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During postulated high-pressure core melt accident scenarios, temperature values of more than 800°C can be reached in the reactor coolant line and the surge line of a pressurised water reactor (PWR), before the bottom of the reactor pressure vessel experiences a significant temperature increase due to core melting. For the assessment of components of the primary cooling circuit, two methods are used by GRS. One is the simplified method ASTOR (approximated structural time of rupture). This method employs the hypothesis of linear damage accumulation for modeling damage progression. A failure time surface which is generated by structural finite element (FE) analysis of varying pressure and temperature loads serves as a basis for estimations of failure times. The second method is to perform thermohydraulic and structure mechanic calculations for the accident scenario under consideration using complex calculation models. The paper shortly describes both assessment procedures. Validation of the ASTOR method concerning a large-scale test on a pipe section with geometric properties similar to a reactor coolant line is presented as well as severe accident scenarios investigated with both methods.

In face of severe accident scenarios with melted core material which occurred recently at Fukushima Daiichi and in 1979 at Three Mile Island-2 the integrity assessment of primary circuit components requires a special concern. A best estimate simulation of components under severe accident loading scenarios may be complex and time consuming (see second part of the paper). For the accomplishment of a simplified analysis concerning integrity of the components during a severe accident and especially the question which component fails first in framework of thermohydraulic analysis with system codes, an efficient method has been developed which will be described in the following chapters.

The method ASTOR is an easy applicable tool for fast estimation of failure times. Furthermore the reduced complexity enables the integration into thermohydraulic codes and may help to find results of structure mechanical properties which are required for coupled calculation of mechanical and thermohydraulic structure characteristics of primary circuit devices. Moreover the method ASTOR helps to determine the degree of structural damage after a history of load at the actual point of time. Therefore it is possible to determine the remaining durability of components under the assumption that the actual loads will continue at a constant level. The method ASTOR can be employed for failure time calculation without time intensive nonlinear structure-mechanical analysis. The analysis requires a suitable failure time surface. The method ASTOR published already in [

Transient loads on pipe.

Within the defined ranges, cascaded pressure steps and temperature steps are defined. Failure times of the pipe structure under combinations of pressure steps and temperature steps are determined by finite element analysis with the FE-program ADINA [

Performing several numerical analyses of this kind to cover the ranges of temperatures and pressures to be expected in an accident yields a series of structural failure times which can be regarded as discrete pivots of a continuous failure time surface in the failure time-temperature-pressure space (see Figure

Linear damage accumulation hypothesis in ASTOR.

In the framework of further development, a time-consuming method for the determination of failure surfaces has been developed. The chain of software modules consists of three modules. The first module provides a file structure and builds up the framework for forthcoming FE analysis and failure assessment. The module requires input data about FE geometry, material data, data about failure assessment, and information about the number of nodes of the failure surface. After each simulation run, a failure assessment is accomplished by a software module. Failure criteria for plastification and creep failure are used for failure assessment. After all simulation runs and failure assessments are accomplished, a final software module collects all available output and failure data for compilation of the input file for analysis by ASTOR.

Bases for the temperature-dependent stress-strain-relations of the piping material steel 20 MnMoNi 55 used in German NPPs are data measured by the testing facility “Materialprüfungsanstalt (MPA)” of the University of Stuttgart [

Steel 20 MnMoNi 55: true stress-strain curves up to uniform elongation (400°C–1200°C) derived from measured data.

For the simulation of creep behaviour of components, the FE-codes usually include material models which describe the time dependence of creep strain with parameters stress and temperature. On the other hand the material characterisation is usually determined by load-controlled creep curves. Exemplary in Figure

Linear approximation of measured creep curves (load controlled) of steel 20 MnMoNi 55 at 1000°C.

