PSI - Issue 39

N.A. Makhutov et al. / Procedia Structural Integrity 39 (2022) 247–255 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3

= √2 ,

(2) where P is the bending force; M b is the bending moment; W o is the section modulus; b is the width of cross-section; l is the crack depth; r is the distance from the crack tip, K I is the stress intensity factor.

Fig. 1. General scheme of loading. The nominal elastic stresses in the central cross sections of the smooth/uncreacked (Fig.2,a) and cracked (Fig.2,c) specimens are determined using the equations of strength of materials = = 4 ( ℎ2 / 6 ) ; ℓ = 4 [ ( ℎ−ℓ ) 2 / 6 ] . (1) Local stresses at the crack tip are determined according to the equation of linear fracture mechanics (Fig.2, b ) (Makhutov, 1981; Makhutov, 2008): = √2 , (2) where P is the bending force; M b is the bending moment; W o is the section modulus; b is the width of cross-section; l is the crack depth; r is the distance from the crack tip, K I is the stress intensity factor.

Fig. 2. Distribution of elastic stresses in the dangerous cross-section. a - nominal stresses for the smooth specimen; b - local stresses σ r in the cracked specimen; c - nominal stresses in the cross-section, weakened by a crack According to the equations of linear fracture mechanics the stress intensity factor is determined by the equation: = √ ℓ ∙ , (3) where f Ik is a dimensionless correction function depending on the l / h ratio. The correction function f Ik is determined using the so-called section method = 1/ � 1 − ℓ / ℎ . (4) The dependence of the equivalent true stress σ vs. equivalent true strain e has two ranges (Makhutov, 1981;