PSI - Issue 13

Takehiro Shimada et al. / Procedia Structural Integrity 13 (2018) 1873–1878 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

1875

3

n

n

s

y

2 3 2 1 A 



1 3 2 1 A 



2

1

s

y

eq

eq

cr

vp

ε

ε

= 

= 

,

(3)

vp   +  c 

vp   +  

s

y

eq

eq

Effective stress can be expressed as the difference of deviatoric stress and deviatoric back stress (see equation (4)). Back stress is assumed to be decomposed in M parts (Chaboche, 2008) and affected by cyclic hardening as much as drag stress (Ohno et al. 1998). In addition, each part of back stress components is represented by Ohno Wang model (Ohno and Wang, 1993) as described in equation (5) and (6). Cyclic hardening parameter is calculated from equation (7) where visco-plastic strain hardening and thermal recovery are considered.

Fig. 1. Shape of experimental specimens; dimensions in mm

Fig. 2 Experimental inelastic strain rate during hold time and the curve of visco-plastic strain rate, creep strain rate and inelastic strain rate: The test conditions are; mechanical strain: 1.0%, hold time: 60min, strain rate: 0.1%/sec. = − y s a (4)

M

1 = = +  a (1 i

vp i

( ) ( ) i

b

) h 

(5)

( ) i

b b

2 3

(

)

k i

( )

( ) i

( ) i   = − ε vp

( ) i

vp

( ) i

b

ε

b

b

:

(6)

eq

i eq

( )

(

)

vp

vp

( ) vp 



0 (7) Fig. 3 shows the comparison between the experimental data and simulation results of uniaxial creep-fatigue tests using round bar specimen. It can be seen that the simulation accurately predicts the hysteresis loop and stress relaxation behavior respectively for the different mechanical strain ranges, 0.4% and 1.0%. 4. Creep-fatigue damage estimation Creep-fatigue damage can be estimated by linear summation method, and creep damage and fatigue damage can be calculated by time fraction rule, ductile exhaustion method, or modified ductile exhaustion based on non-unified constitutive model. The difference between the damage estimation summed from the initial cycle and the estimation L = − p R −   