18th High Average Power Laser Program Workshop, LANL Progress on the Unified Materials Response Code (UMARCO) Qiyang Hu 1, Jake Blanchard 2, Mike Andersen 3, and Nasr Ghoniem 1 1 : University of California, Los Angeles 2 : University of Wisconsin, Madison 3: Ratheon Corp.,/ UCLA

18th High Average Power Laser Program Workshop, LANL  A. Aoyama* : Hibachi Foil  M. Andersen* :Roughening  J. El-Awady* :Isochoric Heating  A. Hyoungil :Spallation Experiment  M. Narula :Carbon Diffusion  D. Seif* :Helium: Rate Theory/KMC  C. Erel :Structural Analysis (SiC)  K. Nagasawa:Helium: KMC — * US Citizen Manpower Development at UCLA

18th High Average Power Laser Program Workshop, LANL UMARCO Target SpectrumMaterial: SRIM Material: Mech Prop. Ion Implant. ProfileVol. Heat Rate Temperature Module Transient stress strain field Module Constitutive Law elastic, plastic Fracture Mechanics Module Inertial Stress Wave Module Diffusion Module: Ion, Helium, Bubbles, Carbon Fortran’90 Surface Roughening Module

18th High Average Power Laser Program Workshop, LANL In this meeting, we present: Crack Nucleation: Global-Local Surface Roughening Module:  Effects of Surface Plasticity;  Roughening under Pulsed Conditions Crack Growth: Fracture Module added in UMARCO:  Stress intensity factor For single crack For parallel cracks Inertial thermal stress wave in UMARCO:  Longitudinal wave stress: With time ramp

18th High Average Power Laser Program Workshop, LANL VnVn Splines Free Surface (Traction = 0) y x h(x,t) ∞∞ ∞∞  tt Local Surface Roughening Model Global model gives us the boundary bulk stress. Michael Andersen, Akiyuki Takahashi, and Nasr Ghoniem, “Saturation of Surface Roughening Instabilities by Plastic Deformation,” APL, In Press

18th High Average Power Laser Program Workshop, LANL

Stress Evolution without Inertial Effects Steady State Tangential Stress is 700 MPa Too fast to have an effect

18th High Average Power Laser Program Workshop, LANL Initial Surface & Plasticity Effects High Stress Loading ~ 700 MPa leads to surface crack nucleation in a few cycles Benefit from polishing surface.Effects of Surface Plasticity

18th High Average Power Laser Program Workshop, LANL What Causes a Surface to Roughen? Essentially the same solution with different numerical components. Brittle fracture.

18th High Average Power Laser Program Workshop, LANL Fracture module (1): Standard..K~  a^ 1/2 stress intensity factor for single crack Input: stress calculation  From stress module Model:  Superimpose a stress field to make crack surface stress free  End result: a x y

18th High Average Power Laser Program Workshop, LANL Results stress intensity factor for single crack

18th High Average Power Laser Program Workshop, LANL Maximum K I and crack length: K IC  7 MPa·m 1/2 for recrystalz. W (A.V. Babak, 1981)  1.2 msec

18th High Average Power Laser Program Workshop, LANL M. Faleschini *, H. Kreuzer, D. Kiener, R. Pippan, Journal of Nuclear Materials 367–370 (2007) 800–805

18th High Average Power Laser Program Workshop, LANL Fracture module (2): stress intensity factor for parallel cracks Input:  Stress field  Green’s function table From literature Model b x y h

18th High Average Power Laser Program Workshop, LANL Result: stress intensity factor for parallel cracks

18th High Average Power Laser Program Workshop, LANL Inertial thermal stress wave with time ramp: Analytical model (Cozen & Blanchard) Volumetric heating rate: Longitudinal Stresses:

18th High Average Power Laser Program Workshop, LANL Inertial thermal stress wave with time ramp: UMARO ’ s approximation Volumetric heating rate: x0x0 Q0Q0 Blue: calculated Q’’’ Red: curve fitted Q’’’ Let: Area under red (0~x 0 ) = 0.95  total area under blue Thus:

18th High Average Power Laser Program Workshop, LANL Inertial thermal stress wave with time ramp Results  ramp stopped at  In the surface layerThrough the whole wall

18th High Average Power Laser Program Workshop, LANL Inertial thermal stress wave with time step: Results Unrealistic Magnitude 1)Computational? 2)Model?

