PSI - Issue 75

J. Havia et al. / Procedia Structural Integrity 75 (2025) 43–52 Havia et al./ Structural Integrity Procedia (2025)

48 6

The 4R method is a multiparameter notch stress approach, that considers the local elastic-plastic behavior at fatigue critical location. This method includes the material model, true notch geometry, residual stresses and external loading on fatigue assessment using a single reference curve. The method has been developed mainly for ultra-high-strength steels, but previously Havia et al. (2025) have shown that the method could also be extended to aluminium. The local elastic-plastic behavior is captured using Ramberg-Osgood (R-O) N ’ from which the local notch stress-strain behavior can be estimated using following equations:

2

k 

 

 

res +  

1 n



max    E K  

1

R

−

 

(

)

max

max max  

= +

=

(4)

 

E



max

1

(

)

2



k 

2 2 ' E K          

'

n

( )     = +

=

(5)

E





where, σ max is the local maximum stress, σ res Δ σ is the local stress range, and K and n are monotonic stress – strain curve coefficient and strain hardening exponent, while K’ and n’ are corresponding cyclic strain hardening coeffect and exponent. After the local stresses are calculated at the notch, the local stress ratio ( R local ) can be calculated and finally the notch stress is corrected to the R = 0 reference system using Smith-Watson-Topper method.

 



1 = −

.

loca l R

(6)

max



k R 

,ref k   =

1

−

(7)

local

In this study, the ENS method is used to determine notch stresses for the 4R method, and the measured residual stresses are utilized in the 4R analysis. The material parameters for R-O material model for welded 5083 alloy, were acquired from the earlier work by Morgenstern (2006) and presented in Table 4. Table 4. Monotonic and cyclic material properties of welded 5083 alloy (Morgenstern, 2006). K n K’ n' 5083 H111 382 0.14 372 0.052 The procedure is shown in Fig. 6. The DED on plate and DED feature welded on plate are shown as an schematic example with two different force ranges. The external loading together with residual stresses and local SCFs determine the local stress range.