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Abstract: In this work, a conceptual framework is suggested for analyzing thermorheologically simple and complex behavior by using just one approach. Therefore, the linear relation between master time and real time which is required in terms of the time-temperature superposition principle was enhanced to a nonlinear equivalent relation. Furthermore, we evaluate whether there is any relation among well-known existing time-temperature equivalent formulations which makes it possible to generalize different existing formulations. For this purpose, as an example, the power law formulation was used for the definition of the master time. The method introduced here also contributes a further framework for a unification of established time-temperature equivalent formulations, for example the time-temperature superposition principle and time-temperature parameter models. Results show, with additional normalization conditions, most of the developed time-temperature parameter models can be treated as special cases of the new formulation. In the aspect of the arrow of time, the new defined master time is a bended arrow of time, which can help to understand the corresponding physical meaning of the suggested method.
Compared with the original time-temperature superposition (TTS) principle, an extended non-linear time-temperature equivalent (TTE) principle is suggested in this work. Results shown us, all application of TTS and most of the TTE parameters, for example, the Orr-Sherby-Dorn, Manson-Succop, Larson-Müller, Manson-Haferd, Mendelson-Roberts-Manson parameters and the more general ‘single metamodel’ from Haque–Stewart are special cases of the new suggested principle. The merits of this new method are discussed.
Three-dimensional finite element analysis of O-ring metal seals considering manufacture tolerances
(2019)
Metal seals are widely used in various industrial branches with severe working conditions (e.g. high pressure, high temperature, corrosion, or radioactive radiation). For example, O-ring metal seals are applied in the closure lid system of transport and storage casks for radioactive materials to guarantee an approved specified leak-tightness and the safe enclosure of the radioactive inventory. Within safety assessments of those casks under normal or accident conditions during transport and long-term interim storage for several decades, numerical simulations of the thermo-mechanical behavior of metal seals by using finite element (FE) analyses are suitable and effective.
In general, finite element codes provide the possibility to construct a complex three-dimensional (3D) modelling of metal seals with solid elements, cf., where all components of the metal seals are modeled in detail. This modelling is complex but allows the consideration of underlying physical effects such as elastic-plastic deformation, thermal expansion, creep/relaxation, friction and possible local damage. Therefore, this approach permits the investigation and understanding of the complex behavior of metal seals in detail which can hardly be measured for all seal components.
In a prior work, the complex 3D modelling approach was applied to investigate the influence of each seal component on the global seal force by considering varying material properties and different seal diameters. In the present contribution, the influence of manufacturing tolerances is discussed. At first, the results of prior work are summarized. After that, the manufacturing tolerances of the studied O-ring metal seal types are described and the corresponding FE model with all individual components is introduced. Finally, the influence of varying manufacturing tolerances of each seal component on the global seal force is analyzed and discussed.
The long-term sealing behavior of metal seals, assembled in the lid system of casks for transportation and storage of radioactive materials, has been investigated. For that purpose, phenomenological models describing the time- and temperature dependent behavior have been introduced by BAM since 2016, e.g. by using the time-temperature superposition principle. Results have shown that these models describe the relaxation behavior adequately and are suitable for extrapolations. In this work, the applicability of these models is checked by analyzing the necessary scope of tests, which must be carried out to get sufficient information about the long-term behavior of metal seals based on short-term tests.
Metal seals of O-ring form are often used in lid-systems of transport and storage casks for radioactive waste in Germany. To investigate their mechanical behaviour, three dimensional (3D) finite element (FE) models were created using solid elements for all of the seal components. The material behaviour of each component is described with a unified static elastic-plastic material model. The total strain is defined as the sum of linear elastic strain and plastic strain with power-law hardening. The model was carefully validated by comparison of Simulation results with experimental results. The influence of material fluctuation of each seal component due to varying properties and the sensitivity of different seal diameters on the seal force are analysed and discussed.
The results show that the material properties of helical spring have major influence on seal force and that the influence of seal diameters is negligible small in the studied range. This is very important to use the test results from seals with small diameter for the assessment of seal behaviour with larger diameter as used in transport and storage cask.