18th High Average Power Laser Program Workshop, LANL Future Plans: Documentation:  APL paper on roughening, in press  TOFE … 8 abstracts submitted  JNM Paper on Roughening under pulsed conditions, submitted  Comprehensive paper on UMARCO, in progress Model development:  Refine: Inertial stress wave model  Stress gradient effects on bubble diffusion Program integrity Enhancement :  Complete conversion from Fortran to C++  GUI for user-friendly applications.

18th High Average Power Laser Program Workshop, LANL

So, What Does This Mean? Maybe the solution lies with an engineered surface? Solid surface is just too stiff for the high stresses. New critical crack depth increased to over 30 microns for a porosity of 20%!

18th High Average Power Laser Program Workshop, LANL Summary Fracture Module:  Seamlessly combining heat and ion part  Intensity factor calculation Single > parallel Inertial effect of longitudinal stress wave:  More reasonable case: Time: Ramp;Depth: Step

18th High Average Power Laser Program Workshop, LANL UMACRO HAPL ConditionMaterial: SRIM Material: Mech Prop. Ion Implant. ProfileVol. Heat Rate Temperature Module Transient stress strain field Module Constitutive Law elastic, plastic Fracture Module refine Inertial Wave Stress: refine Diffusion Module: Ion, Helium, Bubbles, Carbon C++ GUI

18th High Average Power Laser Program Workshop, LANL Global-Local Modeling Plane Stress, Plane Strain. (Hu, Blanchard) SRIM code used for implantation profiling  tt

18th High Average Power Laser Program Workshop, LANL Roughening Model Continued  The surface material transport is determined by the Nernst-Einstein relation of the diffusion flux proportional to the surface gradient of the chemical potential given as  where D s is the surface diffusivity, k is the Boltzmann’s constant, T is the absolute temperature and the derivative with respect to the arc length, s, is evaluated along the surface. The normal velocity of the surface V n, is then proportional to the divergence of J:  where s is the number of atoms per unit area of the material in the plane normal to the flux direction. This can be extended to the surface profile h(x,t) as Notice the 4 derivatives over the surface, this is where the instability gets its name! Ultimately, the competition is between the strain energy and surface curvature.

18th High Average Power Laser Program Workshop, LANL Linear Perturbation Theory Plane Stress  c =1.88 for =.33

18th High Average Power Laser Program Workshop, LANL Surface Evolution Surface flattens for low stresses Adjacent bumps form for higher stress  c =1.88 for =.33

18th High Average Power Laser Program Workshop, LANL Crack Growth Results  = 2.0  2.5  3.0 Tangential Stresses

18th High Average Power Laser Program Workshop, LANL Plasticity Effects from Dislocation Emission  = 2.5  = 2.75  = 3.0  = 3.0 (No Disl.)

18th High Average Power Laser Program Workshop, LANL Plasticity Effects Continued Chemical potential now contains plastic strain. Dislocations move based on the Peach-Koehler Force. Temperature dependent material properties

18th High Average Power Laser Program Workshop, LANL Inertial thermal stress wave with time ramp Results  ramp not stopped at  Through the whole wallIn the surface layer

18th High Average Power Laser Program Workshop, LANL Tungsten-coated Carbon Velvet survives 1600 pulses amazingly well 520C (nominal), 1600 pulses, 1.5 J/cm 2 /pulse NOTE: W remaining on tips (see below) and sides (ABOVE) 2.8 J/cm 2, 1600 pulses NOTE: bent tips, flat ends have W removed, rounded ends still have W Carbon PAN fibers w/ 1.6 µm W coating, 2% areal coverage

18th High Average Power Laser Program Workshop, LANL 4 μm Carbon Velvet as HAPL’s First Wall Armor Unirradiated CCV 20 μm

18th High Average Power Laser Program Workshop, LANL Back-up Slides Thermal stress wave with time step

18th High Average Power Laser Program Workshop, LANL Inertial thermal stress wave with time step: Analytical model (Cozen & Blanchard) Volumetric heating rate: Longitudinal Stresses: