PSI - Issue 39

Wei Song et al. / Procedia Structural Integrity 39 (2022) 204–213 Author name / Structural Int grity Procedia 00 (2020) 000–000

209

6

2

2

2

(

)

(

)

 

   

 

 

toe

1

1 2

K

+

ω

+

1 ω

  



toe

k

σ

1 1

(4)

1

E toe

WT ：

−

1 λ

K

t

max

=

=    

=

⋅

1

   

σ

1

1

2 σ π ⋅ r

−

1 λ

−

1 λ

r

e

π

n

0

0

1

n

1.414( ) h t

1.414( ) 0.3516( ) h t p t − −

root

0.2553 7.732 − ⋅

9.287 + ⋅

−

k

e

e

=

(5)

Where ：

1

toe

3.691( ) h t

3.177( ) 4.707( ) h t p t − −

1.204 1.284 = − ⋅

6.8 + ⋅

−

k

e

e

(6)

1

p K during the plastic deformation stage was proposed, which is presented as

The notch energy concentration factor W

follows:

    

    

E

  

   

  

σ ε  ∆ ⋅ ∆

( 1 1 1 1 exp F   )

W

P

for

K

= − − −

−

σ ε ∆ ⋅ ∆ ≥

n

n

(7)

y

  

e

K

W

n

n

e K W

N

y

W

where the E and F strands for the characteristic equations related to the material properties and geometries, W y represents the referenced characteristic energy parameter, which is related with the material yield strength. In the equation, the transition phase of the P W K is the function of normalized nominal energy indicator (Δ σ n Δ ε n / W y ). 3.4. Application of the analytical model To illustrate the variations of notch energy concentration degree under large nominal strain amplitudes, the final notch energy concentration factors (NECFs) were plotted according to the semi-empirical analytical solutions proposed in the above section. We further examine the influence of penetration lengths, weld length, and mismatched ratios on the final Notch Energy Concentration Factor (NECF) by 3D contours, as shown in Fig. 4. For the fixed mismatch ratio M= 1, 0.8, 0.6, we see that the NECFs at WR and WT increase with the decreases of penetration length ratio (2a/W increasing). Under the same configuration of penetration and weld length ratio, a lower mismatch ratio leads to an increase of the magnitudes of NECF at WR and WT by the comparison of z axial scale among Fig. 4(a) and (c). The same behavior is observed in terms of the effect of weld length ratio on the NECF distribution for the exact failure location, which is presented by the comparison among Fig. 4(b) and (d). Note that the discrepancy exists between the WT and WR for the same welded joint, which can judge the fatigue failure initiation. Thus, the proposed analytical solutions can determine the transition relationships of the WR and WT failures due to the variations of geometries and yield strength in LCWJs.