Pressure reducing valve (PRV) located before the start-up vessel (SUV) is an essential component that decreases the pressure and temperature of the supercritical state steam by using spray water before it flows into the SUV. The PRV is kept closed during normal operation but opened during start-up and shutdown events, which could initiate thermal fatigue defects due to significant temperature changes. In addition to the thermal shock and internal pressure, system bending and torsional moments may be imparted on the PRV, threatening its integrity. To reinforce these concerns, cracks on the inside surfaces of the PRV have often been reported during planned maintenance activities in nuclear power plants. This research aims at analysing cyclic plasticity of the PRV subjected to cyclic moments, thermal and pressure loadings by means of an advanced direct numerical technique known as the Linear Matching Method (LMM). The cyclic moments are comprised of in-plane and out-of-plane bending, and torsion which are applied to an inlet branch pipe of the PRV. The cyclic thermal load is obtained from the transient heat transfer analysis using real operational data. Two different pressures, which are high and low pressures, are applied to internal surfaces of the PRV body and outlet pipe respectively. The analysed results construct a structural response boundary such as a shakedown limit boundary. The obtained structural response boundary is validated by full cyclic incremental analysis referred to as the step-by-step analysis. The analysed results have demonstrated that the plastic collapse limit is identical to the shakedown limit. Moreover, the results provide engineers with a safe load bearing capacity domain which otherwise requires evaluating structural integrity of the PRV subjected to the complicated cyclic loading condition using detailed assessments and analyses.

Irradiation hardening is one of the most important aging effects of reactor pressure vessel (RPV) steel in long-term service. A number of studies have indicated that irradiation hardening is mainly caused by irradiation induced defects, such as dislocation loops and precipitates. In this paper, we have simulated the irradiation damage of low-copper reactor pressure vessel (RPV) steel. The generation of Mn-Ni-Si precipitates is simulated by the cluster dynamics model based on rate theory. On this basis, the crystal plasticity finite element method based on modified crystal plasticity model is used to simulate the effect of Mn-Ni-Si precipitates on the mechanical properties of RPV steels. The simulated results has been compared with the experimental results from the literature. By coupling the cluster dynamics and the crystal plastic finite element method, we suggest a multi-scale simulation method to simulate and predict irradiation damage of RPV steel.

Back-to-back pipe bends are widely adopted applications in many industries including nuclear sectors. Evaluation of their load bearing capability under complex cyclic loading is very important. Recently, a couple of research reported shakedown boundary of a 90° back-to-back pipe bends by adopting a conservative approach but no comprehensive post yield structural behaviors have been dealt with. In this research the concerning pipe bends subjected to cyclic opening in-plane (IP)/out-of-plane (OP) bending and steady internal pressures are analyzed to construct shakedown and ratchet limit boundary by means of the Linear Matching Method. Analyzed results present that the concerning pipe bends under out-of-plane bending has higher resistance to cyclic bending than under in-plane bending. In additions, the out-of-plane bending causes very small alternating plasticity areas, unlike the in-plane bending. Full cyclic incremental analyses known as step-by-step analysis are performed to verify the structural responses either side of each boundary and confirm correct responses. Parametric studies are carried out with respect to changes in geometry of the concerning pipe bends subjected to the same loading, and semi-empirical equations are derived from relationships of the reverse plasticity limit and the limit pressure with the bend characteristic. This paper offers broad understandings of structural responses of the 90° back-to-back pipe bends under the complex cyclic loading as well as providing key points to be considered for the life assessment of the piping system.

