this problem.The rare event situation is briefly mentioned together with aspects of proof testing and normal and upset loading conditions.     

Critical strains and necking phenomena for different steel sheet specimens under uniaxial loading

When defining ultimate loads or failure criteria for shells, vessels and containment liners, for instance, reference will be made to critical strains of the material under consideration.In general the critical strains are derived from uniaxial tensile test results obtained with rods.The actual deformation behaviour of sheets (plate and shell type structures), however, differs considerably from the uniaxial rod behaviour.From various tests - along with theoretical investigations - it was found that for membrane or even bending stressed sheets higher ultimate strains are reached.The typical strain behaviour caused by increasing load starts with uniform strain distribution over the specimen length and finally ends with localized necking.As “critical strains” the well known uniform elongation strain and the ultimate strain are defined.For sheets in addition the quasi uniform elongation strain has been introduced in this paper.Whereas for rods under tension localized necking is directly following the uniform straining, tests with sheets show a so-called diffuse necking behaviour before localized necking starts.As a consequence the deformation capacity of steel sheets turns out to be significantly higher than relying on the data from standard tension tests with rods.     

Single and multi degree of freedom analysis of steel beams under blast loading

This paper presents detailed analysis of the results of field tests on 13 full scale wide flange steel beams subjected to blast loads generated by the detonation of up to 250 kg of ANFO explosive. The experimental results are analyzed using an equivalent Single-Degree-of-Freedom (SDOF) model of a beam, which includes material nonlinearity and strain rate effects. To account for strain rate effect on beam stiffness and strength, its full moment-curvature response is determined by dividing its cross-section into a number of layers and a strain rate-dependent stress-strain relationship, based on the Cowper–Symonds strain rate model, is used to capture the nonlinear stress distribution over the section. To determine the effects of higher modes of vibration and the variation of beam mechanical properties along its length on its dynamic response, the test beams are also analyzed using a Multi-Degree-of-Freedom (MDOF) model involving beam finite elements. Each element has two nodes and three degrees of freedom and is again divided into a number of layers to capture the strain rate effect and nonlinear stress distribution over its depth. The predicted displacements and strains by the two models are compared with the corresponding experimental data and the results show that for the given beams, the time-dependant deformations, internal forces, and moments can be adequately predicted by either model because the first mode of vibration is found to dominate their response; however, the use of a constant strain rate through the so-called Dynamic Increase Factor (DIF) can lead to highly conservative estimate of the actual strength of such members.     

Deformation behavior of recrystallized and stress-relieved Zircaloy-4 fuel cladding under biaxial stress conditions

Pellet–cladding mechanical interaction (PCMI) under reactivity-initiated accident conditions may lead to the failure of high-burnup fuel rods. Biaxial stress states generated by PCMI in Zircaloy cladding may make the cladding more susceptible to failure. In this study, we investigated the deformation behavior of Zircaloy cladding under biaxial stress conditions based on the concept of contours of equal plastic work. The major axis angles of the initial work contours of recrystallized (RX) and stress-relieved (SR) specimens were investigated and it was found that the shapes of the initial work contours of these kinds of specimens were almost symmetric across the direction where the ratio of axial stress to circumferential stress is 1. The shapes of subsequent work contours tended to change for the RX specimen while being the same as the initial for the SR specimen, as deformation proceeded. It was suggested that the textures and slip systems in the RX and SR specimens affect their initial work contours while the slip system in the RX specimens and the residual strain in the SR specimens influence the subsequent work contours.     

Behavior of annealed type 316 stainless steel under monotonic and cyclic biaxial loading at room temperature

This paper addresses the elastic-plastic behavior of type 316 stainless steel, one of the major structural alloys used in liquid-metal fast breeder reactor components. The study was part of a continuing program to develop a structural design technology applicable to advanced reactor systems. Here, the behavior of solution annealed material was examined through biaxial stress experiments conducted at room temperature under radial loadings (√3τ = σ) in tension-torsion stress space. The effects of both stress limited monotonic loading and strain limited cyclic loading were determined on the size, shape, and position of yield loci corresponding to a small offset strain (10 microstrain) definition of yield.In the present work, the aim was to determine the extent to which the constitutive laws previously recommended for type 304 stainless steel are applicable to type 316 stainless steel. It was concluded that for the conditions investigated, the inelastic behavior of the two materials are qualitatively similar. Specifically, the von Mises yield criterion provides a reasonable approximation of initial yield behavior and the subsequent hardening behavior, at least under small offset definitions of yield, is to the first order kinematic in nature.     

