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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.
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.
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.
Practical methods for the safety assessment of postulated crack-like material defects of cubic containers made of ductile cast iron are presented. A formula for the stress intensity factor of a crack in a fillet with a radius from 20 to 200 mm under static load conditions is given. From that, an assessment diagram is derived for the critical depth of a crack in a fillet. The formula may be used to estimate the stress intensity factor of a dynamically loaded crack for special cases. As an application the results of the estimation procedure are compared with the results of a dynamic finite element calculation.
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.
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.
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 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.
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.
Dynamic and quasi-static FE calculation of impact from 9 metre drop of spent fuel transport cask
(2009)
The drop from 9 m height onto a rigid target is one of the required proofs of safety for packages of radioactive materials. Direct dynamic finite element method (FEM) calculations and combined two step analytical quasi-static finite element (FE) calculations are both applied for the simulation of a 9 m drop test. This paper gives a comparative example of both approaches for the 9 m side drop simulation of the spent fuel transport cask with wood filled impact limiter. The model for dynamic FEM consists of cask body and impact limiter. Detailed material properties and geometry descriptions from each component of the impact limiter are required. The results (stress fields in the cask body) are obtained directly from the calculation. The combined method provides as intermediate results the force-deformation characteristic of impact limiter. The maximum impact limiter force determined by the law of energy conservation during the drop is then - in a second step - applied on the cask body in a quasi-static FE model in order to calculate the stresses. In this paper, the rigid body deceleration and the maximum stress in the middle of the cask body are used for the comparison between the dynamic FEM and the combined method. Similar maximum rigid body deceleration-time curves were obtained by both methods for the horizontal 9 m free fall. Concerning the stress in the cask body the dynamic FEM results oscillate about values calculated by the combined quasi-static approach. If the combined quasi-static approach is used in the safety assessment of a cask, a suitable factor has to be applied on its results to take into account the additional dynamic effects.
The 9 meter drop onto an unyielding target is one of the important mechanical tests within the safety assessment of transport casks for radioactive material. In general, the cask is equipped with impact limiters to reduce the dynamic load on the cask body by absorbing a major part of the kinetic energy. The impact limiters are often made of wood or aluminium. In this study an elastic-plastic material model with volume change was used to describe the stress-strain behaviour of wood found in crush tests. For aluminium, an elastic-incremental plastic material model with Cowper-Symonds parameters for strain rate depending material hardening was used to model the adiabatic stress-strain relations measured at specimens at constant ambient temperature. Hereafter simulations with a sophisticated finite element model were carried out and compared with different drop tests. Four drop tests of a half-scale cask model equipped with wood and aluminium impact limiters with different drop positions were selected to investigate the impact limiter behaviour during a 9 meter drop test. All drop tests were simulated with the same FE mesh but under different boundary and initial conditions.
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.