The thimble tube, which is made of Zircaly-4, is one of the main components of a PWR fuel assembly. The thimble tube has an important role as a structural member of the skeleton. Another role of the thimble tube is to guide a rod cluster control assembly (RCCA) for insertion during the reactor operation, and the function has to be assured not only in normal operation but in a seismic event. In a horizontal seismic event, the fuel assembly vibrates laterally, which gives bending moment to the thimble tube. In addition, axial compressive force acts on the thimble tube in a vertical seismic event. The integrity of the thimble tube has to be maintained while this force and moment act. Mitsubishi has confirmed by the elastic stress analysis that the stress of the thimble tube is lower than the limit value requested for the seismic event. The stress evaluation method is based on the ASME code. The ASME code also describes the limit analysis which is available when the predicted stress is beyond elastic region of the material. In the analysis, the material is assumed to be elastic-perfectly plastic, and the maximum load that the structure can carry is calculated. For the reason mentioned above, the allowable limit of the thimble tube should be determined as a function between the force and the moment. We are planning to examine the allowable limit experimentally. As a step before testing, an analytical approach for the limit is discussed in this paper. Firstly, the allowable limit is calculated by a beam model assuming elastic-perfectly plastic material, based on the ASME code. Secondly, a 3D model analysis with elastic-plastic material is performed to predict the practical strength. Based on the comparison with the analysis using elastic-perfectly plastic material, ASME based limit is considerably conservative compared with the one with the actual stress-strain curve. Conversely, this means there is enough room to rationalize the allowable limit. As the future work, the experiment will be conducted to obtain the practical limit of the thimble tube and to verify the analysis results.

A new 3D fuel behavior solver is currently under collaborative development at the Laboratory for Reactor Physics and Systems Behaviour of the École Polytechnique Fédérale de Lausanne and at the Paul Scherrer Institut. The long term objective is to enable a more accurate simulation of inherently 3D safety-relevant phenomena which affect the performance of the nuclear fuel. The current implementation is a coupled three-dimensional heat conduction and linear elastic small strain solver, which models the effects of burnup- and temperature dependent material properties, swelling, relocation and gap conductance. The near future developments will include the introduction of a smeared pellet cracking model and of material inleasticities, such as creep and plasticity. After an overview of the theoretical background, equations and models behind the solver, this work focuses on the recent preliminary verification and validation efforts. The radial temperature and stress profiles predicted by the solver for the case of an infinitely long rod are compared against their analytical solution, allowing the verification of the thermo-mechanics equations and of the gap heat transfer model. Then, an axisymmetric model is created for 4 rods belonging to the Halden assembly IFA-432. These models are used to predict the fuel centerline temperature during power ramps recorded at the beginning of life, when the fuel rod performance is still not affected by more complex high burnup effects. Finally, the predictions are compared with the experimental measurements coming from the IFPE database. This first preliminary results allow a careful validation of the temperature-dependent material properties and of the gap conductance models.

High confidence of low probability of failure (HCLPF) values of equipment, representing the seismic capacities of the equipment, are the fundamental ingredient in seismic probability safety assessment (SPSA) and seismic margin analyses (SMA). In this paper, two methods for calculating the HCLPF values of equipment were investigated, fragility analysis, and conservative deterministic failure margin (CDFM). These methods are linear methods. Based on these methods, HCLPF value of equipment can be computed conveniently by scaling the results of the existing seismic analysis. For a nonlinear systems, the HCLPF values based on these linear scaling methods are unrealistic. For a complicated nonlinear equipment or structure, a detail nonlinear model was used to derive the seismic capacity. The results by this method are realistic, but cost calculation time. In this paper, a nonlinear model of reactor coolant system coupled reactor building was built. This model includes the steam generator and considers the nonlinear factors of steam generator such as gap in the supports, plasticity of hot leg and cold leg. Forced motion was applied to the base of reactor building. And seismic response of the steam generator was calculated iteratively by scaling the ground motion level step by step. Based on these calculations, a curve of load on the supports VS peak ground acceleration (PGA) can be obtained. Then based on these curves and allowable load of supports of steam generator, which derived from stress analysis on support of steam generator, seismic capacity of the supports of steam generator was determined. Then the HCLPF Value of the supports of steam generator was obtained by this nonlinear time history analysis and was compared with the results based on the CDFM. The two results were different. Therefore, the HCLPF seismic capacity of equipment with nonlinearity, such as gap nonlinearity, should be calculated by nonlinear time history method.

