18th High Average Power Laser Program Workshop, LANL Progress on the Unified Materials Response Code...

18th High Average Power Laser Program Workshop, LANL18th High Average Power Laser Program Workshop, LANL

Progress on the Unified Materials Response Code (UMARCO)

Qiyang Hu1, Jake Blanchard2, Mike Andersen3, and Nasr Ghoniem1

1: University of California, Los Angeles2: University of Wisconsin, Madison

3: Ratheon Corp.,/ UCLA


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


UMARCO

Target Spectrum Material: SRIM Material: Mech Prop.

Ion Implant. Profile Vol. Heat Rate

Temperature Module

Transient stress strain field Module

Constitutive Lawelastic, plastic

Fracture Mechanics

Module

Inertial Stress Wave Module

Diffusion Module:Ion, Helium,

Bubbles, Carbon

Fortran’90

Surface Roughening

Module


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


Vn

Splines Free Surface (Traction = 0)

y

x h(x,t)

∞∞

tt

Local Surface Roughening Model

*

2

2

21

121

tts

b

ijij

E

E

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


Stress Evolution without Inertial Effects

Steady State Tangential Stress is 700 MPa

Too fast to have an effect

1

32

7

8

56

4


Initial Surface & Plasticity EffectsHigh Stress Loading ~ 700 MPa leads to surface crack nucleation in a few cycles

Benefit from polishing surface. Effects of Surface Plasticity


What Causes a Surface to Roughen?

Essentially the same solution with different numerical components.

Brittle fracture.

2

2

4

)2()(2

xx

xx

E

ccE

G

2

22

42

2

12

),(

Ea

aU

aE

aU


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:

0

2

2 ( , ) ( )

1( , ) 1 0.6147 1 0.2502 1

a

I yyK M a x x dx

x xM a xa aa x

a

x

y


Resultsstress intensity factor for single crack


1E-4 1E-3 0.01 0.10

1000

2000

3000

4000

5000

6000

7000

8000

K I (MPa

x m

1/2 )

Time (sec)

0

4

8

12

16

20

24

28

Crack Length (m) w

ith Max K

I

Maximum KI and crack length:

KIC 7 MPa·m1/2

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

1.2 msec


M. Faleschini *, H. Kreuzer, D. Kiener, R. Pippan, Journal of Nuclear Materials 367–370 (2007) 800–805


Fracture module (2): stress intensity factor for parallel cracks Input:

Stress field Green’s function table

From literature

Model

1

0d

1I yy

G sK b s s

s

b

x

yh

0.0 0.2 0.4 0.6 0.8 1.0-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Calculated by H.F. Nied in 1987

h/b = 0.5

h/b = 1h/b = 2

h/b = 4

h/b = 8

h/b = infinity

Gre

en's

Fun

ctio

ns G

(s)

s=x/b


Result: stress intensity factor for parallel cracks

1E-4 1E-3 0.010

1000

2000

3000

4000

5000

6000

7000Single Crack

h/b = 0.5h/b = 1h/b = 2

h/b = 4

h/b = 8h/b = 108

K

I (MP

a x m

1/2 )

Time (sec)


Inertial thermal stress wave with time ramp: Analytical model (Cozen & Blanchard) Volumetric heating rate:

Longitudinal Stresses:


Inertial thermal stress wave with time ramp: UMARO’s approximation Volumetric heating rate:

x0

Q0Blue: calculated Q’’’Red: curve fitted Q’’’

Let: Area under red (0~x0) = 0.95 total area under blue

Thus: 0

0

ln 1 0.95

UMARCO

x

Q Q


Inertial thermal stress wave with time ramp Results ramp stopped at In the surface layerThrough the whole wall


Inertial thermal stress wave with time step: Results

Unrealistic Magnitude1) Computational?2) Model?


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.


So, What Does This Mean? Maybe the solution lies

with an engineered surface?

Solid surface is just too stiff for the high stresses.

)(

)(

31.1)(

2*

00

00

2

EE

mEa

New critical crack depth increased to over 30 microns for a porosity of 20%!


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


UMACRO

HAPL Condition Material: SRIM Material: Mech Prop.

Ion Implant. Profile Vol. Heat Rate

Temperature Module

Transient stress strain field Module

Constitutive Lawelastic, plastic

FractureModule

Inertial Wave Stress: refinerefine

Diffusion Module:Ion, Helium,

Bubbles, Carbon

C++ GUIC++ GUI


Global-Local Modeling

)1ln( DECE

EB

AdxdE

Plane Stress, Plane Strain.(Hu, Blanchard) SRIM code used for

implantation profiling

tt


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 Ds 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 Vn, 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

skTD

J s

2

2

skTD

V ssn

kTDD

xh

xD

th

ss

x

2

21

21

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.


Linear Perturbation Theory

2

432

0

0

1

1)2(

)(

)2cos(

EE

H

kkHD

eAtA

xAh

t

Plane Stress

c =1.88 for =.33

kTDD

DE

s2

421

,


Surface EvolutionSurface flattens for

low stressesAdjacent bumps form for

higher stress

c =1.88 for =.33


Crack Growth Results

= 2.0 2.5 3.0

Tangential Stresses


Plasticity Effects from Dislocation Emission

= 2.5 = 2.75 = 3.0

= 3.0 (No Disl.)


Plasticity Effects Continued

Chemical potential now contains plastic strain.

Dislocations move based on the Peach-Koehler Force. m

kjlijki

ipi

N

i

pip

pe

vv

btFAbl

D

)(

)(*

00

Temperature dependent material properties


Inertial thermal stress wave with time ramp Results ramp not stopped at Through the whole wall In the surface layer


Tungsten-coated Carbon Velvet survives 1600 pulses amazingly well

520C (nominal), 1600 pulses, 1.5 J/cm2/pulse

NOTE: W remaining on tips (see below)

and sides

(ABOVE)2.8 J/cm2, 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


4 μm

4 μm

Carbon Velvet as HAPL’s First Wall Armor

Unirradiated CCV

20 μm


Back-up Slides

Thermal stress wave with time step


Inertial thermal stress wave with time step: Analytical model (Cozen & Blanchard) Volumetric heating rate:

LongitudinalStresses:

00

00

00 0

00 0

12 2

1 2

2 0, ,

, ,

,

xxp

Q ct x xxct ct x H t ct x x Hc c c c

x x x xct x x H t ct x H t ct x H x tc c c

ct x xxct x H x t ct x x H x xc c

ct x xct x x H x x

c

02ctH x x

18th High Average Power Laser Program Workshop, LANL Progress on the Unified Materials Response Code...

Documents

Transcript of 18th High Average Power Laser Program Workshop, LANL Progress on the Unified Materials Response Code...