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
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