The safety evaluation of cask components made of ductile cast iron includes investigations to prevent brittle fracture. Generally, ductile cast iron is endangered by brittle fracture especially at low temperatures (down to -40°C) and in combination with existing crack-like material defects. An applicable method is the assessment of fracture resistance using fracture mechanics according to the IAEA guidelines. The approach is based on the prevention of fracture initiation. For application of these principles for drop loads, account must be taken both of dynamic stresses within the component and dynamic material behavior. Basically, the dynamic stress intensity factor of postulated pre-existing crack-like defects is compared with the dynamic fracture toughness of the material. Applicable numerical and experimental methods for the safety assessment of cask components are demonstrated for the case of an artificially pre-cracked cylindrical cast iron cask which undergoes dynamic loading conditions as result of the hard impact between the cask and a concrete target. The proposed evaluation procedure is a combination of numerical and experimental steps. Exemplarily, the calculated stress intensity factor is compared with measured fracture toughness values from single edge notched bending specimens.
In order to study the time- and temperature-dependent long-term behavior of metal seals, experimental investigations on special metal seals have been carried out at five different temperatures in a temperature range between 20 and 150°C for more than 7 years. Experimental results indicate a noticeable change of relevant sealing properties like seal force and usable resilience depending on time and temperature. In this study, the metal seals are treated as a homogeneous material block so that the identified decrease in seal force can be treated as a material relaxation effect. For the time-dependent behavior of seal force, an enhanced power-law model is introduced for the first time and is compared with the currently used power-law model. Additionally, regarding the influence of temperature, the timetemperature superposition principle is applied to metal seals for the first time with a clearly defined process. Thus, possible mistakes in the application of principle could be avoided. The introduced method is widely available for different applications regarding effects the principle with time and temperature.
The shock absorbing material damping concrete is for the foundation in dry interim storage facilities for radioactive waste in Germany. In case of a potential cask drop damping concrete minimizes the mechanical loads to the cask. In course of safety analyzes this accident scenario is considered by numerical simulations using the finite element method. To get reliable results of numerical simulations a suitable material model is needed to take the characteristics of damping concrete into account. Due to the lack of sufficient material knowledge a research project was started to characterize the material’s behavior under different load conditions. This paper presents the test program to analyze the material behavior of damping concrete which is characterized by large volume change and
strain rate hardening dependence. The determined Parameters were used to adapt an existing material model of the FE-code ABAQUS®. This model has to handle the mechanical damage behavior of damping concrete which occurs under compression and shear loads during a potential cask drop. To verify the material model numerical simulations are compared with dynamic penetration tests, which were conducted with specimens assembled similar to the real application of the damping concrete footings. The transferability of the material
model to a real accident scenario was verified by a drop test with a full-scale cask on a damping concrete footing.
For the application of the time-temperature superposition principle a suitable relation is needed to describe the time-temperature shift factor α. Therefore, the Arrhenius equation is widely used due to its simple form and often leads to suitable results. Where, the Arrhenius equation presents a linear relation for the temperature-dependent shift factor in logarithmic scale ln(α) with the absolute inverse temperature (1/ϑ). However, in cases with a large temperature range which eventually include more complex reaction processes, the functional relation between ln(α) and (1/ϑ) is nonlinear in the ‘Arrhenius plot’. In those cases, the monotone change of the nonlinear range in the ‘Arrhenius plot’ can be interpreted as a transient range between two approximately linear or constant regions. An extended application of the modified Arrhenius equation from Nakamura (1989) is presented in this study for this transient range. The introduced method was applied to describe the time-temperature equivalence in the relaxation analysis of restoring seal force of metal seals, which are used in lid-systems of transport and interim storage casks for radioactive materials. But, the method is widely valid and can be used for different objectives which are characterized by thermorheologically simple behavior with nonlinear sensitivity to inverse temperature.
