European Coordination for Accelerator
Research and Development
Work package 8: ColMat
Collimators & materials for higher beam power beam
2nd WP meeting - 22 March 2010
L. Peroni, M. Scapin
Dipartimento di Meccanica, Politecnico di Torino
DIMEC
Dipartimento di Meccanica



POLITO Actions
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DIMEC
Dipartimento di Meccanica
A fundamental aspect of this task is the development of competences and methodologies of
analysis based to numerical simulations of the complete problem. To do this, it is essential to
look to a multidisciplinary approach. As a matter of fact, the problem involves different fields,
such as structural and mechanical engineering, thermodynamics, hydrodynamics and physics.
Thermodynamics/hydrodynamics
Physics
GSI - BIG2
Structural/mechanical
engineering
CERN -FLUKA
Pressure, density,
temperature
Energy
Complex geometry, material behaviour, boundaries…
CERN -ANSYS
Stress, strain, damage
The task
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DIMEC
Dipartimento di Meccanica
In each point of the structure we must identify the stress tensor; it can be expressed as the sum of
two other stress tensors:
a mean hydrostatic or volumetric stress tensor which tends to change the volume of the stressed body;
a deviatoric component called the stress deviator tensor, which tends to distort it.
 ij  sij ( ij ,  ij )  p ij
el
 y  f ( eff , , T , p)
Material model:
Johnson–Cook
Steinberg–Cochran–Guinan–Lund
Zerilli–Armstrong
Mechanical Threshold Stress
Preston–Tonks–Wallace
pl
p=f (r,E,T…)
Equation of state:
Grüneisen
Polynomial
Tillotson
GRAY
Tabular (SESAME, EOSPRO…)
From a mechanical point of view
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DIMEC
Dipartimento di Meccanica
Constitutive plasticity model
(Glidcop)

 



 A  B 1  C ln 1  T 

y
n
pl
Johnson Cook



 f   D1  D2 exp D3
BIG2 [Bushman & Fortov]
*m

0

p 
 
1  D4 ln
1  D5 * T 
 eff 
0 
SESAME
Pressure (GPa)
10
10
10
4
2
EOS
(Copper)
0
2
1.5
x 10
4
20
15
1
10
0.5
Temperature (K)
5
0
0
Density (g/cm3)
Glidcop/Copper
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DIMEC
Dipartimento di Meccanica
850°C
150 °C
Glidcop
500
True stress (MPa)
400
300
200
100
0
0
0.05
0.1
0.15
True plastic strain (-)
0.2
Experimental test
J-C fit
1
Temperature coefficient
1000°C
850°C
700°C
600°C
500°C
400°C
300°C
200°C
100°C
20°C
0.8
0.6


 y  A  B pln 1  C ln


m
 
 1 T *
0 

0.4
0.2
0
373 473 573 673 773 873 973
Temperature (K)
1123
1273
Plasticity - Temperature
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DIMEC
Dipartimento di Meccanica
Hopkinson Bar
Strainrate
Taylor test
216
m/s
1.5
Glidcop
600
500
400
300
strain-rate 10-3 s-1
200
strain-rate 10-1 s-1
strain-rate 101 s-1
100
Strain-rate coefficient
True stress (MPa)
1.4


 y  A  B pln 1  C ln

Taylor test
1.2
SHPB
1.1
1
Experimental test
J-C fit
strain-rate 10 s
0.05
0.1
0.15
True plastic strain (-)
0.2

1.3
3 -1
0
0

m
 
 1 T *
0 
0.9
10
-3
10
-1
1
10
10
-1
Strain-rate (s )
3
10
5
Plasticity - Strainrate
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DIMEC
Dipartimento di Meccanica
Objectives:
Numerical simulation of a complex mechanical structure
(collimator) subjected to beam impact: energy deposition, shock
waves, damage …
Energy
Numerical code: LSDyna
General purpose transient dynamic finite element program
capable of simulating complex real world problems. It is
optimized for shared and distributed memory Unix Linux and
Windows platforms.
2D and 3D Lagrangian, Eulerian, ALE, SPH, meshfree
Preliminary model (Benchmark)
A Glidcop bar (5 mm radius, 1 m long) facially irradiated with 8 bunches
of 7 TeV/c protons (each bunch comprises 1.15x1011 protons)
2D axisymmetric FEM model - 2500 elements
Numerical modeling
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DIMEC
Dipartimento di Meccanica
The particle beam energy distribution is applied by using a
200 ns ramp (constant power)
Explicit integration scheme, time step magnitude 10-8÷10-9 s
About 30 second of CPU time to simulate 10 ms
time step
Since a LSDyna tabular EOS routine is under developing (using the user-def
capabilities and the Fortran routine written for SESAME and CTH, thank you
to Gerald Kerley) a polynomial EOS is used to fit tabular data.
8
x 10
SESAME
Linear interpolation
r
4
1
2
x 10
0.5
10
1.6
SESAME
Polynomial
1.4
SESAME
Polynomial
1.2
P(m)/E
0
P(m)
Pressure (Pa)
6
10
0
-0.5
1
0.8
0.6
-2
0
-1
1
2
3
4
Specific energy (J/m3)
5
6
x 10
10
-1.5
-0.6
0.4
-0.4
-0.2
m
0
0.2
0.2
-0.6
-0.4
-0.2
m
0
0.2
Numerical modeling - EOS
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DIMEC
Dipartimento di Meccanica
Volumetric strain
Pressure (Pa)
Density
Temperature (K)
End of deposition t~200 ns
- No increase of penetration depth of
protons due to density reduction
(FLUKA coupling in the future?)
- Temperature evaluated with the heat
capacity of solid (only for J-C model)
Preliminary results (I)
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DIMEC
Dipartimento di Meccanica
Pressure (Pa)
2E-8 s
2E-7 s
6E-7 s
1E-6 s
Volumetric
strain
Preliminary results (II)
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DIMEC
Dipartimento di Meccanica
Von Mises
(Pa)
2E-8 s
2E-7 s
6E-7 s
1E-6 s
Strainrate
(s-1)
Preliminary results (III)
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DIMEC
Dipartimento di Meccanica
Pressure
8
x 10
Elements deletion for high volumetric
strain (low density) and low pressure
Pressure (Pa)
6
10
SESAME
Linear interpolation
r
4
2
0
deletion
-2
0
1
2
3
4
Specific energy (J/m3)
5
6
x 10
10
Preliminar results (IV)
European Coordination for Accelerator
Research and Development
Thank you for your attention
L. Peroni, M. Scapin
Dipartimento di Meccanica, Politecnico di Torino