The dynamic analysis of nuclear waste cask under impact loading

The dynamic analysis of nuclear waste cask under impact loading

Annals of Nuclear Energy 30 (2003) 1473–1485 www.elsevier.com/locate/anucene The dynamic analysis of nuclear waste cask under impact loading T.L. Ten...

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Annals of Nuclear Energy 30 (2003) 1473–1485 www.elsevier.com/locate/anucene

The dynamic analysis of nuclear waste cask under impact loading T.L. Tenga,*, Y.A. Chub, F.A. Changc, H.S. Chind, M.C. Leee a

Department of Mechanical and Automation Engineering, Da-Yeh University, 112. Shan-Jiau Rd., Da-Tsuen, Changhua 515, Taiwan, ROC b Chung-Shan Institute of Science and Technology, P . Box 90008-17-10, Lung-Tan, Tao-Yuan 325, Taiwan, ROC c Department of Civil Engineering, University of National Defense Chung Cheng Institute of Technology, Ta-Shi, Tao-Yuan 335, Taiwan, ROC d Institute of System Engineering, University of National Defense Chung Cheng Institute of Technology, Ta-Shi, Tao-Yuan 335, Taiwan, ROC e Material Test and Evaluation Service, Combined Logistics Command, Nan Kang, Taipei, 115, Taiwan, ROC Received 6 January 2003; accepted 21 March 2003

Abstract Nuclear waste is sealed in steel casks and transported through the public domain to disposal sites. The casks are designed primarily to transport and store 30–55 gallon drums of waste. The casks meet safety requirements that govern how they respond to an accidental drop onto rigid ground. In this paper, a finite element method was used to perform impact analysis on a cask. The calculation simulates the deformation of a 55 gallon cask during and after an edge impact form a height of 1.2 m, falling at a 30 incline onto rigid ground. The regulations require that the plastic strain at an impact corner must not exceed the yielding strain of the cask material. # 2003 Elsevier Science Ltd. All rights reserved.

1. Introduction People are using increasing amounts of electricity. Compared to other energy sources, nuclear power generation is cheap, plentiful and clean. Nuclear energy now provides about 17% of the world’s electricity. The United States, France, Japan, * Corresponding author. Tel.: +886-4-8511221; fax: +886-4-8511224. E-mail address: [email protected] (T.L. Teng). 0306-4549/03/$ - see front matter # 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0306-4549(03)00080-X

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and Germany are the world leaders in its production. Nuclear power is clearly become the energy of the future. However, nuclear accidents and the disposal of nuclear wastes are the important popular concerns. Nuclear waste is a byproduct of nuclear reactors and fuel processing plants. Radiation from nuclear waste may causes human body cell death, genetic mutation, cancer, leukemia, birth defects, and disorders of the reproductive, immune and endocrine systems. The environmental effect of nuclear waste has proven to be much greater than originally estimated by the fledgling industry. The problem of safely transporting and storing the nuclear waste is yet to be solved. Consequently, progress on nuclear waste disposal is widely considered a prerequisite for any future growth of nuclear power. Generally, nuclear waste is sealed in steel casks and transported through the public domain to disposal sites. The casks are designed primarily to transport and store 30–55 gallon drums of waste. The casks meet safety requirements that govern how they respond to an accidental drop onto rigid ground. Accordingly, the drop testing and impact analysis of casks for transportation, with reference to designing shielded casks are important. Previous studies have developed many methods for evaluating the strength of casks on accidental impact. Newly developed computer techniques, have further enhanced the finite element method for analyzing damage behavior on impact. Yagawa et al. (1984) performed two types of numerical tests using various computer codes to investigate the dynamic behavior of a cask used to ship nuclear fuel when impacting onto a rigid floor, following an accidental fall from a height of 9 m. Diersch et al. (1994) used an analytical and finite element approaches to combine the dynamic compression curves and thus determine the maximum cask deceleration and the maximum deformation on impact, for a 9 m drop, ending in a end-on, a side or an edge impact. The results are compared with experimentally obtained results for original casks. Calculations were found to agree with experimental results. McGreesh, et al. (1995) assessed the impact analyses of a one-third scale model of the thick-walled cask, and compared the results obtained from a series of drop tests with those predicted by finite element analyses using the computer code DYNA3D. Close agreement was obtained for the accelerations and impact displacements. Dreier et al. (1997) considered three drop tests using a DCI (Ductile Cast Iron) cask. The casks were dropped from 9 m such that the impacts were flat on the cylindrical shell of the shock absorbers at the top and the bottom. Casks were also dropped from 1 m, impacting on the bar in the center of the cylinder wall. Ettemeyer et al. (1997) performed computer simulations instead of the drop tests. The simulations were performed using computer programs based on the finite element method. Richins et al. (2000) performed non-linear, dynamic finite element analyses to simulate the drop tests onto a rigid surface required for US Department of Transportation (DOT) 7A Type A certification. The results provide assurance that the containers will pass the required DOT certification tests. The methods used were applied to other waste-shipping containers, to optimize their designs without performing actual impact tests. Lee (2000) performed impact analyses of nuclear waste dry storage containers to simulate an accidental drop onto an unyielding surface at three different drop orientations. The finite element technique uses MSC/PATRAN for pre- and post-processing, while the analyses are performed using the hydro-