Influence of impact angle and real target properties on drop test results of cubic containers
(2017)
Drop test scenarios with cubic containers without impact limiters at interim storage sites or in a final repository have been investigated by numerical simulations. An ideally flat drop is impossible to conduct as a free fall of a container even under laboratory conditions. Dynamic stresses and strains inside the container structure are sensitive to the impact angle. Even very small impact angles cause remarkable changes in the experimental or numerical results when a flat bottom or wall of a container hits a flat target. For drop tests with transport packages the International Atomic Energy Agency (IAEA) regulations define an essentially unyielding target. In contrast, potential accident scenarios for storage containers are derived from site-specific safety analyses or acceptance criteria in Germany. Each interim storage site or repository has a yielding or so-called real target with individual structural and material properties. The real target acts as a kind of impact limiter. A more conservative container design is required if the impact limiting effect of the target is not considered.
The safety and integrity of casks for radioactive waste in accidental scenarios is analysed by BAM Federal institute tor Materials Research and Testing. An accidental scenario in German interim storage facilities is the drop from a crane during the handling operation. To reduce the mechanical loads to the cask a shock absorbing footing with high energy absorption capability is used in these areas. In order to analyse and evaluate such impact scenarios of casks, numerical simulations are performed. For a comprehensive simulation of an accidental scenario the behaviour of the damping concrete footing has to be taken into account as well and therefor a material model is needed. Material parameters under different loading conditions are the basis for a numerical model. For that reason a government funded research project (Kasparek, 2012) was conducted to characterise damping concrete under quasi-static as well as highly dynamic impact loading conditions. The performed tests include compression tests with and without lateral constraint small-scale and midscale penetration tests with different indenters, and finally a full-scale drop test onto a damping concrete footing.
Damping concrete with high energy absorption capability consists of a cement matrix with embedded small polystyrene balls and is investigated experimentally and numerically under high static compression with and without clamping. A material model is derived which describes the fundamental effects of damping concrete like non-linear elastic-plastic behaviour, volume change, volume strain dependent hardening as well as shear failure with an adequate description of damage initiation and evolution. The suggested material model is validated by simulation of penetration tests.
The safety assessment of casks for radioactive material at interim storage facilities or in final repositories includes the investigation of possible handling accidents if clearly defined test conditions are not available from the regulations. Specific handling accidents usually are the drop of a cask onto the transport vehicle or the floor as well as the collision with the wall of the storage building or another cask. For such load cases an experimental demonstration of cask safety would be difficult. Therefore, numerical analyses of the entire load scenario are preferred. The lessons learnt from dynamic finite element analyses of accident scenarios with thick-walled cubical containers or cylindrical casks are presented. The dependency of calculation results on initial and boundary conditions, material models, and contact conditions is discussed. Parameter sets used should be verified by numerical simulation of experimentally investigated similar test scenarios. On the other hand, decisions have to be made whether a parameter or property is modeled in a realistic or conservative manner. For example, a very small variation of the initial impact angle of a container can cause significantly different stresses and strains. In sophisticated cases an investigation of simpler limit load scenarios could be advantageous instead of analyzing a very complicated load scenario.
Metal gaskets in the lid system of transport and storage casks for radioactive material have to guarantee leak-tightness and safe enclosure of the radioactive inventory under normal and accident conditions during transport, in case of accidents and for the longterm interim storage. For safety assessments by nurnerical simulation of the thermomechanical behaviour of a lid system with metal gaskets, the finite element method offers three options to use: i) special gasket elements, ii) complex three-dimensional modeHing with solid elements, and iii) a simplified axisymmetric approach. Gasket elements can be adjusted by many parameters, but they give only a global representation of the experimentally observed gasket behaviour. For calculations of the entire cask including the lid system with gaskets, nonetheless this approach is recommended. To investigate the hardly measurable impact behaviour in detail or to extrapolate the long-term behaviour, a local modeHing of all parts of a gasket and their interactions with effects like elastic-plastic deformation, creep, relaxation, and friction is necessary. The three-dimensional model can describe the change of contact area between outer jacket of the gasket and flange dependent on the load conditions, what overcomes an essential limitation of special gasket elements. To simplify the problern of investigating the underlying physical effects, an axisymmetric lid system can be modelled with axisymmetric finite elements. Usually an approximation is only necessary for the helical spring of a metal gasket. This paper explains basic ideas for an adequate finite element simulation of cask lid systems with metal gaskets and their thermo-mechanical behaviour under specific load scenarios.
