Operating Windows in Tungsten-Coated Steel Walls

Jake Blanchard – MWG

Greg Moses, Jerry Kulcinski, Bob Peterson, Don Haynes - University of

Wisconsin

HAPLAlbuquerque – April 2003

Goal

• Determine Operating Windows of Tungsten-Coated Steel Walls in HAPL

Previous Work

• Establish operating windows for tungsten-clad steel walls using melting of tungsten and steel criteria as the limits

• This established feasibility of this concept• Now we must address other design criteria

Design Criteria

• Vaporization• Melting• Roughening• Fatigue• Surface Cracks• Crack Growth• Cracks Propagating into Steel• Blistering

Roughening• Z and RHEPP experiments show

roughening in Tungsten at 1-3 J/cm2

• Roughening in tungsten is result of pitting and cracking

• Assumption is that this is stress-driven and thus controlled by peak temperature

• Hence, model Z and RHEPP and estimate temperatures that caused roughening

• Use these temperatures as roughening criteria

Roughening Temperatures

• RHEPP results modeled by Peterson

Fluence (J/cm2)

Predicted Surface Temperature (C)

1 1400

2 2900

3 3600

Operating Windows Established from >50 BUCKY runs

40 MJ Target on Tungsten

0

510

15

20

2530

35

3 4 5 6 7 8

Radius (m)

Pres

sure

(mT

orr)

1 J/cm2 (RHEPP)2 J/cm2 (RHEPP)no meltno vaporization<0.02 microns

Working Designs by RHEPP CriteriaLow (150 MJ) Yield Target

Temperature Limit (C) Chamber Size (m) and Xe Pressure (mTorr)

3600 (3 J/cm2 on RHEPP) 5.5, 10

2900 (2 J/cm2) 6.5, 10

1400 (1 J/cm2) >7.5, 20

Fatigue Approach

• Begin with S/N type fatigue analysis (elastic plastic) to assess scope of problem

• Perform crack growth analysis to assess likelihood of cracks reaching steel

• Assess likelihood of interface crack to either cause debonding or cracks in steel

• Following results are for nominal case

Temperature Histories - first cycle

6.5 meter chamberNo gas150 MJ target

Temperature Histories – 10 cycles

6.5 meter chamberNo gas150 MJ target

Temperature History at Surface of Steel

6.5 meter chamberNo gas150 MJ target

Strain Distributions – Tungsten after last pulse

6.5 meter chamberNo gas150 MJ target

Stress Distributions – Steel after last pulse

6.5 meter chamberNo gas150 MJ target

Stress-Strain Behavior at W Surface1 Cycle

6.5 meter chamberNo gas150 MJ target

Stress-Strain History at W Surface10 cycles Superimposed

Fatigue Data for Annealed Tungsten

0.01

0.1

1

10

100

10 100 1000 10000 100000

Stra

in R

ange

(%)

Cycles to Failure

plastic = 3.4546*(Nf)-0.24

elastic = 7.895*(Nf)-0.48

total = (7.895*(Nf)-0.48) + (3.4546*(Nf)-0.24)

Annealed Pure W, 815 C

BB

B B

BBJ

J

JJ

J

J

H H H H

HH

GG

GG

E E EE

ÇÇ

ÇÇ

0.01

0.1

1

10

100

10 100 1000 10000 100000

Stra

in R

ange

(%)

Cycles to Failure

Stress-Relieved

B Total Strain at 815°C

J Elastic Strain at 815

H Plastic Strain at 815

G Total Strain at 1232°C

E Elastic Strain at 1232°C

Ç Plastic Strain at 1232°C

Total Strain CurveElastic Strain CurvePlastic Strain Curve

Fatigue Data for Stress-Relieved Tungsten

Pure W, 815 and 1232 C

Fatigue AnalysisChamber Radius

(m)Xe Pressure

(mTorr)Multiaxial Strain

Range (%)Cycles to Cracking

6.5 0 2.4 3007.5 0 1.6 10005.5 10 3.0 2006.5 10 2.0 5007.5 10 0.8 30007.5 20 0.7 4000

6.5 (40 MJ target) 0 0.13 >105

Crack Growth Through Thickness is Governed by Stress Gradients

Conclusions

• Extensive BUCKY runs for 40 MJ target reveal that for Xe pressures of 32 mTorr, minimum chamber radii are:– 3 m for <0.02 microns vaporized– 3 m for no vaporization– 4 m for no melting– 4.5 m for the 2 J/cm2 RHEPP roughening limit– 6.5 m for the 1 J/cm2 RHEPP roughening limit

Conclusions

• Fatigue analysis predicts cracking in approximately 100s to 1000s of cycles for the low yield target and reasonable chamber sizes

• There appears to be little driving force for cracks to reach steel, unless heating directly heats crack tip

• Fracture analysis for crack reaching steel surface is pending