PSI - Issue 2_B

B. Fedelich et al. / Procedia Structural Integrity 2 (2016) 2190–2197 Author name / Structural Integrity Procedia 00 (2016) 000–000

2195

6



 2 E    HCF eff cyc

aY

2

,

(5)

HCF CTOD d 



'

n

where HCF eff  denotes the effective stress range, that is the range of the stress in excess of the opening stress op  . The cyclic yield stress is denoted by cyc  , ' n d is a function of the cyclic hardening exponent ' n (see Shih, 1981), Y is a geometric factor and E the Young's modulus. It is assumed that the HCF loading becomes only effective when HCF CTOD  overruns the threshold th CTOD  . The critical crack depth can be expressed as function of this threshold as

cyc E CTOD

 Y    

1

th

.

(6)

a



th

d

 2

HCF

'

n

eff

HCF CTOD  can also

Since the temperature and the effective stress range can change during the cycle, the value

HCF CTOD  during a TMF+HCF block is regarded as

change during a TMF block. The maximal value attained by being critical for the impact of the HCF vibrations. Thus we consider



 2

E 

HCF eff

(7)

Sup

Sup

,

HCF CTOD aY   

d

a  

2

HCF

'

n

eff



HCF Cycles

HCF Cycles

cyc

where



 2

E 

HCF eff

.

(8)

Sup

2 Y d

HCF eff  



'

n



HCF Cycles

cyc

From equ. (4) to (8) finally result the following estimate for the lifetime reduction

TMF HCF TMF N N  factor:

, CTOD N a th



TMF HCF 

If

1,

HCF eff  



N

TMF

f

  

  

0 CTOD a  HCF eff



Log

th

CTOD

CTOD N





TMF HCF 

(9)

If

,

,

th

th

HCF eff   



0       f a a

a

a

N

TMF

0

f

Log

, CTOD N a th



TMF HCF 

If

0.

HCF eff  



N

TMF

0

In the present work, various solutions for the crack opening stress op  have been tested. It was found that taking the whole stress range i.e. HCF HCF eff    yielded the best results in terms of the correlation   , HCF TMF HCF TMF eff N N   . In other words, we set



 2

E 

HCF

.

(10)

Sup

,

2 Y d

HCF     HCF



max HCF      HCF

min HCF

'

eff

n



HCF Cycles

cyc