Asian Pacific Conference for Materials and Mechanics 2009 at Yokohama, Japan, November 13-16

CREEP-FATIGUE INTERACTION: ITS MECHANISM AND

PREDICTABILITY

Yukio Takahashi

Central Research Institute of Electric Power Industry

yukio@criepi.denken.or.jp

1. Background

Failure due to repeated load variations called as fatigue failure is a quite common phenomenon

which should be taken into account in the design of various machineries and plant components.

Range of the stress variation is a principal parameter governing its significance regardless of

time spent during the cycle. However, time-dependencies appear under some circumstances.

They include the phenomena dependent on environment as well as those independent of it. In

the former situation, crack initiation and/or propagation are accelerated as a result of certain

chemical interaction between materials and the surrounding fluids whereas the internal damage is

a main driving force for accelerating the failure process in the latter. The potential of the latter

phenomena is strongly dependent on temperature, being associated with diffusion of atoms, and

customarily called creep-fatigue interaction. As this is an important failure mode to be

considered in the design of high-temperature reactor plants, many efforts have been taken

worldwide to clarify the underlying mechanism and develop sound evaluation methods. This

paper summarizes the author’s view on the mechanism and the predictability of failure life based

on the recent investigations [1][2].

2. Mechanism of creep-fatigue interaction and its modeling

It is well known that the number of cycles to failure decreases by putting the hold time into the

cycle and/or decresing the strain rate, both increasing the chance of atom diffusion. Change of

crack morphology from trans-granular to inter-granular one often accimanies. This implies that

the main mechanism of creep-fatigue interaction is the acceleration of crack growth by the

accumulated creep damage especially at grain boundaries or other discontinuous locations. This

microstructural effect appears as the reduction of ductility at a macroscopic level and may be

expressed by a quantity defined as [1]

Asian Pacific Conference for Materials and Mechanics 2009 at Yokohama, Japan, November 13-16

0

0cD

(1)

where 0 is the ductility at a sufficiently high strain rate considered as free from creep damage

thus permitting the use of the ductility obtained in the conventional tensile tests whreas

represents the ductility the material has at the time of evaluation.

This definition along with a law representing the effect of acceleration of fatigue damage

quantitively expresses interaction between creep damage, cD and fatigue damage,

fD .

Assumption of a simple relation

0

( )1

f in

f

c

dDf D

dN D

(2)

motivated by the well-known Manson-Coffin’s law [3] using the inelastic strain range, in

provides the following equations representing the combination of accumulated damages at

failure for the regular creep-fatigue condition [1]:

1

111 1

1 ( 1) /c

c f

D forD D

(3a)

1 exp 1c

c

f

DD for

D

(3b)

Failure loci predicted by these equations are drawn in Figure 1 for several values of . Linear

damage summation rule ( 1c fD D ) holds for =2 and deviation from it is not significant for

the practical range of . This justifies to make failure assessment by a comparison of linear

summation of both damages with unity.

The following equation consistent with

eq.(1) has been also derived with the

assumption that the inelastic strain is a

principal parameter governing the creep

damage [1]:

0

1 1

( )

c in

in

dD d

dt dt

, (4)

This expression is similar to the

conventional ductility exhaustion method,

as recommended in R5 procedure [3], but

it includes the second term in the

paranthesis, which brings about smaller

creep damage/

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

=1=1.5=2=2.5=5

Accumulated fatigue damage、Nfdf

Accu

mulate

d cree

p da

mage

、N fd c

Figure 1 Failure loci derived from eq. (1)

Asian Pacific Conference for Materials and Mechanics 2009 at Yokohama, Japan, November 13-16

3. Results of life prediction

The “modified ductility exhaustion (MDE) method” outlined above was applied to calculate

accumulated creep damage at failure in creep-fatigue tests performed on three kinds of high

chromium ferritic steels used in recent fossil plants. Fatigue damage is simply calculated as a

ratio of the number of cycles to failure in the creep-fatigue test to that in pure fatigue test

conducted at the same strain range. The accumulated creep damages calculated by eq.(4) are

plotted with the accumulated fatigue damage in Figure 2. It can be seen that the sum of both

damages is around the unity with all points within a factor of 2, supporting the linear damage

summation hypothesis.

For comparison, a similar plot obtained by the traditional time fraction approach which uses

stress value as a principal parameter governing creep stress is displayed in Figure 3. Most of the

data lies below the linear damage summation relation in this case. Points for the tests at 550°C

lie around the failure envelope recommended in the ASME code [4] while the points move

upward and approach the envelope given in the RCC-MR [5] (equivalent to envelope for type

304/316 stainless steel in ASME code) as the temperature becomes higher. As analyzed in [1],

significant increase in the inelastic deformation by cyclically re-generated transient behavior is

caused by the change of internal or back stress by an excursion to reversed yielding. This

behavior can be taken into account by using strain-based approach instead of stress-based

approach and this would be a main reason for the large difference between the two methods.

Figure 2 Damages predicted by MDE method

650℃600℃550℃

Grade 91Grade 122

TMK1

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1 1.2

Accumulated Creep Damage

, D

c

Accumulated Fatigue Damage, Df

Df+D

c=1

Df+D

c=0.5

Df+D

c=2

650℃600℃550℃

Grade 91Grade 122

TMK1

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

Accumulated Creep Damage

Accumulated Fatigue Damage

RCC-MR

ASME

Df+D

c=1

Figure 3 Damage predicted by Time fraction approach

Asian Pacific Conference for Materials and Mechanics 2009 at Yokohama, Japan, November 13-16

In order to summarize life predictability,

the ratios of predicted life to experimental

life were calculated and plotted against the

actual time to failure in Figure 4. The time

fraction approach with the ASME criterion

gave too conservative life predictions for

short-term tests but reasonable accuracy was

obtained for the tests taking longer than

several thousand hours. On the contrary,

the RCC-MR criterion gave good

predictions for short-term tests but became

very unconservative as the time to failure

increased. Therefore, from the viewpoint of

application, the ASME criterion would be

favorable but the applicability to the conditions leading to longer failure time is difficult to judge.

The modified ductility exhaustion approach gave a stable accuracy throughout a range of the

present tests, without a noticeable dependency on the failure time and seems much more relisble.

.

4. Conclusion

Based on the idea that the main mechanism of creep-fatigue interaction is the acceleration of

fatigue damage due to reduction of ductility caused by creep damage, a simple format for creep

damage evaluation has been derived as well as justification of linear summation of both damages.

Its application to many creep-fatigue tests on high chromium steels has demonstrated its clear

superiority against more empirical approaches such as time fraction summation.

5. References

1. Takahashi, Y., Int. J. Pressure Vessels. Piping, Vol. 85, 406–422, 2008.

2. Takahashi, Y., Dogan, B. and Gandy, D., Proceedings of PVP2009, PVP2009-77990, American Society of Mechanical Engineers, 2009.

3. British Energy, Assessment procedure for the high temperature response of structures, R5 Issue 3; 2003.

4. American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section III, subsection-NH, 2005.

5. afcen, Design and construction rules for mechanical components of FBR nuclear islands, RCC-MR, 2002.

0.01

0.1

1

10

100

100 1000 10000 100000

Time fraction with RCC-MR interactionTime fraction with ASME interactionModified ductility exhaustion

Predicted life / Experimental Life

Time to failure (h)

factor of 2

Figure 4 Comparison of life predictability