For modeling of creep properties of the steel 20 MnMoNi 55, a “Creep Law” of the FE program ADINA [

The steel 20 MnMoNi 55 does not show a pronounced primary creep phase. Therefore, the secondary phase, which is important for the progress of creep, can be approximated by a straight line determined by the stress- and temperature-dependent parameter

Both failures due to plastification and due to creep are employed as failure criteria for an integrity assessment based on FE analysis. Due to the higher level of stresses and strains, failure at the inside of the pipe structure is considered. To predict the time to failure of a piping based on a FE analysis it is necessary to define criteria for failure. The analysis results are assessed concerning failure on basis of a strain criterion. An ADINA material model is employed which considers plastic strains as well as creep strains. The value of strain is determined by the temperature-dependent strength and the temperature/stress-dependent creep characteristic of the relevant material. As the uniaxial strain limit for plastification, the uniform elongation is considered. Based on calculations of large-scale creep experiments, the limit of uniaxial creep strain is determined by 60% of the creep failure strain of the uniaxial creep tests for a safety-related assessment [

Steel 20 MnMoNi 55. Approach for definition of uniaxial creep limit.

For consideration of multiaxial stress and strain states it is common practice to reduce the strain limits by division with a triaxial-factor TF which appears in the following form [

The abstraction from the pipe structure to the analysis model is displayed in Figure

2D representation of pipe structure, dimensions, loads, and boundary conditions.

Loads (forces and temperature) as well as boundary conditions are defined. Because of the rotational symmetry, it is possible to define loads and boundaries on lines. The temperature is defined as a homogenous temperature load on all elements.

In the following a failure surface of a PWR reactor coolant line (RCL) with the geometry inner diameter 750 mm and wall thickness 62 mm is considered. In Figure

Failure time diagram for a RCL of 20 MnMoNi 55.

For validation of the employed FE simulation and the failure assessment, procedure test data of a component test [

Loading conditions in the test pipe.

Accumulated creep strain and strain limit curve (failure at 12470 s).

In the following section the results of an FE-based failure assessment and an ASTOR failure analysis for an RCL loaded during a severe accident scenario are compared. Due to an assumed station blackout scenario of a PWR, molten core material in the reactor pressure vessel-lower head (RPV-LH) may cause catastrophic consequences. The time of failure of the RCL is of special concern because a failure before the RPV-LH’s failure may enable a significant pressure decrease. In the following a reactor coolant line, as considered in Section

Failure assessment criteria.

Run # | Creep failure assessment | Plastic failure assessment |
---|---|---|

A | 60% limit curve (see Figure | Uniform elongation/variable TF |

B | 100% limit curve (see Figure | Uniform elongation/constant TF |

Figure

Temperature and pressure progression.

In Run A the creep strains meet the limit strain prior to the plastic strains based on the safety-related failure criterion with consideration of the triaxial stress factor after about 47471 s (see Figure

Accumulated creep strain and strain limit curve (failure at 47471 s): overview and detailed view.

In Run B after about 47500 s, a strong increase of the plastic strains can be observed. The calculated plastic strains meet the criterion for failure as a matter of fact after about 47656 s.

Figure

Summation of damage increments (ASTOR).

Figure

Failure times and load progression.

As a further example, the integrity of components in the primary circuit of a PWR loaded by a core-melt scenario with remaining high-pressure in the primary cooling circuit has been investigated with a complex analysis model. Thermohydraulic evaluations for this case show that the reactor pressure vessel (RPV) bottom, the main coolant lines (MCL), and the surge line can reach temperatures above 800°C. A main aim of the study was to clarify whether the pipe lines will fail earlier than the RPV bottom or vice versa.

To estimate the failure temperatures and times, structure mechanic calculations with the FE code ADINA [

For the Thermohydraulic calculation of the assumed accident scenario, the program MELCOR [

Temperatures versus transient time for different positions.

Pressures versus transient time for primary and secondary circuit positions.

For the FE calculations with ADINA [

FE model of the coolant loop including surge line and pressurizer.

As the model is loaded by temperatures up to nearly 1000°C, corresponding high-temperature material data have to be used. For the ferritic parts, the stress-strain curves shown in Figure

As mentioned already, the load functions for the FE model concerning the wall temperatures of the components and the internal pressure are delivered by results of MELCOR calculations (accident scenario “total station blackout”). At 35 positions of the FE loop model, the temperature inside and outside the wall was evaluated. The temperature values between these positions are gained by interpolation. Also the temperature values in the middle of the wall were found by interpolation.

As described before a strain-based approach is used for the failure assessment. From the material side, the temperature-dependent strain value at uniform elongation is considered. To take constraint effects into account, this value is divided by the stress triaxiality factor TF as defined before. If the calculated accumulated effective plastic strain exceeds the strain limit at some integration point, the failure of the component is assumed in the sense of a safety-related assessment. Furthermore an assessment concerning failure as a matter of fact is performed with TF = 1.

