PSI - Issue 39

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

248

2

main attention is paid to the influence of the stress triaxiality at the crack tip on crack shape and size at the initial stage of the crack development.

Nomenclature b

width of cross section factor of plasticity reduction modulus of elasticity

D e σ

E

e strain yield strain ̅ normalized true fracture strain at the specimen neck ̇ strain rate ̇ 0 standard strain rate F { θ , r } coordinate function f Ik correction function K I stress intensity factor � strain intensity factor theoretical stress concentration factor strain concentration factor l crack depth m strain hardening exponent M b bending moment; P bending force ̅ normalized fracture resistance ° room temperature W o the section modulus r distance from the crack tip yield stress ̇ yield stress at temperature t and strain rate ̇ von Mises equivalent yield stress

factor of the increase of the resistance to plastic deformation due to stress triaxiality

nominal elastic stresses in the central cross-sections of the uncracked specimen nominal elastic stresses in the central cross-sections of the cracked specimen local stresses at the crack tip ultimate strength ultimate strength at temperature t � j -th normalized principal stresses relative narrowing of the cross-sectional area in the neck at fracture ∆ℓ crack increment 2. Basic design equations The initial model of a specimen subjected to static and dynamic loading is shown in Fig. 1 (Makhutov, Reznikov, 2020). The nominal elastic stresses in the central cross sections of the 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):