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dynamic code DYNA3D. Responses in terms of energy, momentum, contact force, stresses, strains and deformation during and after impact are closely compared. Ku et al. (2000) analyzed the characteristics of the intermittent welding of the cask impact limiter by testing intermittently welded specimens, and the effect of weldment rupture on the absorbing behavior of the cask on impact was evaluated by finite element analysis. According to the regulations of the radioactive waste material cask (The Executive Yuan of the Atomic Energy Council Fuel Cycle and Materials Administration, 1998), a 55-gallon radioactive waste cask must be designed to be sufficiently strong to prevent unacceptable leakage in the case of accidental impact. The high costs of experimental testing are such that studies to replace drop testing with computer simulations have become very important. In this paper, a finite element methodology was used to perform impact analysis on a cask. The calculation simulates the deformation of a 55-gallon cask during and after an edge impact from a height of 1.2 m, falling at a 30 degrees incline onto rigid ground. The regulations require that the plastic strain at an impact corner must not exceed the yielding strain of the cask material. The analysis ensures that the cask will meet the test regulations. The simulation method used here can be applied to other waste casks to optimize designs without performing actual impact testing.

2. Finite element calculation In this paper, the drop simulations are performed using the computer program, MSC/Dytran, based on the finite element method. The MSC/Dytran program is a three-dimensional analysis code for analyzing the dynamic, nonlinear behavior of solid components, structures and fluids. The program uses classic explicit finite element technology to solve dynamic structural analysis problems. The program includes all of the element types and material models required to solve various practical engineering problems, including problems involving 3-D contact and sliding effects. Such problems arises in structural crashworthiness analysis, component drop test simulations, tri-hub burst containment analysis, and sheet metal stamping. The Lagrangian processor was used in this study. The impact of a radioactive waste cask is theoretically simulated using continuum mechanics, to describe the process of material deformation and the explicit direct time integration. The explicit methods are conditionally stable, depending on the selected time step but do not require the simultaneous equations to be solved. The pre- and post-processors MSC/ PATRAN is used to prepare and evaluate the MSC/Dytran results.

