PSI - Issue 22

N. Makhutov et al. / Procedia Structural Integrity 22 (2019) 93–101 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

98 6





  

  

0.5(1 ) 1 m

 

    

n

Y n p f 

    

   

Y 

.

(19)

max max          p f p f



p f 

Thus, t ransformation Φ M is analogous to Neuber transformation Φ N . It maps the points A p-f ( σ p-f ; ε p-f ) of the curve of pseudoplastic states to the points ( ) max M A (σ max ; ε max ) of the stress-strain curve . But in contrast to transformation Φ N the proposed transformation Φ M allows accounting for the values of theoretical stress concentration factors K t , nominal stresses σ n , and power hardening exponent m . Thus, determining the relationship between fictitious pseudoplastic states ( σ p-f ; ε p-f ) and maximum local stress and strains ( σ max , ε max ) at the notch zone for the wide range of nominal stresses σ n .

Fig.3. Stress strain conversion rules for different strain ranges 1 – Stress-strain curve, 2 – Pseudoelastic states; 3 – Pseudoplastic states; Φ N is a Neuber’s mapping according to ( 15) Φ M is a Makhutov mapping according to (19); I – range of elastic strains; II – range of limited plastic strains; III – range of extensive plastic strains Fig.4 provides a geometrical interpretation of the proposed rule. It is quite similar to the well known geometrical interpretation of the Neuber rule (15) that reads that the area of triangles 0 e f e f A    and ( ) ( ) max max 0 N N A  are equal. According to the presented approach the following relationship between the areas of triangles 0 p f p f A    and ( ) ( ) max max 0 M M A  holds:

2 1 F    .

(20)