530.352 Materials Selection

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530.352 Materials Selection
Lecture 26 High Temperature Creep - II
TuesdayNovember 15th, 2005
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Sherby-Dorn Equation
.
?ss C ??n exp (- Qdiffusion / RT)
Temperature dependence
Stress dependence
Constants
Use this equation to calculate creep rate at any
given or new stress or temperature !!
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Example of creep based design

• Ni-base superalloys that are used for jet turbine
  applications exhibit Qcreep 320 kJ/mol and
  n5.
• What is the creep rate at 925 oC and 350 MPa if
  C1.7x10-7 and R8.314 J/mol-oC ?
• What would the creep rate be if the stress were
  increased by 25 MPa ?
• What would the creep rate be if the temperature
  were increased by 25 oC ?
• If your boss wanted to increase the operating
  temperature by 50 oC, how much would you have to
  decrease the stress to maintain the same creep
  rate ?

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Creep rate T925 oC and s350 MPa
.
?ss C ??n exp (- Q / RT)
.
?ss 1.7x10-7 3505 exp( -320,000/8.314 x
1198 K ) 1.7x10-7 x 5.25x1012 x
11.1x10-15 10-8 sec-1
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Is 10-8 sec-1 fast ?
Is short for a service life but long for a
graduate student -- must extrapolate from short
tests to long times !!
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Increasing by 25 MPa
.
.
?1 / ?2 (?1/ ?2 )n (350/375)5 0.708 ?2
1.4 x 10-8 sec
.
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Increasing by 25 oC
?2 1.92 x 10-8 sec
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Changing both T and s
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Creep Mechanisms (metals and ceramics)

• Diffusion creep
• Dislocation creep (power-law creep)
• Stress Relaxation
• Creep Fracture

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Diffusion creep
?
grain boundary diffusion ????d??
?
bulk crystal diffusion ????d??
?
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Dislocation creep
Diffusion assisted climb important
1. Annihilation
poof !
2. By passing obstacles
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Dislocation Climb
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Stress Relaxation
.
.
?total ?el ?pl 0 so ?el - ?pl ?el ?
/ E and ?pl ?c A ?n (_at_ cont. T) ??-n d?
- A E dt ?1-n ? - A E t 0
.
.
.
.
t
s
o
?p
?
?
?el
time
time
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Tertiary creep
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Design against creep (metals)

• Minimize T / Tmelting to slow diffusion, climb,
  and creep.
• Arrange for large grain sizes to slowdiffusion.
• Use precipitates (oxide particles) and solid
  solutions to slow dislocations.

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Creep in ceramics

• Very little dislocation motion - mostly diffusion
  creep or something else.
• Glassy phases (oxides) that form at grain
  boundaries soften and high T and lead to grain
  boundary sliding.

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Design against creep (ceramics)

• Similar to metals, reduce diffusion and
  dislocation motion, but must also ...
• Reduce/control grain boundary phases.

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Creep Mechanisms (polymers)

• Tg replaces Tm at the critical T and Tg is often
  close to RT !!!
• Viscous flow is like creep ? C ?1 exp (-Qv /
  RT)
• Qviscous not QDiffusion, Qvicsous is Q slide
  lumpy molecules past one another
• n 1 for Newtonian viscous flow

.
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Design Against Creep (polymers)

• Increased degree of cross-linking -gtincreased Tg
  and less creep.
• High molecular weight -gt high viscosity-gt low
  creep rate.
• Crystalline polymers better than glassy.
• Add fibers or particles to make composites !!