Fracture of Zircaloy cladding under simulated power ramp conditions

Behaviour of Zircaloy cladding under stresses imposed by fuel dimensional changes is discussed and results presented which suggest that the correct choice of cladding properties, in particular cold-work level and texture, is important if the probability of low ductility failures in fuel pins is to be reduced. Evidence is presented, based on laboratory tests and post-irradiation examination of cladding, which leads to the conclusion that failure of Zircaloy can take place by stress-corrosion cracking in the presence of fission product iodine and it is further demonstrated that the process is strongly stress-dependent. Consideration is given to the influence of irradiation exposure, strain rate and adverse stress systems, for instance at inter-pellet ridges or fuel cracks, on the cracking susceptibility of Zircaloy cladding. The significance of the results is discussed in relation to a proposed stress-corrosion cracking mechanism.     

Fracture initiation and fracture opening under light water reactor conditions

The burst behaviour of fourteen vessels containing longitudinal flaws was investigated. The vessels were made of the two steels: 20 MnMoNi 5 5 with a high upper shelf impact toughness and a special melt of 22 NiMoCr 3 7 with a low upper-shelf impact toughness. The dimensions of the vessels were the same as of the pipes of the primary coolant system (798 O.D. × 47.5 mm wall thickness) of a pressurized water reactor. The test pressure and temperature correspond with the real service conditions of a PWR.Using a highly sophisticated measuring equipment, the time-history of pressure, crack opening and crack-opening area were determined experimentally.     

Crack growth properties of nuclear graphite under cyclic loading conditions

Crack growth properties of four kinds of nuclear graphites under cyclic loading conditions were investigated at room temperature, 373, 673 and 975 K, using double cantilever beam (DCB) specimens. The crack growth rates can be expressed as a function of the stress intensity factor range at the constant mean stress intensity factor (K_mean) and the constant minimum stress intensity factor (K_min): that is, da/dN = CΔK₁ⁿ, where the constants C and n depend upon the kind of graphite and its coke grain size. The crack growth rate at the constant K_mean becomes smaller than that at the constant K_min. For the fine-grained graphite tested at higher temperatures, the crack growth rate increases with increasing temperature. Also cracks in the coarse grained coke graphites extend at a higher rate than that in the fine-grained high strength graphites. It seems that cracks in graphites run mostly along the coke grain boundaries.     

Fracture mechanics investigations on cylindrical large scale specimens under thermal shock loading

To investigate the crack growth and crack arrest behaviour of primary circuit materials large scale experiments were conducted on component-like specimens under pressurized thermal shock loading at MPA Stuttgart. The material characteristics varied from high tough material to low tough material with higher nil ductility transition temperature to simulate EOL or beyond EOL-state. All tests started from in-service conditions and were cooled down to room temperature. The specimens showed both stable and unstable crack growth and partly crack arrest. The crack growth behaviour was verified by post test calculations and could be explained with the help of the multiaxiality of the stress state.     

Description of the flow behaviour of a high strength austenitic steel under biaxial loading by a constitutive equation

Uniaxial and biaxial tension-torsion tests were carried out on a high strength austenitic steel at room temperature in the strain rate range from 10⁻⁵ to 10² s⁻¹. This material shows a strong dependence of strength on strain rate. The yield loci of the combined tests are described by ellipses. The size and the shape of these ellipses are functions of strain and strain rate. The quasi-static and dynamic tension and tension-torsion behaviour of the austenitic steel is described by Perzyna's constitutive equation. There is good agreement between measured and calculated results if a yield criterion as a function of strain and strain rate, and a formula which contains the dependence of flow stress on strain rate based on thermal activation, are included.     

High temperature creep damage under biaxial loading: INCO 718 and 316 (17-12 SPH) steels

The respective influence of the Von-Mises equivalent stress and of the maximum principal stress on high temperature creep damage of two industrial alloys (INCO 718 and 17-12 SPH stainless steel) are pointed out in a quantitative way through tensile-torsion biaxial tests. Through inversions of the shear component, the important part taken by the principal direction corresponding to the maximum principal stress is also shown. The results are observed to be opposite according to whether the alloy suffers cyclic hardening as 17-12 SPH does or cyclic softening which is the case of Inco 718. These results are supported by metallographic observations. They demand an anisotropic form for the damage variable D, while besides a time dependence, the kinetic equation must include the part taken by the strain.     

Dynamic characteristics and structural response of the SWR 1000 under earthquake loading conditions

Based on the conceptual design documentation of the SWR 1000 reactor building as well as specified representative seismological, and soil-dynamic input data, corresponding to prospective sites as a basis, the dynamic characteristics, as well as the in-structure dynamic response of the coupled vibrating structures have been elaborated. The structural design analysis was based on a 3-dimensional mathematical model of the building in which all details of the internal structures as well as the containment including the water in the pools were represented adequately. In order to demonstrate the influence of the soil-structure interaction effects on the dynamic response results, the soil was represented by two different assumptions. At first, considering the state of the art procedures, assuming frequency independent soil capabilities (equivalent stiffnesses and damping values), time domain calculations were carried out. In the second step, based on the frequency-dependency of the soil capabilities, frequency domain calculations were performed. The structural responses obtained by means of both procedures and the same mathematical model of the structures were evaluated and compared. The suitability of the preliminary design concept are discussed and the structural response results obtained on the basis of the bearing capacity and the stresses in the characteristic regions of the structure.     

Fracture mechanics study of a pipe bend with a longitudinal crack under static loading

The regulating norms for nuclear power plant component are based on the assumption that the components have no defects. Therefore it is of major interest to find what values the fracture mechanics parameters assume when a loading which produces in an unflawed elbow stresses which are acceptable according to the regulatory guides is applied to an elbow with cracks. It could be shown that with small flaws ( of arc length, ) calculations assuming linear-elastic behavior give results almost identical as when elastic-plastic behavior is assumed. If the cracks are small and the loading is according to the regulatory guides the initiation value J₁ for stable crack growth is not reached.     

Fracture limit of high-burnup advanced fuel cladding tubes under loss-of-coolant accident conditions

ABSTRACT

To evaluate the fracture limit of high-burnup advanced fuel cladding tubes under loss-of-coolant accident (LOCA) conditions, laboratory-scale integral thermal shock tests were performed using the following advanced fuel cladding tubes with burnups of 73–85 GWd/t: M-MDA^TM, low-tin ZIRLO^TM, M5®, and Zircaloy-2 (LK3). In total eight integral thermal shock tests were performed for these fuel cladding tube specimens, simulating LOCA conditions including ballooning and rupture, oxidation, hydriding, and quenching. During the tests, the specimens were oxidized to 10%–30% equivalent cladding reacted (ECR) at approximately 1473 K and were quenched under axial restraint load of approximately 520–530 N. The effects of burnup extension and use of the advanced fuel cladding tubes on the ballooning and rupture, oxidation, and hydriding under LOCA conditions were inconsiderable. Further, the high-burnup advanced fuel cladding tube specimens did not fracture in the ECR values equal to or lower than the fracture limits of the unirradiated Zircaloy-4 cladding tube reported in previous studies. Therefore, it can be concluded that the fracture limit of fuel cladding tubes is not significantly reduced by extending the burnup to approximately 85 GWd/t and using the advanced fuel cladding tubes, though it slightly decreases with increasing initial hydrogen concentration.     

The viscoplasticity theory based on overstress applied to the analysis of beams under monotonic and cyclic creep loading

The viscoplasticity theory based on total strain and overstress can reproduce rate-dependent inelastic deformation without distinction between plastic and creep strain using two material functions. A viscosity function and an equilibrium stress-strain curve characterize rate-dependency and work hardening, respectively. The theory is used to analyze the creep and cyclic creep behavior of a beam subjected to a linearly increasing moment which is subsequently held constant.The analysis shows the existence of two possible states of equilibrium for creep deformation: termination of primary creep or secondary creep. They occur when the equilibrium stress-strain curve has positive or zero slope in the plastic range.The numerical experiments illustrate that the stress distribution at the end of the moment increase depends on the moment rate. The rate effects disappear with time when stress is redistributed. For practical purposes the equilibrium solution is obtained before 10⁷ s, when the material functions representing AISI Type 304 Stainless Steel at room temperature are used. The other equilibrium solution (secondary creep) is reached after primary creep when the constant moment is above the limiting equilibrium moment which corresponds to the plastic hinge moment of plasticity theory. The stress distribution during stationary creep is shown to be the solution corresponding to the Norton law of creep theory. The numerical experiments also illustrate the influence of various viscosity functions and equilibrium stress levels. A growth law for the equilibrium stress-strain curve is postulated and reversed loading as well as repeated loading are investigated.     

Part III structural reliability assessment under internal and external load conditions

The classical reliability function is used as a risk criterion in the analysis of the containment of a PWR. For the treatment of the internal load case LOCA the probability of occurrence as well as the probability distribution of the load intensity are considered. In recognition of the rare event properties of the internal and external hazards the Poisson process is used as a forecast model. Consequently the asymptotic distributions of the Fisher-Tippett type are utilized to model the load intensities. The investigation concentrates on the analysis of the steel hull for which the governing external hazard of the earthquake is considered. As failure criteria yield and the fracture conditions are used.