To show how the estimation of failure time is carried out, two selected evaluations are shown in Figures

Structure mechanic assessment for a typical integration point in the MCL (eg: strain at uniform elongation concerning the respective temperature, eg/TF: strain at uniform elongation divided by stress triaxiality factor, ep: accumulated plastic strain).

Structure mechanic assessment for a typical integration point in the surge line (eg: strain at uniform elongation concerning the respective temperature, eg/TF: strain at uniform elongation divided by stress triaxiality factor, ep: calculated accumulated plastic strain).

The intersection points of eg/TF and ep deliver the failure times of a safety-related assessment. For the MCL this gives a failure time of about 3.1 h of the transient time. An assessment of the MCL with TF = 1, that is, failure as a matter of fact, gives a failure time of about 3.2 h. For the surge line a failure time of about 3.35 h is found based on a safety related assessment.

Additionally Figure

Temperatures versus transient time for different positions together with times and temperatures of failure for MCL and surge line.

The steep increase of the RPV temperature starts at about 3.5 h transient time. It may be concluded that failure of the MCL is expected about 0.3 h before the temperature increase of the RPV starts. Creep effects have not been considered in this analysis, but they would contribute to an increase of the time difference mentioned before.

The comparison of failure times of a large-scale creep test and FE analysis confirms that the FE analysis method including the used failure criterion is a best estimate method.

The method ASTOR enables a fast estimation of failure times and can be integrated into the framework of thermohydraulic system analysis programs. The application of ASTOR is limited to the boundary conditions concerning pipe geometry, material data, and type of loading used for generation of the failure surface. An uncertainty of the calculated failure times exists but can be constrained by a decrease of the assumed damage limit value. The comparison of ASTOR results with more rigorous FE analysis results requires verifications to quantify error bands. The results of the investigation show that the time of failure is strongly dependent on the changing stress level during the transient loading and the temperature-dependent material properties characterizing plastification as well as the temperature/stress-dependent material properties characterizing creep of the piping material. Also the uncertainty of the employed material data has to be mentioned. The required creep data are derived from load-controlled creep curves by use of a simplification method. Because the material creep data are only available for a limited range of stresses and temperatures, the FE code may use extrapolated data by trend analysis outside the range.

An accident with a core melt scenario under high-pressure loading caused by a station blackout is used as an example for an estimation of failure times by complex thermohydraulic and structure mechanic calculations. The thermohydraulic calculations with MELCOR show that in the course of the transient temperature values of above 800°C are reached at several positions of the cooling circuit. Using the temperatures and pressures evaluated by MELCOR as input for the structure mechanic calculation with ADINA, results in terms of stresses and strains were gained for the primary coolant loop under the accident scenario is considered. Using a strain-based failure assessment, failure times were estimated for the relevant positions of the loop model. While the temperatures in the RPV bottom are still relatively low, plastic strains in the main coolant and surge line reach limit values. Therefore it might be concluded that the MCL fails earlier than the RPV bottom. Since the failure times of the different positions do not differ very much, more studies might be necessary for the quantification of uncertainties. Especially the influence of creep could be considered more precisely. Finally it has to be pointed out that here only a special accident has been treated. Other accidents with different temperature and pressure transients might give other failure sequences.

Dependent on the required accuracy of the time of failure of a pipe, three failure assessment methods are accomplishable:

ASTOR (useful for implementation in system codes, limited applicability, limited accuracy, extensive concerning generation of failure surfaces),

FE analysis with simplified FE model (flexible concerning application, limited applicability concerning complexity, high accuracy),

Complex FE analysis model with consideration of interaction between components [

Automatic dynamic incremental nonlinear analysis

Approximated structural time of rupture

Finite element

Main coolant line

Thermohydraulic system code

Nuclear power plant

Pressurized water reactor

Reactor coolant line

Reactor pressure vessel-lower head

Triaxiality factor.

The work has been predominantly performed in the framework of the Reactor Safety Research Program of the German Federal Ministry of Economics and Technology. The support of parts of the work by the German Federal Ministry for the Environment, Nature Conversation and Nuclear Safety is also acknowledged.