1. 2007-03-07 accident deformation – doyle (rev1) 1/8
Phase II Collimator, Accident Deformation Simulation Transient Stress Analysis – Work in Progress
E. Doyle
March 7, 2007
accident deformation – doyle (rev1) /8

2. 2007-03-07 accident deformation – doyle (rev1) 2/8
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
accident deformation – doyle (rev1) /8

3. 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.
accident deformation – doyle (rev1) /8

4. Review: Permanent Jaw deflection, ux, after 60 sec (1/30/07)
Melted material removed
48 um
Beam side
Far side
54 um
Beam side
Far side
Original constraints
Modified constraints
accident deformation – doyle (rev1) /8

5. 2007-03-07 accident deformation – doyle (rev1) 5/8
New Analysis
Modeling (new steps shown in green)
Original ANSYS model modified – refined mesh near beam
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 > 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
Temperature constant in this elapsed time
Results inconclusive
accident deformation – doyle (rev1) /8

6. Axial stress, sz, compared for two end constraints t=10e-6 sec
Results Identical near mid-jaw
Simple Supports
Constrained in z
accident deformation – doyle (rev1) /8

7. Axial stress, sz, compared for two end constraints
Results Very Similar, Not Identical at Ends
Simple Supports
Constrained in z
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)
accident deformation – doyle (rev1) /8

8. 2007-03-07 accident deformation – doyle (rev1) 8/8
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.
accident deformation – doyle (rev1) /8