work package 8: colmat l. peroni, m. scapin dipartimento di meccanica, politecnico di torino...

Work package 8: ColMat

L. Peroni, M. ScapinDipartimento di Meccanica, Politecnico di Torino

European Coordination for Accelerator Research and Development

Collimators & materials for higher beam power beam2nd WP meeting - 22 March 2010

DIMECDipartimento di Meccanica

POLITO ActionsPOLITO Actions


The taskThe task

3

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.

Energy

PhysicsThermodynamics/hydrodynamics Structural/mechanical

engineering

Pressure, density, temperature

Stress, strain, damage

CERN -FLUKAGSI - BIG2

CERN -ANSYS

Complex geometry, material behaviour, boundaries…


From a mechanical point of viewFrom a mechanical point of view

4

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.

ijpl

ijel

ijijij ps ),(

Equation of state:GrüneisenPolynomialTillotsonGRAYTabular (SESAME, EOSPRO…)

p=f (,E,T…)),,,( pTf effy

Material model:Johnson–CookSteinberg–Cochran–Guinan–LundZerilli–ArmstrongMechanical Threshold StressPreston–Tonks–Wallace


Glidcop/CopperGlidcop/Copper

5

EOS (Copper)

m

TCBA ny

*

0pl 1ln1

TDDp

DDDeff

f *10

ln1exp 54321

Constitutive plasticity model (Glidcop)

05

1015

20

0

0.5

1

1.5

2

x 104

100

102

104

Density (g/cm3)Temperature (K)

Pre

ssu

re (

GP

a)

Johnson Cook

SESAMEBIG2 [Bushman & Fortov]


Plasticity - TemperaturePlasticity - Temperature

6

0 0.05 0.1 0.15 0.20

100

200

300

400

500

True plastic strain (-)

Tru

e s

tre

ss (

MP

a)

1000°C850°C700°C600°C500°C400°C300°C200°C100°C20°C

373 473 573 673 773 873 973 1123 12730

0.2

0.4

0.6

0.8

1

Te

mp

era

ture

co

effi

cie

nt

Temperature (K)

Experimental testJ-C fit

850°C

150 °C

Glidcop

m

TCBA ny

*

0pl 1ln1


10-3

10-1

101

103

105

0.9

1

1.1

1.2

1.3

1.4

1.5

Strain-rate (s-1)

Str

ain

-ra

te c

oe

ffici

en

t

Experimental testJ-C fit

Plasticity - StrainratePlasticity - Strainrate

7

0 0.05 0.1 0.15 0.20

100

200

300

400

500

600

True plastic strain (-)

Tru

e s

tre

ss (

MP

a)

strain-rate 10-3 s-1

strain-rate 10-1 s-1

strain-rate 101 s-1

strain-rate 103 s-1

Glidcop

Hopkinson Bar Taylor test

m

TCBA ny

*

0pl 1ln1

216 216 m/sm/s

Strainrate

Taylor test

SHPB


Numerical modelingNumerical modeling

Objectives:Numerical simulation of a complex mechanical structure

(collimator) subjected to beam impact: energy deposition, shock waves, damage …

Numerical code: LSDynaGeneral 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

8

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

Energy


Numerical modeling - EOSNumerical modeling - EOS

9

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 sAbout 30 second of CPU time to simulate 10 s

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.

-0.6 -0.4 -0.2 0 0.2-1.5

-1

-0.5

0

0.5

1x 10

10

P(

)

SESAMEPolynomial

0 1 2 3 4 5 6

x 1010

-2

0

2

4

6

8x 10

10

Specific energy (J/m3)

Pre

ssur

e (P

a)

SESAMELinear interpolation

-0.6 -0.4 -0.2 0 0.20.2

0.4

0.6

0.8

1

1.2

1.4

1.6

P(

)/E

SESAMEPolynomial


Preliminary results (I)Preliminary results (I)

10

Pressure (Pa)

Temperature (K)

Volumetric strain

Density

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 (II)Preliminary results (II)

11

Pressure (Pa)

Volumetric strain

2E-8 s 2E-7 s 6E-7 s 1E-6 s


Preliminary results (III)Preliminary results (III)

12

Von Mises (Pa)

Strainrate (s-1)

2E-8 s 2E-7 s 6E-7 s 1E-6 s


Preliminar results (IV)Preliminar results (IV)

13

Elements deletion for high volumetric strain (low density) and low pressure

Pressure

0 1 2 3 4 5 6

x 1010

-2

0

2

4

6

8x 10

10

Specific energy (J/m3)

Pre

ssur

e (P

a)

SESAMELinear interpolation

deletion

Thank you for your attention

L. Peroni, M. ScapinDipartimento di Meccanica, Politecnico di Torino

European Coordination for Accelerator Research and Development

work package 8: colmat l. peroni, m. scapin dipartimento di meccanica, politecnico di torino...

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