u nified m a terials r esponse c o de (umarco) update & thermal response of dendrites

UUnified MAMAterials RResponse CCOde (UMARCO) update& Thermal Response of DendritesQiyang Hu (UCLA)

Aaron Oyama (UCLA)Shahram Sharafat (UCLA)Jake Blanchard (Wisc) Nasr Ghoniem (UCLA)

19th HAPL MeetingUniversity of Wisconsin, Madison

Oct. 22-23, 2008

2

Unified Simulation Unified Model would

Avoid inconsistencies Simplify modeling of wide variety of situations

New tool will model: Heating profile (x-rays and ions) Transient temperatures, stresses, strains Fracture mechanics Ion deposition profile, diffusion, and clustering

UMACROHAPL pellet

spectrum Material: SRIM Material: Mech Prop.

Ion Implant. Profile Vol. Heating Rate

Temperature CoupledCoupled

Transient stress strain field Module

Constitutive Lawelastic, plastic

Fracture Module ImprovedImproved

Stress Waves CoupledCoupled

Diffusion Module:Ion, Helium,

Bubbles, Carbon

Fortran’90 C++

1

2

4

Modeling of Surface Cracking

0

2

4

6

8

10

12

0 25 50 75 100 125 150

ChamberIon Beam

Sre

ss In

tens

ity (M

Pa-

m1/

2 )

Crack depth (m)

•Stress intensity factor decreases as cracks grow further from surface

•Crack growth will arrest

•Crack arrest will be more shallow for short pulse experiments (like RHEPP)

UW

Crack Arrays What if we have

an array of cracks?

This will tend to relieve the stresses

TOFE 20085

h

Results for Crack Arrays

1E-4 1E-3 0.01

0

1000

2000

3000

4000

5000

6000

7000

h/b=8 (new)h/b=12 (new)

h/b=108 (nied)

h/b=2 (nied)

h/b=4 (nied)

h/b=2 (new)

h/b=4 (new)

h/b=20 (new)Single Crack

K

I (MP

a x m

1/2 )

Time (sec)

by Different G(s)

KIC 7 MPa·m1/2

for recrystal W(A.V. Babak, 1981)

Reproducing HEROS User defined f(t,y)

f(t,y) = react + diff + drift reaction + drift term:

13(18) variables: Alhajji-Sharafat-Ghoniem 13+2 (temperature & carbon)

Test Results: Single shot case:

UNC, UWM, ITER: OK! Diffusion behavior is more obvious.

Multiple shot case: 2 shots of “const temperature” HAPL case: OK!

Non-const temperature: Linear from 400 C to 2000 C: OK!

Solving thermal stress wave problem Thermal wave stress governing equations:

System specifications:

Stress-free& adiabatic

10 m 3mm

20 ~ 200 Grids Stress-free& temperature const.

Q’’’

Numerical considerations 3 ODE equations:

A proper cvode option tested by bubble diffusion: Solver: Krylov solver SPGMR Precondition: CVBANDPRE module Activate stability limit detection

Spatial finite-difference scheme:

Heating Rate (Q’’’) in HAPL

Depth (m)Vo

lHea

tRat

eQ

'''(J

/m3 /s

ec)

2 4 6 8 10 120

2E+15

4E+15

6E+15

8E+15

1E+16

Time = 0.8224E-06 sec

• Ion implantation: ~0.1sec per step

The most severe case:

Quasi-static Decomposition Stress wave propagation time:

Thermal diffusion time scale:

Decomposition

Fast (high frequency) Slow (quasi-static)

Low Frequency Thermo-elastic Wave

High-Frequency Thermo-elastic Waves forSelected Heating Step (duration 0.11sec)

Stress Magnitudes from Elastic Waves

Time (sec)

Stre

ssM

agni

tude

(GPa

)

0 3E-08 6E-08 9E-08 1.2E-07 1.5E-070

0.05

0.1

0.15

0.2

0.25

Max StressStd Stress

Roughening or Dendrite

Roughening aims at minimizing energies (surface strain & stress) Ultimately results in NANO- or MICRO-CASTELLATION

Why not start with a micro-castellated surface, similar to the UW-Madison Coral structure

Or simply start with Dendrites: No surface stress or strains on dendrite surface

Tungsten Dendrite Structures

Dendrite Thermal Response to HAPL ThreatHAPL Threat for 10.5 m radius chamber:

Source Arrival Time (ns)

Pulse Width (ns)

Avg Heating Rate (W/m3)

Photons 0 0.5 4.27E+18Neutrons (tungsten) 280 35 4.23E+14Burn ions 200 800 9.04E+15Debris ions 800 3263 1.52E+16

Tip Radius: 1.5 m

Dendrite Thermal Response to HAPL Threat

95.71 m

D

D=0

D=95.71

Max Tip Temperature = 3836 °Cat 4063 ns (end of shot)

Max Base Temperature = 1308 °C at 120 μs after shot

Effect of Tip Radius on Temperature Transient Profile

95.71 m

r=1 m

r=3 m

r=5 m

Summary & Conclusions UMARCO (C++) framework completed Fatigue of Interface Between W/Fe is a Concern. Tungsten dendrite structure can be fabricated

with various aspect ratios and tip radii A tip radius of 5 mm will prevent tip melting Mechanical modeling to be done, however

stress and strains should remain fairly low because of dendrite geometry

Sputtering modeling including re-deposition shows minimal overall loss of material (see Tim Knowles’s poster).

Extra Slides

Surface temperature comparison

UMARCO

Sputtering & Redeposition For Dense Needle Configuration Carbon velvet carpets have been used in

space applications for ion thruster wall, with encouraging sputtering results after years of operation

Sputtering plus Redeposition modeling shows little loss of geometry (see next viewgraph).

From Tim Knowles Poster

Using CVODESUite of Nonlinear and DIfferential/Algebraic equation Solvers

by Alan C. Hindmarsh and Radu Serban

Direct:

Krylov:

Scaled Preconditioned

Generalized Minimal Residual method

26

Crack Depth Measurements in RHEPP