For a better use of titanium alloy in nuclear industry, development of integrated computational materials engineering (ICME) model is necessary to optimize alloy microstructure and thus the performance of titanium component. Within an ICME toolset, constitutive models play an important role in quantitatively capturing the interrelationship between processing, microstructure and property. In this paper, texture evolution during hot extrusion of near-alpha Ti6242S bar were studied with respect to the deformation and transformation texture component. Experimentally measured alpha and beta phase textures were instantiated in a three dimensional rate-dependent crystal plasticity model. The model is able to accurately predict the deformation textures of both the alpha and beta phases at extrusion temperature. While decomposition of the metastable beta phase occurred during the post-extrusion cooling, most of the transformation texture components formed aligned [0001] with the extrusion direction, which formed the primary component of extruded alpha texture. The transformation texture was predicted by numerically decomposing the simulated beta texture according to appropriate variant selection rule. Also demonstrated was the capability of a crystal plasticity model incorporating microstructure information, such as phase fraction and lamellar spacing. The crystal plasticity model was validated by comparing with the experimental elastoplasticity behaviors of Ti6242S bars with various microstructures.

In order to gain high strength, fine grain size, stronger anti-corrosion property, and especially low permeability, the material 022Cr19Ni10N was chosen to manufacture the Rod Travel Housing Forging (RTHF) for Control Rod Drive Mechanism (CRDM). But, cracks were found in some forgings failing to meet the requirements of ultrasonic testing (UT). The causes of the forging cracks of this austenitic stainless steel forging were investigated by means of metallography, scanning electron microscopy (SEM) and other experimental methodology. The results indicated that the second δ-ferrite phase leads to the forging cracks between γ-δ interface during the low temperature forging process, and finally leads to the forging failure. It’s found that the cracks are distributing along the stripe δ-ferrite, and almost distributing in the same area as the large size δ-ferrite by metallography & SEM microstructure observation. The δ-ferrite is firstly found in the electroslag ingot, and in which, the distribution and size is different from the case to the core. The largest size δ-ferrite is around the core area, and this characteristic passes on to the final forging microstructure, although the shape, quantity & distribution of the δ-ferrite changed during the manufacturing process. Most forging cracks were found around the core area of the forging by UT examination. In the final forging process, when the forging temperature drops to 750∼850°C, the δ-ferrite have been forged to stripe shape and hundreds-micron size while the plasticity of the austenite reduce. What’s more, there are large hot plasticity differences between the δ-ferrite and the austenite, so the forging cracks initiate between γ-δ interface and extend to the area around to be a long crack in the low temperature forging process. In order to avoid the forging cracks in the Rod Travel Housing Forging, it’s necessary to reduce the content of δ-ferrite or improve the final forging temperature. Improving the final forging temperature, to guarantee the plasticity of the δ-ferrite and austenite, is another process to reduce the cracks. But while the temperature improves, the grain size grows rapidly, and may form mixed structure. So the most effective mean to reduce the content of δ-ferrite is to redesign the chemical components, mainly by increasing the nitrogen content from 0.06 (wt, %) to 0.12(wt, %), which makes the low temperature forging process for fine grain size possible. In the high-nitrogen-content forging, the δ-ferrite distributed sporadically and no δ-ferrite strip is found. By increasing the austenite forming elements (especially nitrogen), the cracks during low temperature forging process are avoided. What’s more, owning to the optimization of chemical compositions and manufacturing processes, the Rod Travel Housing Forging got fine grain size, low relative permeability, and good comprehensive mechanical properties with the ultimate tensile strength up to 570MPa.

