PSI - Issue 39

N.A. Makhutov et al. / Procedia Structural Integrity 39 (2022) 247–255 Author name / Structural Integrity Procedia 00 (2019) 000–000 7 In case of occurrence of plastic deformations, application of the strain-based fracture criteria = and accounting for equations (7) the equation for crack increment the ∆ℓ can be rewritten as: ∆ℓ = 2 1 ( � ̅ ) 2 , (19) where � is strain intensity factor The transition from � to � was carried out in studies (Makhutov, 1981; Makhutov, 2008) in the same way as the transition in studies (Makhutov, Reznikov, 2020; Makhutov, Reznikov, 2019a; Makhutov, Reznikov, 2019b) from the theoretical stress concentration factor to the strain concentration factor . In this case, the initial value for the crack tip was calculated as = = � � As it was shown in (Makhutov, 1981; Makhutov, 2008) the value of � depends on � and subsequently on the level of nominal stresses � determined by equation (1) and the strain hardening exponent m that can be estimated using equations (8) and (10). This approach for a material with a stress-strain curve as shown in Fig. 3 made it possible to obtain a power-law expression for � (Makhutov, 1981; Makhutov, 2008): � = � , (20) where = 2− ( 1− )( 1− � ) 1+ , (21) here n is a constant that can be taken equal to 0.5. In the calculations, it was assumed that the initial crack growth in the specimen according to Fig. 1 starts at nominal stresses σ n equal to the yield strength σ y . Then, for � =1 the value of according to (21) will be equal: = 2/(1 + ) . (22) As in (Makhutov, 2008), the calculations were performed for steel St3 with the main mechanical properties σ y =252 MPa, σ u =507 MPa, ψ c =0.543. The geometrical dimensions of the specimen were as follows: b = 10 mm, h = 10 mm, l = 2 mm, L = 40 mm. 253