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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Fig. 4. Model of the crack of depth l . The stresses in expression (17) are used to determine the principal stresses at the crack tip 1 , 2 , 3 (or � 1 , � 2 , � 3 ). Then the von Mises equivalent stresses and strains are estimated. After that, the reduction in fracture strain at the crack tip is evaluated according to equation (16). The distribution of the normalized principal stresses in the direction of the axis z (along the thickness b of the specimen, Fig. 1) according to data of FEM calculations (Makhutov, 1981; Makhutov, 2008) are generalized in Fig. 5.

Fig. 5. Distributions of principal stresses 1 2 3 , , σ σ σ and the factor of plasticity reduction D e σ along the thickness in the crack zone. These data allow calculating the values of according to equation (15) and D e according to equation (16) at the crack tip zone and estimate the fracture strain under static and dynamic bending at room temperature ( 0 =2 0 0 ) and low-temperature t = -80 0 C. 6. Analytical determination of the initial shape of the crack The value of the crack increment ∆ℓ can be estimated using strain-based fracture criterion (fracture stress = ), and equations of linear fracture mechanics (expression (2)) and assuming that the value of stress at the crack tip (for = ∆ℓ ) = : ∆ℓ = 2 1 ( ) 2 , (18) where K I is the stress intensity factor estimated according to equations (3) and (4).