PSI - Issue 13

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

1874

2

the non-unified constitutive model. Furthermore, for inelastic strain during hold time several physical mechanisms occur, depending on the stress applied. (Priest and Ellison, 1981, Wen et al., 2016). Therefore, the amount of creep damage depends on the stress level under the stress relaxation in creep-fatigue test. In this paper, for the sake of accurate assessment of creep and fatigue damage, the FE analysis is conducted by utilizing non-unified constitutive model to consider the effect of the stress level on the creep damage.

Nomenclature ε , el ε , in ε

total strain, elastic strain, and inelastic strain respectively visco-plastic strain and creep strain respectively

vp ε , cr ε

el D

isotropic elastic stiffness

σ , y , s , a

stress, effective stress, deviatoric stress and deviatoric back stress respectively

( ) i b

i -th non-dimensional back stress number of back stress parts visco-plasticity parameters

M

1 A , 1 n 2 A , 2 n

creep parameters



parameter of visco-plastic strain range dependence on cyclic hardening

c

constant of cyclic hardening effect on creep

vp  ( ) i h

cyclic hardening parameter

i -th incipient kinematic hardening modulus constants of i -th back stress evolution

( ) i  , ( ) i k

L , 0  R ,  c d , f d

strain hardening constants thermal recovery constants

creep damage, and fatigue damage per cycle

f 

creep rupture elongation

B , m

constants of relationship between plastic strain range and number of cycles to failure

2. Testing method and test condition

The material used is 316H stainless steel. Uniaxial creep-fatigue test with tensile strain holding were conducted at 700 ℃ . The mechanical strain rate is 0.001 s -1 and strain ratio is the value of -1. The mechanical strain ranges are 0.4%, 0.7% and 1.0%, and dwell times are 1min and 10min in the case that mechanical strain rate is 0.4%, and 10min and 30min in the case that mechanical strain rate is 0.7% and 1.0%. The shape of smooth round bar specimens is illustrated in Fig. 1. 3. Constitutive model Figure 2 shows the experimental inelastic strain rate during dwell. It can be seen that the inelastic strain rate during hold time is changed at the point approximately 1.0 × 10 -6 s -1 . This is probably because the physical mechanisms of the inelastic strain are changed from the glide deformation to the dislocation creep. Therefore, in the constitutive model, the inelastic strain is assumed to be decomposed into visco-plastic strain and creep strain as shown in equation (1), and elastic strain is given by in equation (2) using Hooke ’ s low. el in = + ε ε ε , in vp cr = + ε ε ε (1) : el el = σ D ε (2) In this paper, it is considered that the visco-plastic strain rate is analogous to the creep strain rate, shown in equation (3). It is assumed that both visco-plastic strain rate and creep strain rate are affected by cyclic hardening. However, it can be seen in Fig. 2 that cyclic hardening affects more on the visco-plastic strain rate than on creep strain rate (Ohno et al., 2018). In addition, it is known that cyclic hardening is also affected by the plastic strain range, Ohno et al. (2017) proposed the following equation, where the plastic strain range dependent cyclic hardening is considered.