GH3128, which is one of the domestic Ni-base super alloy, shows good performances under high temperature. Preliminary research has shown that this alloy is promising as structural material for Intermediate Heat Exchangers (IHX), which are the key components of Very High Temperature Reactor (VHTR). In this paper, the tensile properties of GH3128 are tested by the uniaxial tension experiments, and then the fractographic evaluation is conducted by using the scanning electron microscope (SEM). In the paper, the variation tendency of tensile strengths of GH3128 as well as plasticity is described along with the variation of temperature. The results also show that the tension fracture mode will gradually transform from ductile fracture to cleavage-intergranular compound fracture with the increasing of temperature, and the transition of fracture mechanism corresponds well with the variation of alloy plasticity.

A nuclear piping system which is found to be disqualified, i.e. overstressed, in design evaluation in accordance with ASME B&PV code, Section III, can still be qualified if further non-linear design requirements can be satisfied in refined non-linear analyses in which material plasticity and other non-linear conditions are taken into account. Our work presented earlier in ICONE16-20 categorized the design rules in the code into linear and non-linear design rules and attempted to clarify the corresponding design requirements. In this paper, an in-depth review of these rules and relevant requirements for time-history dynamic loads designated in Service Limit Levels C and D, such as those caused by e.g. water-hammer effects, is given. In particular, several changes of these rules in the current edition of the codes and their applications are addressed, and several rules which are intensively applied but often found to be inconsistent and confusing in Sweden are discussed. It is suggested that the design evaluation can be made directly through non-linear transient finite element analysis using a strain-based criterion for time-history dynamic loads of either reversing or non-reversing type.

Stainless steel is a commonly used material in safety-important components of nuclear power plants. In order to study degradation mechanisms in stainless steels, like crack initiation and propagation, it is important to characterize the degree of plastic strain on microstructural level. One way to estimate local plastic strain is by measuring local crystal orientations of the scanned surfaces: the electron backscatter diffraction (EBSD) measurements on stainless steel revealed a strong correlation between the spread of crystal orientations within the individual grains and the imposed macroscopic plastic strain. Similar behavior was also reproduced by finite element simulations where stainless steel was modeled by an anisotropic elasto-plastic constitutive model. In that model the anisotropic Hill’s plasticity function for yield criteria was used and calibrated against the EBSD measurements and macroscopic tensile curve. In this work the Hill’s phenomenological model is upgraded to a more sophisticated crystal plasticity model where plastic deformation is assumed to be a sum of crystalline slips in all activated slip systems. The hardening laws of Peirce, Asaro and Needleman and of Bassani and Wu are applied in crystal plasticity theory and implemented numerically within the user subroutine in ABAQUS. The corresponding material parameters are taken from literature for 316L stainless steel. Finite element simulations are conducted on the analytical Voronoi tessellation with 100 grains and initial random crystallographic orientations. From the simulations, crystal and modified crystal deformation parameters are calculated, which quantify mean and median spread of crystal orientations within individual grains with respect to central grain orientation. The results are compared to EBSD measurements and previous simulations performed with Hill’s plasticity model.

To investigate the effects of Mo and Bi on mechanical properties of a Zr-Fe-Cr alloy at room temperature, seven Zr-Fe-Cr-Mo-Bi alloys with different compositions were designed. They were subjected to a series of rolling processes and heat treatments, and then sampled to measure mechanical properties by hardness and tensile test and to characterize microstructures by scanning electron microscope (SEM) and electron channel contrast (ECC) technique. Results indicated that among them two types of Zr-Fe-Cr-Mo-Bi alloys achieve the designed goals on mechanical properties and have the following advantages: (i) the hardness of the alloys, up to 334HV after annealing, is 40% higher than traditional Zr-4. (ii) The yield strength (YS) and ultimate tensile strength (UTS) of the alloys are 526 MP a and 889 MP a after hot rolling and annealing, markedly higher than the traditional Zr alloy. (iii) Good plasticity of the new Zr-Fe-Cr-Mo-Bi alloy is obtained with about 40% elongation, which is greatly higher than the Zr-Fe-Cr-Mo alloy thanks to the addition of Bi offsetting the disadvantage of addition Mo. Furthermore, according to observations of the microstructure observation, the reasons of the effect of the Mo and Bi elements on the mechanical performance of Zr-Fe-Cr alloy were studied and discussed.