The deformation and damage behaviour of damping concrete under impact loading conditions is investigated experimentally and numerically. The material model is based on the assumption of crushable foam with volumetric or isotropic hardening combined with ductile and shear damage criteria. Model parameters are determined in static and dynamic compression tests of confined cubic specimens. The derived material model is validated by numerical simulation of penetration tests. The static and dynamic penetration of indenters into uniform as well as assembled bricks made of damping concrete is discussed. Finally, the successful calculation of a large-scale drop test with a heavy cask-like test object onto a realistic damping concrete foundation is demonstrated.
Cylindrical casks made of ductile cast iron are used for transport, interim storage and final disposal of radioactive waste in Germany. A basic design criterion is the ability to withstand a horizontal drop without impact Binders onto a foundation representative for the real ground of a storage facility. The increasing use of more cost-effective material compositions requires optimized cask geometries to reduce stresses and strains in the cask structure. For example, a non-uniform wall thickness was introduced to reduce maximum wall bending stresses. As a result, the load characteristics changed from line load to point load at bottom and lid side under horizontal drop fest conditions. Hereby, the position of highest stress inside the structure has shifted significantly. This was the reason for a systematic investigation of effects caused by small design changes or small variations of fest conditions. It led to a better understanding of the positions of high local stresses, their time history and maximum value for cylindrical casks under horizontal drop test conditions. Hence, the paper presents the lessons learnt from modeling and simulating such scenarios considering an impact without limiters onto a realistic target.
The safety of transport packages may be demonstrated by numerical calculation of load scenarios defined in the IAEA regulations. Possible handling accidents of casks at interim storage sites or in a final repository are typically analyzed by dynamic finite element computations. In each case the investigated load scenario must be transferred into a mathematical model. Secondly the mathematical model must be transferred into a numerical model. Reliable finite element models should be developed by assembling verified sub-models of components. The finite element mesh, material modeling, initial and boundary conditions, contact definitions, and time integration as well as the benefit of pre- and post-calculations are discussed. The paper presents lessons learnt from modeling dynamic test scenarios for finite element analyses over the years.
Finite element analysis (FEA) has been carried out for investigation of damping concrete under different impact loading conditions with a built-in material model and damage criteria available in FEA code ABAQUS.
At first, all parameters for the selected material model had been derived from compression Tests of cubic specimens. After that, a validation was carried out with different static and dynamic penetration tests. Finally, a 5 meter real drop test with a 23 Mg cylindrical cask could successfully be simulated.
Validation of numerical simulation models for transport and storage casks using drop test results
(2012)
The safety assessment of new designs for transport and storage casks for radioactive materials is a challenging task accomplished using different methods such as prototype tests, model tests, calculations and analogy reflections. At BAM (Federal Institute for Materials Research and Testing), the test procedures for the mechanical IAEA (International Atomic Energy Agency) test conditions often start with preliminary finite element (FE) calculations mostly with a small-scale cask model for verification of the proposed test cask instrumentation and test plan. On that basis the extensive test cask instrumentation is applied and checked. After that, a series of drop tests consisting of different test sequences is performed.
Following the drop tests, numerical post-analyses are carried out. These analyses offer the possibility of a detailed calculation and assessment of stresses and strains in the entire test cask construction. The calculation results have to be carefully compared with the measurement data over the impact history to find out all relevant parameters for a realistic simulation of the impact scenario. The desired ideal boundary test conditions often cannot be met exactly during the drop tests. Therefore, the numerical post-analyses are carried out by using the real boundary conditions of the drop tests. The objective is to find a validated model, where the results of the numerical simulations satisfactorily meet the experimental results.
Under test conditions according to the IAEA transport regulations, casks are usually equipped with impact limiters and dropped onto a so-called unyielding target. In general, it is difficult to verify a complex FE model by using results from only one drop test because of the complex impact process and the complex structure of such packages. After each drop test, numerical post-analyses should be carried out. Only if all drop tests were simulated successfully by using the same FE model under different test conditions, it is possible to obtain a validated numerical model for further investigations. In this case the results of the numerical simulations meet satisfactorily the experimental results. In this paper a study is presented, where the influence of different components on the cask loading is investigated systematically.