PSI - Issue 39

Jesús Toribio et al. / Procedia Structural Integrity 39 (2022) 479–483 Author name / Procedia Structural Integrity 00 (2021) 000–000

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With regard to crack bifurcation, branching produces an accentuated trend to fatigue crack growth in the direction of the original crack (Pärletun, 1979). Also, the stress intensity factor (SIF) of a branched crack can be considerably smaller than that of a straight crack with identical projected length (Meggiolaro et al ., 2005). For symmetric crack branching, the SIF value decreases with the branch length if the latter is small compared to the total crack length (Kitagawa et al ., 1975). The main aim of this research paper is to study the retardation in plasticity-induced fatigue crack growth due to the bifurcation in the near-tip area, i.e., i.e., the bifurcation-induced fatigue crack growth retardation , the key variables being the initial crack tip geometry and the fatigue intensity. 2. Numerical procedure A numerical simulation by using the finite element method (FEM) under small scale yielding (SSY) was performed by the MSC.Marc software. Material was elastic/perfectly-plastic with the properties corresponding to a medium strength steel: Young modulus E = 200 GPa, Poisson coefficient ν = 0.3 and yield strength σ Y = 300 MPa. The von Mises yield criterion, large strains and large geometry changes were used with an updated lagrangian formulation under plane strain. Fig. 1 shows the finite element mesh (four-node isoparametric quadrilateral elements were used). A symmetric bifurcated crack tip was used with two branches of equal length and angle, as shown in Fig. 2. In addition, the totally straight crack was used as reference configuration.

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Fig. 1. Finite element mesh: (a) full plate; (b) crack tip detail.

l´

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α

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Fig. 2. Initial geometry with two branches.

The parameters characterizing the initial geometry of the bifurcated crack tip (Fig. 2) are as follows: α , angle of deflection of each branch in relation to the main crack; l ’, projected length of each branch in the direction of the main crack; d , distance between the crack tip points of each branch. The plate had the same height and width, and the projected length of the crack was a fifth part of the plate half-width and 15000 times the crack width (5 µm), so that the notch is sharp enough that it can be considered as a crack and the SIF governs the process. For the crack with bifurcated tip, the dimensions characterizing the initial geometries were as follows: (i) branch projected length l ’ = 25, 50 and 75 μm; (ii) branch angle α = 15, 30 and 45º.