3. Numerical verification The calculation result of the proposed computer code was compared with the experimental datas of Wilkins and Guinan (1973) to verify the accuracy of the calculation. The impact of cylinder at various initial velocities onto the rigid surface is

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analytically described for this study. Copper cylinders are 23.47 mm in length, and 6.4 mm in diameter were used. Table 1 shows the material properties. A quartersection of the cylinder was modeled to elucidate its impact onto a rigid surface, using symmetric planes, and the boundary conditions determined by symmetry were applied to all nodes on the geometry. The symmetric model includes 225 solid elements and 368 nodes. The rigid surface model consists of 25 shell elements and 36 nodes. All circular ccopper cylinder nodes in the model were given various initial velocities of 89 m/s to 210 m/s, impact vertically on a rigid surface. The results of finite element analysis were then compared to experimental data and listed in Table 2. Notably, the results are similar. The computed Lf/L0 ratios (where L0 represents the copper cylinder initial length, and Lf represents the final length after deformation) are slightly lower than experimental results. Fig. 1 shows the final deformation contour distribution in the circular copper cylinder at approximately 65 ms. The copper cylinder elements were jostled more closer to the surface of impact, and the contact surface nodes were seriously squeezed out. Fig. 2 plots the Lf/L0 ratio versus the initial impact velocity. Comparing the circular copper cylinder impact analysis results confirms the ability of the finite element computer code to specify non-linear processes. Therefore, the analysis procedure presented here is suited to analyzing the integrity of the radioactive waste cask, under incidental drop conditions.

Table 1 Material properties of copper cylinder 8.9 g/cm3 117 Gpa

mass density  Young’s modulus E poisson’s ratio 

0.35

yield strength y

0.38 Gpa

Table 2 Impact of copper cylinder on a rigid boundary Impact velocity (m/s)

Experimenta Lf/L0

MSC.Dytran Lf/L0

Error (%)

89 123 153 183 204 210

0.895 0.835 0.780 0.716 0.669 0.643

0.884 0.821 0.756 0.686 0.634 0.619

1.2 1.6 3.0 4.1 5.2 3.7

a

From Wilkins and Guinan (1973).

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Fig. 1. The deformation contour distribution in the copper cylinder (t=65 ms).

Fig. 2. Lf =L0 ratio versus the initial impact velocity.

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4. Cask impact analysis According to the regulations of the radioactive waste material cask, (The Executive Yuan of the Atomic Energy Council Fuel Cycle and Materials Administration, 1998), the casks must have an internal diameter and a total length of 572 and 906.3 mm, respectively. The cladding and the bottom plate of the cask must be 1.5 mm thick and the lid of the cask must be 1.8 mm, as shown in Fig. 3. The radioactive waste cask material is AISI 1020 carbon steel, with a density of  ¼ 7870 kg=m3 , Young’s modulus E ¼ 205 GPa, Poisson ratio  ¼ 0:256, Yield stress y ¼ 310 MPa, and an ultimate strain of 0.36. For simulating drop testing, the total weight of the cask must reach 400 kg. Therefore, the cask interior is tamped with

Fig. 3. Configuration of cask.

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plumbum, with a material density of  ¼ 1650 kg=m3 , Young’s modulus E ¼ 140 GPa, Poisson ratio  ¼ 0:42, Yield stress y ¼ 27:58 MPa; and an ultimate strain of 0.33. 4.1. Finite element modelling Finite element models were developed for each impact attitude for analysis using computer code, and the radioactive waste cask (including the inner lining of plumbum) modeling was constructed using a pre-processor computer code technique. Two types of elements were used: (1) 7550 solid elements and 8951 nodes to simulate the radioactive waste cask and (2) 100 shell elements and 121 nodes to represent the rigid floor. Fig. 4 schematically depicts the finite element mesh plots of the cask. No slippage was allowed between the cask’s outer steel shell and the internal plumbum material. Both the steel and plumbum materials constitutive equations were employed as elastic perfectly plastic with the maximum stress set to the yield stress; the Von-Mises yielding criterion was adopted. All nodes in the cask model were assigned an initial velocity of 49 m/s toward the rigid floor surface, to simulate a hypothetical fall from a height of 1.2 m, at an angle of impact of 30 from the horizontal. The initial distance between the surface of the rigid floor and the cask was 0.5 mm. In the analyses, the maximum plastic strain at the impacted corner of the outer shell of the contained must not exceed the ultimate strain of the material, to

Fig. 4. Finite element meshes for the cask .