We propose a simple anisotropic elasto-plastic finite element model to quantify the deformation heterogeneity locally within the grains of a polycrystal under plastic deformation. The model is calibrated against the electron backscatter diffraction measurements on stainless steel under uniaxial tensile loading. The spatial model of the specimen is generated by Voronoi tessellation using initial random orientation of the grains. The calibration of the model is provided by statistical means by calculating and comparing the crystal deformation parameter, which quantifies the spread of the crystal orientation within individual grains from the central grain orientation. It is confirmed that this parameter has a good correlation to the degree of the plastic strain.

A nuclear piping system which is found to be disqualified, i.e. overstressed, in design evaluation in accordance with ASME B&PV code, Section III, can still be qualified if further nonlinear design requirements can be satisfied in refined non-linear analyses in which material plasticity and other non-linear conditions are taken into account. Our work presented earlier in ICONE16-19 categorized the design rules in the code into linear design and non-linear design rules and attempted to clarify the corresponding design requirements. In this paper, an in-depth review of these rules and relevant requirements for time-history dynamic loads designated in Service Limit Levels C and D, such as those caused by e.g. water-hammer effects and others, is given. In particular, several rules which are currently intensively applied but often found to be inconsistent and confusing in Sweden are studied and discussed in detail. Suggestions for a reasonable application of these rules, which are currently practiced in several ongoing projects for the power uprate and life-extension of BWR power plants, are given.

Aged degradations of structural materials of boiling water reactors by stress corrosion cracking (SCC) have been frequently reported. SCC is the results of the synergistic interaction of mechanical stress and corrosive environment, and the investigation of this phenomenon has been an important issue. Although many kinds of studies for SCC have been carried out, we have not clarified the fundamental mechanisms of SCC initiation and propagation yet. In the recent experimental studies, nano-scale observation around crack tips using transmission electron microscopy have shown three characteristics of SCC of nuclear structural materials as follows; the size of crack tip is nanometer order, the opening crack is filled with the oxides, and oxygen atoms exist in the grain boundary beyond the crack tips. The second and third ones show that the corrosive environment is mainly influenced on the SCC propagation behavior. Furthermore, electron back scatter diffraction pattern analyses have shown that about 10–20% of plastic strain exists around the crack tips and crack sides. The existence of oxygen atoms along grain boundaries and plastic strains around grain boundaries could be related to the crack propagation mechanism of SCC. In this study, in order to observe the influence of oxygen atoms on the SCC propagation behavior, the two-dimensional SCC propagation model considering diffusion of oxygen atoms along grain boundaries is developed. In this model, the stress distribution of polycrystalline system is obtained by the crystal plasticity theory, and the concentration of oxygen atoms depending on stress localization around cracks is calculated using the diffusion equation of oxygen atoms considering the stress gradient. The density distribution of oxygen atoms is adopted for the threshold of the crack propagation. Relation between the threshold of crack propagation as a viewpoint of density of oxygen atoms along grain boundaries and the geometry of SCC is discussed in this paper.

The paper describes basis of a microplane concrete material model which was implemented in a commercial FE -code using user subroutine interface. The material model is called M4. The motivation for this implementation was a need for a concrete model which would perform well in a soft missile impact analysis. Numerical integration over the surface of a unit sphere is crucial to microplane material models. We tested our microplane implementation using several numerical integration formulas presented in literature. The two fairly simple test cases described in this paper revealed clearly the numerical anisotropy induced by the integration formulations. The impact problem was a medium size, medium velocity soft missile impact test case from an international research program. We compared our implementation of M4 model to a tensorial based damage plasticity concrete model and found out that the results were almost identical. However, the numerical results did not agree well with the measurements in this test case. We concluded this disagreement might be consequence of nonlinear phenomena beyond material constitutive relations.

