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Title: Modeling Dynamic Fracture of Cryogenic Pellets

Abstract

This work is part of an investigation with the long-range objective of predicting the size distribution function and velocity dispersion of shattered pellet fragments after a large cryogenic pellet impacts a solid surface at high velocity. The study is vitally important for the shattered pellet injection (SPI) technique, one of the leading technologies being implemented at ORNL for the mitigation of disruption damage on current tokamaks and ITER. The report contains three parts that are somewhat interwoven. In Part I we formulated a self-similar model for the expansion dynamics and velocity dispersion of the debris cloud following pellet impact against a thick (rigid) target plate. Also presented in Part I is an analytical fracture model that predicts the nominal or mean size of the fragments in the debris cloud and agrees well with known SPI data. The aim of Part II is to gain an understanding of the pellet fracturing process when a pellet is shattered inside a miter tube with a sharp bend. Because miter tubes have a thin stainless steel (SS) wall a permanent deformation (dishing) of the wall is produced at the site of the impact. A review of the literature indicates that most projectile impact onmore » thin plates are those for which the target is deformed and the projectile is perfectly rigid. Such impacts result in “projectile embedding” where the projectile speed is reduced to zero during the interaction so that all the kinetic energy (KE) of the projectile goes into the energy stored in plastic deformation. Much of the literature deals with perforation of the target. The problem here is quite different; the softer pellet easily undergoes complete material failure causing only a small transfer of KE to stored energy of wall deformation. For the real miter tube, we derived a strain energy function for the wall deflection using a non-linear (plastic) stress-strain relation for 304 SS. Using a dishing profile identical to the linear Kirchkoff-Love profile (for lack of a rigorously derived profile) we derived the strain energy associated with the deflection and applied a virtual work principle to find a relationship between the impact (load) pressure to the measured wall deflection depth. The inferred impact pressure was in good agreement with the expected pressure for oblique cryogenic pellet impacts where the pellet shear stress causing cleavage fracture is well above the yield stress for pure shear. The section is concluded with additional discussion on how this wall deformation data lends further support to the analytical fracture model presented in Part I. In Part III we present three different size distribution models. A summary, with a few brief suggestions for a follow on study, is provided at the end of this report.« less

Authors:
 [1]
  1. General Atomics, San Diego, CA (United States)
Publication Date:
Research Org.:
General Atomics, San Diego, CA (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE)
OSTI Identifier:
1344852
Report Number(s):
GA-A28352
DOE Contract Number:
AC05-00OR22725
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English

Citation Formats

Parks, Paul. Modeling Dynamic Fracture of Cryogenic Pellets. United States: N. p., 2016. Web. doi:10.2172/1344852.
Parks, Paul. Modeling Dynamic Fracture of Cryogenic Pellets. United States. doi:10.2172/1344852.
Parks, Paul. 2016. "Modeling Dynamic Fracture of Cryogenic Pellets". United States. doi:10.2172/1344852. https://www.osti.gov/servlets/purl/1344852.
@article{osti_1344852,
title = {Modeling Dynamic Fracture of Cryogenic Pellets},
author = {Parks, Paul},
abstractNote = {This work is part of an investigation with the long-range objective of predicting the size distribution function and velocity dispersion of shattered pellet fragments after a large cryogenic pellet impacts a solid surface at high velocity. The study is vitally important for the shattered pellet injection (SPI) technique, one of the leading technologies being implemented at ORNL for the mitigation of disruption damage on current tokamaks and ITER. The report contains three parts that are somewhat interwoven. In Part I we formulated a self-similar model for the expansion dynamics and velocity dispersion of the debris cloud following pellet impact against a thick (rigid) target plate. Also presented in Part I is an analytical fracture model that predicts the nominal or mean size of the fragments in the debris cloud and agrees well with known SPI data. The aim of Part II is to gain an understanding of the pellet fracturing process when a pellet is shattered inside a miter tube with a sharp bend. Because miter tubes have a thin stainless steel (SS) wall a permanent deformation (dishing) of the wall is produced at the site of the impact. A review of the literature indicates that most projectile impact on thin plates are those for which the target is deformed and the projectile is perfectly rigid. Such impacts result in “projectile embedding” where the projectile speed is reduced to zero during the interaction so that all the kinetic energy (KE) of the projectile goes into the energy stored in plastic deformation. Much of the literature deals with perforation of the target. The problem here is quite different; the softer pellet easily undergoes complete material failure causing only a small transfer of KE to stored energy of wall deformation. For the real miter tube, we derived a strain energy function for the wall deflection using a non-linear (plastic) stress-strain relation for 304 SS. Using a dishing profile identical to the linear Kirchkoff-Love profile (for lack of a rigorously derived profile) we derived the strain energy associated with the deflection and applied a virtual work principle to find a relationship between the impact (load) pressure to the measured wall deflection depth. The inferred impact pressure was in good agreement with the expected pressure for oblique cryogenic pellet impacts where the pellet shear stress causing cleavage fracture is well above the yield stress for pure shear. The section is concluded with additional discussion on how this wall deformation data lends further support to the analytical fracture model presented in Part I. In Part III we present three different size distribution models. A summary, with a few brief suggestions for a follow on study, is provided at the end of this report.},
doi = {10.2172/1344852},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2016,
month = 6
}

Technical Report:

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  • This paper illustrates the use of advanced constitutive models in ABAQUS/Explicit together with highly focused finite element meshes to simulate the propagation of a fracture in a ductile medium. A double edge-cracked specimen under far field dynamic tensile loading is analyzed, and shows both rectilinear motion or unstable oscillatory motion of the crack depending on the material property constraints. Results are also presented for a simulation of ASTM`s standard fracture test E399. Comparisons of ABAQUS/Explicit results with experiments or other analytical/numerical results are made.
  • In this time period, we have continued to focus on (i) refining the thermo-mechanical fracture model for zirconium (Zr) alloys subjected to large deformations and high temperatures that accounts for the cracking of ZrH and ZrH2 hydrides, (ii) formulating a framework to account intergranular fracture due to iodine diffusion and pit formation in grain-boundaries (GBs). Our future objectives are focused on extending to a combined population of ZrH and ZrH2 populations and understanding how thermo-mechanical behavior affects hydride reorientation and cracking. We will also refine the intergranular failure mechanisms for grain boundaries with pits.
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  • We have established previously that typical DT pellets cannot be kept solid with external cooling through pure vacuum, and can only be maintained solid within DT gas-filled spaces over a limited range of cooling temperatures. This report examines whether low-density (0.01 g/cm/sup 3/ or 0.05 g/cm/sup 3/) polyethylene foam or helium gas have sufficient conductivity to allow inner tritium-containing shells to be kept solid. For both conductors the answer is affirmative, but some uncertainty exists concerning the conductivity of foams and the worst excursions might not provide enough conductivity. For helium much less than one millitorr pressure suffices for coolingmore » typical pellets. For cooling the same nuclear fuel concentrated in the form of a central ball, the lightest foams are marginal but might be satisfactory at the highest excursion of our conductivity error. Required helium pressures for ball cooling are in the region of a millitorr. A simple model for the ratio of foam to solid conductivity of a substance is developed.« less