Phase II Collimator, Accident Deformation Simulation Transient Stress Analysis Work in Progress

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Phase II Collimator, Accident Deformation
SimulationTransient Stress Analysis Work in
Progress

• E. Doyle
• March 7, 2007

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Overview

• As reported12/12/06
• medium resolution 3-D ANSYS FLUKA models
• Thermal heating/cooling analysis followed by
  quasi-static stress analysis
• .27 MJ deposited in 200 ns
• Molten material removed from model before
  cool-down phase
• Modifications per Bertarelli (1/30/07)
• Goal simulate plastic deformation due to jaw
  inertia during energy deposit
• Method Jaw ends constrained in z for stress
  solution during energy deposit phase to simulate
  inertia, released for 60 sec cool-down phase
• Result Effect on permanent deformation is
  slight, 10 increase (thermal inertia has a
  similar effect the large mass of cool material
  restrains sudden expansion of the small mass of
  hot material, which causes it to yield)
• Further Modifications (3/7/07)
• Goal directly simulate shock wave effects
• Method reduce time step during stress pass of
  transient cool-down, maintain complete
  z-constraints to simulate inertia of jaw material
• Problem how to coordinate separate transient
  solutions (thermal and stress)
• Compromise true transient stress solution during
  initial cool-down when temperature can be
  considered to be constant
• Result inconclusive. Need longer compute time,
  measure of accumulated plastic deformation

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Review Jaw End Constraints (1/30/07)
During energy deposit (0 200 ns). All nodes
(both ends) constrained in z simulates inertia
effect in quasi-static analysis
After energy deposit (200ns 60 sec),
z-constraints released. Original analysis used
this constraint at all times.
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Review Permanent Jaw deflection, ux, after 60
sec (1/30/07)
Melted material removed
Original constraints
Modified constraints
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New Analysis

• Modeling (new steps shown in green)
• Original ANSYS model modified refined mesh near
  beam
• Elements _at_ O.D. 2.5 x 2.5 x 50mm (r,f,z)
  were 2.5 x 8.0 x 50
• Jaw length 95cm, ends not tapered
• Temperature dependent stress-strain (bilinear
  isotropic hardening)
• Other properties independent of temperature
• FLUKA accident simulation for refined mesh model
• Element-to-element mapping
• .27 MJ in 200 ns
• Axial distribution very similar to ultra-fine
  model (reported 3/28/06)
• r,f distribution more diffuse
• Transient analysis of temperatures (energy
  deposit cool-down)
• After 200 ns energy deposit, all elements
  containing any node with temp gt 1100C melting
  point killed
• As if melted and drained from system
• Model allowed to cool for 60 sec to steady
  temperature
• Transient stress analysis response to step
  temperature increase of energy deposit (
  Previously quasi-static analysis of stress at
  each time step)
• Two analyses jaw ends constrained in z vs.
  simple supports for comparison
• 200 x 10-9 time step, elapsed time 10 x 10-6
  sec computation time 4 hrs

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Axial stress, sz, compared for two end
constraintst10e-6 sec
Results Identical near mid-jaw
Simple Supports
Constrained in z
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Axial stress, sz, compared for two end constraints
Results Very Similar, Not Identical at Ends
Constrained in z
Simple Supports
Similarity of results at mid-jaw analysis time
too short for stress waves to travel from
ends. Jaw end result inconclusive. Need a way to
compare cumulative plastic deformations after jaw
cools to uniform temperature Note Speed of
stress wave 5500 m/s (check Cu sonic velocity
at room temperature 3600 m/s)
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Discussion

• The author does not expect the modified boundary
  condition to make a significant difference
• Thermal and mass inertia have a similar effect
  the large mass of cool material restrains sudden
  expansion of the small mass of hot material,
  causing it to yield
• The incrementally greater deformation (1/30/07
  results) with the modified BC is due to the
  harder constraint it provides (not necessarily
  more realistic).
• The true transient analysis is likely to be more
  accurate than the quasi-static analysis
• Reflections of stress waves can cause localized
  doubling of stress (and more severe yielding)
  near boundaries (not simulated by the
  quasi-static stress analysis)
• Difficulties in true transient stress analysis
• Long compute time
• How to maintain continuity of stress waves while
  updating temperature transient
• this analysis is valid because the temperature is
  essentially constant
• Next step Assume most plastic deformation in
  first moments after beam hits (?) Run transient
  stress as long as practical, allow to cool, note
  plastic deformation
• Bottom line permanent jaw deformation in the
  accident case is likely to be a problem. To
  accurately quantify it requires
• a true transient thermal shock analysis
• consideration of temperature dependency of
  several material properties
• consideration of alternative melting/freezing
  scenarios.