PSI - Issue 17

Eduardo A. Lima et al. / Procedia Structural Integrity 17 (2019) 246–253 Eduardo A. Lima/ Structural Integrity Procedia 00 (2019) 000 – 000

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2.3. Fatigue Life Model

The Dang Van criterion was used to estimate the fatigue life and is expressed by Eq. (4). This criterion predicts that after the plastic strain stabilization (shakedown elastic), failure (nucleation of the crack) will occur if any point of the loading path exceeds the limits stated, as shown in Fig. (4) (Van and Griveau, 1989; Socie and Marques,1999).

(4) (5) (6) (7)

t ( )

t   ( )





= 

e 

a

DV H

   − e e 2

  

s s 

2 3

=



e

DV

e s

 0.5 =

uts

e s 0.577 = 

e

Fig. 4. Graphic representation of Dang Van criterion for a plane where the stress varies: a) No fatigue failure; b) Fatigue failure predicted; c) Local coordinate system for discretization of space in planes employing two angles θ and ϕ , adapted from Socie and Marques (1999).

The loading path is a connection of data results calculated through the combination of shear ( τ ) and hydrostatic stress ( σ H ) in all planes ( Ø,θ ) in each point p , Fig. (4c). All the elements of a selected portion of the cross-section of the wheel were evaluated, Fig. (5). This region corresponds to the center of the semi-arc of the wheel rim, around the contact region. Morrison and Cram (in Norton, 2014) states that it is expected that the failure by contact fatigue occurs at some point in the useful life of the component, even though the material does not present an inflection point in the Wohler curve. Therefore, the maximum Dang Van stress from Eq. (8) is inserted Eq. (9), as a way to obtain the number of cycles N . Table (1) presents the parameters used for Dang Van-modified criterion.

(8) (9)

max | ( , , ) p 

( ) | p    

 

=



DV

a

DV H

'

b

'

2 N 

=

DV

f

max

Fig. 5. Region of the wheel to apply modified Dang Van criterion.