PSI - Issue 52

7

Valery Shlyannikov et al. / Procedia Structural Integrity 52 (2024) 214–223 V.Shlyannikov, A.Sulamanidze, D.Kosov/ Structural Integrity Procedia 00 (2023) 000 – 000

220

(

)

( r   = , FEM ij FEM ij r ,   

0

FEM

K

=

(3)

)

1

0

r

=

The stress-intensity factor was estimated from the same FE model as in the compliance method used for assessing the crack length. Across all the performed numerical calculations, the power of the crack tip stress singularity or 1 2 r − slope, which is inherent to a linear-elastic state, is observed for all tested samples. Applying the general expression of the stress-intensity factor, the geometrical parameter Y(a/w) as a function of crack length was obtained from computing the elastic SIF K I at a prescribed nominal stress σ max and crack length a

1 FEM a K

w     =  

(4)

Y

a  

where w is specimen width. Figure 6 shows the elastic SIF K 1 behavior in the SENT specimen as a function of a crack length with applied different nominal stress level and temperature. This figure represents a comparison of numerical data for isothermal fatigue ( T =23˚C, 400˚C, 650˚C) , creep-fatigue interaction ( T =400˚C, 650˚C) and IP and OOP thermo-mechanical fatigue ( T =400˚C - 650˚C) conditions . As one would expect, under load or nominal stress-controlled isothermal testing observed moderate effect of thermal strains arising from temperature induced expansion and the elastic modulus variation, i.e. elastic stress intensity factor K 1 in the range a/w < 0.7 is almost temperature-independent (Fig.6,a,b). However, with an increase in the crack length from 5 mm to 15 mm under both in-phase and out-of phase cyclic deformation, the elastic SIF amplitudes for TMF conditions are deviating from conventional isothermal solution (Fig.6c). It's obvious that employment of multi-physics approach to modeling of the TMF test conditions considered in this study shown that computed elastic stress-intensity factor for given applied load under TMF is different from isothermal conditions, or, that computed elastic crack tip field under TMF is different from that, under isothermal conditions at the same applied load and temperature. These results confirm the need to model heat transfer from induction heating and associated thermal strain component that leads contribute to change in stress strain field under a given applied load.

a)

b)

c)

Fig. 6. Geometry dependent correction factors for different loading conditions: (a) pure fatigue; (b) creep-fatigue interaction; (c) TMF.

The values of elastic SIF of the finite element model evaluated as the average stress intensity factor along the whole crack front in the SENT specimen with the thickness of 5mm. By varying the crack length over the set of finite element models, a functional dependences of Y(a/w) were acquired, see Fig. 6, which were fitted using a polynomial expression for each tested specimen.