PSI - Issue 5

Chmelko Vladimír et al. / Procedia Structural Integrity 5 (2017) 825–831 Chmelko, V., Margetin, M./ Structural Integrity Procedia 00 (2017) 000 – 000

827

3

E   n s n

,





(3)

S

E

( 1  

)  



s n n

where for nominal stress σ n represents in coordinate system of σ - ε the equation of hyperbole with asymptotes (Fig.1):

    

n     

S

S

E n n

( - 1)

    

(4)

S

S

Fig. 1. Determination of the stress-strain relationships in the root of the notch by Eq. (3)

Another method for estimating the stress-strain relationship at the root of the notch, is Neuber ’s theory, where was derived the expression between notch coefficients of the stress  σ and strain  ε in non-linear (elastic-plastic) area, and technical coefficient of stress concentration β in linear (elastic) area by Neuber (1959, 1968): 2       . (5)

n S    ,

 

F     ,

n S

 

 





,

where α – represents theoretic ("elastic") coefficient of stress concentration in the area of elastic deformation, ρ – root radius of the notch, ρ F – virtual radius considering the influence of material microstructure. Multiplying the Eq. (5) by coefficient of nominal stress  n and nominal strain  n according the diagram of tensile curve  –  , the Neuber practically obtained the useful relationship between peak value stresses and strains at the root of the notch σ S , ε S and nominal stress and strain  n ,  n in the form

2 

    

(6)

S S

n n

This equation also represents teh hyperbole in the coordinate system  –  . Comparison of both methods on the deformation characteristic of material AlCu4Mg for flat plate with orifice is displayed in Fig. 2. The good results of