PSI - Issue 38

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Jacques Berthellemy et al. / Procedia Structural Integrity 38 (2022) 428–446 Jacques Berthellemy / Structural Integrity Procedia 00 (2021) 000 – 000

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4. Proposed stress concentration factor k f for the flange

In this case, the governing principal stress is used to directly evaluate the SCF in comparison with the experimental case whose detail class is known at 71 MPa. In the corners of the cope hole, the fatigue is multiaxial then the orientation of the principal stresses tensor is varying and the use of a modified stress according to the Woehler theory and the Eurocodes is only a first approximation. Future research will rather use the Dang Van theory to represent the reality more accurately. In these conditions the modifying factors of the type (25/t) n were not considered regarding the thickness of the plates. Of course, the following formulae have to be used without using modifying factors of the type (25/t) n to avoid a double application of this factor. The figure 17 presents the finite element results regarding the evaluation of the governing principal stress in the flange. In red color is represented the SCF factor according to the formulas (3) and (4) proposed below. In comparison, every point in blue color is the result of a finite element evaluation.

Figure 17 : Overview of FEM results and proposed concentration factor

The stress concentration factor k f is defined as follow : f = Max ( 1; g ) where g = Min ( g1 ; g2 ) with t 1 1 , , t 2 and e in millimetres and g1 = ( A 1 − ) 1 . 6 + B. ( 2 1 − X ) 2 + + ( D 1 − ) . ( ⁄ ) 2 . 2 ( eq. 3 ) with e = 16 mm A = 25 mm 1 . 6 B = 0.25C = 1D = 100 mm X = ( 1 +125 ) 70 g2 = ( a 1 − ) + b. ( 2 1 ) + + ( d 1 − ) . ( ⁄ ) ( eq. 4 ) with a = 3 mm b = 0.22 c = 0.6 d = 25 mm