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Fig. 5. Displacement time histories of the bottom plate of the cask on impact.

Fig. 6. Strain time histories of the bottom plate of the cask on impact.

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Fig. 7. Effective stress time histories of the bottom plate of the cask on impact.

Fig. 8. Strain time histories of the cask’s inner plumbum element on impact.

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ensure that the cask is sufficiently tough, and does not fracture under the hypothetical conditions. When the body deforms, the Lagrangian grid points move in space and the elements distort. The erosion algorithm incorporated into the analyses enables highly strained elements in the cask to be eroded. Since elements that had been part of the cask surface will be deleted, the code must dynamically redefine the contact surfaces during the calculation. 4.2. Results and discussion In this paper, analyses were performed using the finite element computer code. The simulated results are reported and discussed in terms of displacement, stress and strain. The numerical analyses of the radioactive waste cask’s impacts onto rigid floors took in 6 ms. Fig. 5 presents the displacement time histories of the bottom plate of the cask on impact. The displacement increases rapidly until the maximum displacement of 19 mm is reached at the impacted corner. The maximum displace-

Fig. 9. (a) Final deformation of the cask (t=6 ms). (b) Final deformation of the cask (at t=6 ms). (c) Final deformation of the cask (at t=6 ms).

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Fig. 9. (continued)

ment is at approximately 4.1 ms after initial contact, and the value do not further increase after 6 ms, the strain has by then obtained its maximum value of 0.257. Fig. 6 plots the strain time histories of the bottom ring of the steel cask. During the initial stage of contact, the strain reaches 0.18, which is maintained until the second stage of contact occurs. The cask’s bottom ring was deformed on the initial contact. The deformed part was tuck into the bottom plate of the cask and the second stage of contact was at around 3.7 ms. Fig. 7 plots the effective stress and time histories. The maximum stress is around 335.4 MPa at approximately 0.605 ms, and is maintained from 0.605 to 2.3 ms during the first contact stage. Then, the stress begins to decline at 2.3 ms when the impacted corner of the bottom ring of the cask continues to be deformed until the second contact stage begins. The analysis ends when the stress has begun to increase after reaching 160 MPa at approximately 6 ms. Fig. 8 presents the strain time histories of the cask’s inner plumbum element during impact. In the initial stage, from zero to 4 ms, the strain increases slowly. After 4 ms, the strain begins to increase rapidly, until its maximum value of 0.12 is reached at approximately 6 ms. Fig. 9(a)–(c) plots the final deformation of the cask

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Fig. 9. (continued)

impact limiter system. After the impact, the bottom ring of the cask, which bears impact corner, is seriously deformed. In the aforementioned free drop corner impact case, the highest impact strain of the cask bottom ring is below the material’s ultimate strain of 0.36. This comparison is based on peak values at a particular time, and the cask body remains virtually elastic throughout impact in the present cases. Therefore, the cask’s ability to withstand the hypothetical drops without loss of leak-tightness is established.

5. Conclusion This paper applies a numerical method to analyze the accidental impact of a cask. The results of this study yield the following conclusions. 1. The maximum deformation of the cask itself is insignificant. The outer shells are found to have maximum strains well below the ultimate strains, except at the impacted corner where the final deformation is acceptable. The deformation remains essentially elastic during the impact.

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2. Non-linear, dynamic finite element analyses can determine the responses of the radioactive waste cask system in terms of stress, strain, and displacement time histories under dynamic impact conditions. The results ensure that the deformation of the cask’s on impact pass regulation certification tests. Further design calculations can thus be performed, and the information used to optimize other cask’s designs without the incurring the expense of performing real drop tests.

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