E  MCH  315    Mechanical  Response  of  Engineering  Materials  

Lecture  28  Creep  II Chap.  10  

FALL  2013:    EMCH  315     Lecture  28:  Slide  1  

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Table of melting or softening temperatures.

(Light bulb)

Creep occurs at > ½ Tm

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ε

I II III

t

2. Creep Rupture

I

II

III

At constant T

ε0

εss = (σ/σ0)m e-ΔH/kT Dorn-Miller steady state creep

rate equation.

Some  design  situaBons  will  be  constrained  by  complete  failure  due  to  creep.    This  is  called  “creep  rupture”  (failure).  

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Taken from www3.toshiba.co.jp/ddc/eng/materials/e_tan_3.htm

Grain boundary

Voids, holes Inter-grainular failure

Strain-induced micro-voids grow, coalesce, and form macro-scale cracks.

Fish mouth failure, very spectacular rupture, very damaging failure.

Figures 4 & 5 are from Understanding How Components Fall, Second Edition. Written by, Donald J. Wulpi. 1999. Pgs.231 & 232.

Super heater tube of stainless steel (ASME SA-213)

1 µm

LIFETIME-­‐LIMITED  DESIGN    LifeBme  of  the  component  prior  to  failure  is  criBcal  (creep  strains  can  be  tolerated):  requires  predicBve  equaBons  for  creep  rupture.      

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•  We  want  to  determine  ε  =  f  (material  properBes,  σ,  T,  t).  •  Rupture  phenomenon  is________________________  

process.  •  Challenge  is  to  predict  service  life  using  experimental  

data.  –  Service  life  –  up  to  _____________  –  Experimental  creep  data  only  ___________________  

•  Use  data  from  relaBvely  short  Bme  tests,  but  at  temperatures  above  the  service  temperature  of  interest.    Then  ___________________  the  behavior  for  the  longer  Bmes  at  the  service  temperature.  

thermally activated rate

Creep  Life  PredicBon:    Temperature-­‐compensated  Bme    •  For  accelerated  tesBng,  a  higher  

temperature  is  used  at  the  same  stress  so  as  to  cause  a  shorter  Bme  to  failure  such  that  temperature  is  traded  for  Bme.  

•  Based  on  the  fact  that  there  is  an  Arrhenius  relaBon  between  creep  rate  and  temperature  has  led  to  a  number  of  Bme  temperature  parameters  to  be  developed  which  enable  extrapolaBon  and  predicBon  of  creep  rates  or  creep  rupture  Bmes  to  longer  Bmes  than  have  been  measured.  

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General Example of Arrhenius Relationships and Plots

•  It  is  assumed  that  the  failure  mechanism  does  not  change  and  hence  is  not  a  funcBon  of  temperature  or  Bme.  

new coefficient ___ is a mat’l parameter

The  governing  Arrhenius  relaBonship  for  Bme-­‐to-­‐rupture,  tr  

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tr-1 = _________

Define ΔHr for creep rupture process In general, ΔHr ≠ ΔHss (“ss” = steady-state)

NOTE: infinite T is physically meaningless and so is tr = to

Decomposing the Arrhenius relationship logarithmically

and thus log tr

−1( ) = log to−1e

−ΔHrkT⎡

⎣⎢

⎤

⎦⎥⇒ (0.434) ΔHr

kT= − log10 t0 + log10 tr

log10 (tr−1) = log10 (1)− log10 (tr )

log10 (to−1)x e

−ΔHrkT

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥ = log10 (1 / to )[ ]+ log10 e

−ΔHrkT

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

= log10 (1)− log10 (to )[ ]+ − ΔHr

kTlog10 e

⎡⎣⎢

⎤⎦⎥

Time-­‐to-­‐rupture  depends  on  stress  and  temperature.  

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⬆σ ⬆T

Stage III – creep strain accumulate until strain-induced micro-voids grow and coalesce to form micro-cracks. Hence, there isn’t enough material to bear load and rupture (failure) ensues.

Creep rupture data plotted in log10tr vs 1/T Rearrange for plotting as

Experimental  observaBons  reveal  two  rupture  responses  for  differing  materials  .  

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(0.434) ΔHr

kT= − log10 to + log10 tr

Employ parametric approaches A single parameter is used to relate variables instead of a general predictive equation relating stress, temperature, and time-to-rupture

experimental temperatures __________ than actual service temperatures to __________ rupture to within 102 to 104 hours

Experimental  observaBons  reveal  two  rupture  responses  for  differing  materials.  

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Case 1 – _____________________ : ___________________ creep rupture prediction via ___________________

parametric approach [______________________________________]

Case 2 - ________________________ : ________________ creep rupture prediction via ___________________

parametric approach

ΔHr depends on stress

most commonly used in engineering practice

ΔHr independent of σ

_____________________

__________________

____

Case I. Collections of data log10tr vs. 1/T for different σ’s

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________________ t0

1/T

σ3> σ2 > σ1

log10 t0

log 1

0 tr

σ1 σ2 σ3

= 0.434 ΔHr/k

(°Abs)

____________________

Δ(1/T)

Δ(1/T): range of T, within which creep rupture occurs in moderate amounts of testing time

Larson-­‐Miller  Approach  

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“C” is material dependent.

log10 tr = log10 t0 + (0.434)ΔHr(σ )

k1T

P = T (o Abs) C + log10 tr[ ]Defines Larson-Miller constant, C:

based on rate theory, to on the order of ______

experimental variations suggest ________________ 10-15 to 10-30

commonly ranges from 15 to 30

Defines Larson-Miller parameter, P:

Master  Life  Curve  

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P = T(° Abs)[C + log10 tr]

Results of many experiments of the type used to generate the failure lines lo

g 10 σ

Actual shape of curve depends on the material

Because the underlying stress relationship is unknown,

the Larson Miller parametric correlation is used to relate the variable for any given material.

P ≡ (0.434) ΔHr(σ )k

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1/T

Case  2:  same  slope  and  different  y  intercept    

log10t0 (varies with stress)

log 1

0tr

Master life curves for case 2: log10σ vs Dorn parameter Most researchers have found that t0 is stress independent, as shown in Case 1. So case I is closer to reality.

σ1 σ2

Same slope

(°Abs) to has a σ dependence

ΔHr does not vary with stress.

different intercept

log10 tr = log10 t0 + (0.434)ΔHr(σ )

k1T

log10 to = log10 tr − (0.434)ΔHr(σ )

k1T

rearrange previous equation to reflect stress dependence of to

Take antilog of new eqn

to = tre−ΔHr (σ )

kT = ′PDorn parameter

15

#5. A plot between log10 σ vs T(°Abs)(C + log10 tr) #6. Use the master life curve plotted in #5 and determine:

(a)  maximum operating stress for at least 300,000 hours at 1325 °F

(b)  If the data for the point on the master life curve used in the first part (part a), were to be obtained from a 1,000 hr creep rupture test, what would be the best temperature.

FALL  2013:    EMCH  315    

Hints for Home Work 6 (Chapter 10)