1. Modeling of Surface Roughening M. Andersen, S. Sharafat, N. Ghoniem HAPL Surface-Thermomechanics in W and Sic Armor UCLA Workshop May 16 th 2006

2. Outline  Basic mechanism for roughening—stress representation needed.  Discuss SRIM Calculation from Perkins Energy Spectra.  Ion Deposition  Energy Deposition  Thermal Stresses from Laser Pulse (Hector, Hetnarski).  Timeline for future work.  Additional slides on phase-field methods if interested.

3. Grinfeld Instability  Pioneered 1972.  Considers the movement of material.  Heteroepitaxial (thin films), atoms move along the surface.  Chemical etching, atoms move in and out of the surface.  As shown, can be cumbersome. solid-melt solid-vacuum

4. SRIM Code Ion Concentration  Goal: create a fast process for finding updated concentration of ions/vacancies and develop heat generation plots.  Any interest in this material?

5. Energy Deposition in W&SiC SRIM work provides volumetric heating…need this for thermal stress. SiC experiences smaller Q over greater distance compared with W.

6. Detailed Temperature Profile X-rays Ions Discretize for Roughening Model

7. Formulation: Stresses due to a Laser Pulse  Thermal Field  Stress Field  Dimensionless formulation  Stresses  Temporal Pulse

8. Temporal Pulse  The rise and fall time of each pulse is accounted for.  Can be adjusted (a=0.4,b=7.0,c=3.0).  Consider a Gaussian Surface Source. z r

9. Steady-State Variation of Radial Stress  Surface experiences the largest compressive radial stresses.  Explained by surface elements expanding against “cooler” sub-surface material. Material Surface

10. Evolution of Surface Stresses at Selected R.  Maximum stresses are located at the center of the beam. Similar profiles away from center.  Occurs shortly after maximum energy is reached (rise time)—time needed to develop stress from absorbed energy. Beam Center

11. Evolution of Stress Field under Surface  It is shown that small tensile stresses are developed for radial, hoop, and shear stresses.  Normal stress is still compressive.  Cold regions deep in material and around edges of beam.

12. Axial Variation in Radial Stress  Notice that the radial stress reaches maximum tensile stress as the beam approaches its rise time.  Compressive stresses occur while beam deactivates. t > t_rise t = t_rise

13. Conclusions on Stress  Compressive radial stresses developed on surface.  Subsurface compressive axial stress develops tensile radial stress. (before deactivation)  Elastic solution—addition of plasticity and possibly wave effects (tension -> compression)

14. Future Research Plans  Finished:  Formulation of the problem (roughening, stress field).  Energy deposition calculations (SRIM).  Where’s the problem? Method to fix it.  Computational Tools:  Efficient elastic model – varying biaxial stress, temperature dependence, MG ( June ’06)  Elasto-plastic model using laser pulse model (August ’06)  Validate with comparisons to RHEPP, XAPPER, Dragonfire (Sept. ’06)  Fatigue Analysis:  Criteria to establish the transition to cracks/cusps (December ‘06)  Experimental validation (January-March ’07)  Extension to other materials??? (April ’07)

15. ATG Phase Field  Follow the total free energy of the system and account for the phase change, Kassner 2001.  Provides smoothing of sharp-interface method. Consider only the most severe location. Energy Density Length parameter

16. ATG Continued  Invariant form of free energy allows summation of elastic (f e ), gravity (f gravity ), double well—phase change (f dw ), and equilibrium control (f c ) potentials.

17. ATG Continued  H is the solid fraction function, 1 for solid and 0 for vapor as relative maxima and minima.  G accounts for the possibility for a phase transition where the two minima 0,1 correspond to the phases vapor and solid respectively

18. ATG Continued   must then solve the relaxation equation:  Which leads to: Essentially a time scale