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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.
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.
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.
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.
This paper demonstrates exemplarily how numerical and experimental approaches can be combined reasonably in mechanical assessment of package integrity according to the IAEA regulations. The paper also concentrates on the question about how static mechanical approaches can be applied, and what their problems are in relation to dynamic calculation approaches. Under defined impact tests, which represent accident transport conditions, the package has to withstand impact loading, e.g. resulting from a 9 m free drop onto an unyielding target in sequence with a 1 m puncture drop test. Owing to the local character of the interaction between the puncture bar and the cask body, it is possible to develop a dynamic numerical model for the 1 m puncture drop which allows an appropriate simulation of the interaction area. Results from existing experimental drop tests with prototype or small scale cask models can be used for verification and validation of applied analysis codes and models. The link between analysis and experimental drop testing is described exemplarily by considering a regulatory 1 m puncture bar drop test onto the cask body of a recently approved German high level waste transport package. For the 9 m drop test of the package, it is difficult to develop a dynamic numerical model of the package due to the complexity of the interaction between cask body, impact limiters and unyielding target. Dynamic calculations require an extensive verification with experimental results. The simulation of a 9 m drop of a package with impact limiters is thereby often more complex than the simulation of a 1 m puncture drop onto the cask body. A different approximation method can be applied for the consideration of dynamic effects on the impact loading of the package. In a first step, maximum impact force and rigid body deceleration of the cask body during the impact process can be calculated with simplified numerical tools. This rigid body deceleration can subsequently be applied on a verified static numerical model. Dynamic effects, which cannot be covered by the static numerical analysis, have therefore to be considered by using an additional dynamic factor. The paper describes this approach exemplarily for a 9 m horizontal drop of a typical spent fuel cask design.
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.