PSI - Issue 40

N.A. Makhutov et al. / Procedia Structural Integrity 40 (2022) 283–295 N.A. Makhutov at al. / Structural Integrity Procedia 00 (2022) 000 – 000 where – equivalent nominal deformation in critical cross-section in the concentrator zone; Е – elastic modulus; – strain concentration factor at the elastic-plastic deformation stage. Relation between stresses or , , and deformations e or , , (Fig. 6) for elastic and elastic plastic area is expressed using linear and exponential equation k  for , m y e E       (10) where m – hardening exponent depending on ratio / and plasticity of steel. It is determined experimentally by tensioning standard samples or calculating using equation where – percent reduction of sample cross-section area at break. For pipe steels with increased tensile strength (420 ≤ ≤ 750 MPa) at 0.4 ≤ ≤ 0,7 and 2 ≥ / ≥ 1, 2 the value of m is reduced (0.30 ≤ ≤ 0,15) . For elastic deformation = 1. For tensile diagrams (in true stresses and deformations) the value m corresponds to the true uniform deformation at the tensile strength u m e  (12) For the standard forms of identified defects the value ( ) is determined experimentally or by solving elasticity problem using FEM. Value of or ( ) in expression (9) depends on or ( ) and m .  291 9 lg (1 1, 4 ) u    , lg ln(1/ (1 ))    k y k y m E                   (11)

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Figure 6. Diagram of deformation in elastic ( Е ) and elastic-plastic ( m ) zone Modified Neuber expression can be used for verification calculations of pipeline strength