Microstructural features play a prominent role in the initialization and propagation of microstructurally short cracks. These features include crystallographic orientations of grains, grain boundaries, inclusions, voids, material phases, etc. Their influence is expected to vanish both with increased distance from the crack tip as well as with increased crack length. Current engineering fracture mechanics techniques do not account for these features and can therefore only be applied to sufficiently long cracks. From the engineering point of view it is therefore quite useful to have an estimate of this length. In this paper we build upon the authors’ previous work to estimate decreasing influence from the surrounding microstructural features with increasing crack length. To achieve this, a model containing a large number of randomly sized, shaped and oriented grains is employed. The grain structure is modeled using a Voronoi tessellation. A series of cracks with lengths from one to several grain lengths are inserted into the model, extending from a grain at the surface towards the interior of the model. The crack tip opening displacements (CTOD) are estimated and statistically analyzed for a series of random crystallographic orientation sets assigned to the grains adjacent to the crack. Anisotropic elasticity and crystal plasticity constitutive models are employed at the grain size scale. A rapid decrease of the CTOD scatter is observed with increasing crack length showing a clear tendency to stabilize at standard deviation of about 5% at the effective crack length of about 6 average grain sizes (0.3 mm in AISI 316 stainless steel. A crack with the length exceeding about 10 average grain sizes can be safely taken as a macroscopic crack.

A nuclear piping system which is found to be disqualified, i.e. overstressed, in design evaluation in accordance with ASME III, can still be qualified if further non-linear design requirements can be satisfied in refined non-linear analyses in which material plasticity and other non-linear conditions are taken into account. Our work presented earlier in ICONE16 categorized the design rules in ASME III into linear design and non-linear design rules and examined the corresponding design requirements. In this paper, a more in-depth review of these rules for service limit level D is conducted. In particular, several rules which are currently intensively applied but often found to be inconsistent and confusing in Sweden are studied and discussed in detail. Suggestions for improvements and guides for a reasonable application of these rules, which have been practiced in several ongoing projects, are given.

An experimental approach is introduced for understanding how the engineered barriers of a deep geological repository system are affected by fault movement. The experiments are conducted using laboratory simulation test equipment. So far, the experiments indicate that the metal overpack is rotated within the bentonite buffer due to its plasticity, but not breached. Numerical analyses are also carried out to supplement the range of the experiments, which is limited by the capability of the test equipment.

Material ageing and fatigue effects play a significant role in safe operation of nuclear power plants. Particular issues are the initialization and propagation of microstructurally small cracks which can represent a significant proportion of a component’s life time. These cracks are still not well understood, one of the reason being that a number of microstructural features have a significant influence on such cracks: crystallographic orientations of grains, grain boundaries, inclusions, voids, material phases, etc. Microstructural features away from the crack have smaller effect on the crack tip parameters. Crack length also plays a role. For a long crack the influence of the surrounding microstructural features will be smaller than for a small crack. A crack of sufficient length can be modeled using classical fracture mechanics methods. The question is when do we reach this point? To try to answer this question we create a model containing a large number of randomly sized, shaped and oriented grains with a crack inserted into a surface grain. Random grain structure is modelled using a given Voronoi tessellation. We then extend the crack up to 7 grains in length and estimate the standard deviation of crack tip opening displacements (CTOD) due to the random crystallographic orientations of the grains surrounding the crack. To account for the deformation mechanism at the grain size scale anisotropic elasticity and crystal plasticity constitutive models are employed. We show that even at crack length equivalent to 7 grains the standard deviation of the crack tip opening displacements due to the surrounding crystallographic orientations is still 7.3% and that from engineering point of view a crack with length of less than 10 average grain sizes can not be taken as independent of the surrounding microstructural features.