1. Work package 8: ColMat L. Peroni, M. Scapin Dipartimento di Meccanica, Politecnico di Torino European Coordination for Accelerator Research and Development Collimators & materials for higher beam power beam 2 nd WP meeting - 22 March 2010

2. DIMEC Dipartimento di Meccanica POLITO Actions

3. DIMEC Dipartimento di Meccanica The 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 Physics Thermodynamics/hydrodynamicsStructural/mechanical engineering Pressure, density, temperature Stress, strain, damage CERN -FLUKA GSI - BIG2 CERN -ANSYS Complex geometry, material behaviour, boundaries…

4. DIMEC Dipartimento di Meccanica From 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. Equation of state: Grüneisen Polynomial Tillotson GRAY Tabular (SESAME, EOSPRO…) p=f ( ,E,T…) Material model: Johnson–Cook Steinberg–Cochran–Guinan–Lund Zerilli–Armstrong Mechanical Threshold Stress Preston–Tonks–Wallace

5. DIMEC Dipartimento di Meccanica Glidcop/Copper 5 EOS (Copper) Constitutive plasticity model (Glidcop) Johnson Cook SESAMEBIG2 [ Bushman & Fortov]

6. DIMEC Dipartimento di Meccanica Plasticity - Temperature 6 850°C 150 °C Glidcop

7. DIMEC Dipartimento di Meccanica Plasticity - Strainrate 7 Glidcop Hopkinson Bar Taylor test 216 m/s Strainrate Taylor test SHPB

8. DIMEC Dipartimento di Meccanica Numerical modeling Objectives: Numerical simulation of a complex mechanical structure (collimator) subjected to beam impact: energy deposition, shock waves, damage … 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 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 1.15x10 11 protons) 2D axisymmetric FEM model - 2500 elements Energy

9. DIMEC Dipartimento di Meccanica Numerical 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 s About 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. 

10. DIMEC Dipartimento di Meccanica 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)

11. DIMEC Dipartimento di Meccanica Preliminary results (II) 11 Pressure (Pa) Volumetric strain 2E-8 s2E-7 s6E-7 s1E-6 s

12. DIMEC Dipartimento di Meccanica Preliminary results (III) 12 Von Mises (Pa) Strainrate (s -1 ) 2E-8 s2E-7 s6E-7 s1E-6 s

13. DIMEC Dipartimento di Meccanica Preliminar results (IV) 13 Elements deletion for high volumetric strain (low density) and low pressure Pressure  deletion

14. Thank you for your attention L. Peroni, M. Scapin Dipartimento di Meccanica, Politecnico di Torino European Coordination for Accelerator Research and Development