PSI - Issue 37

R. Baptista et al. / Procedia Structural Integrity 37 (2022) 57–64 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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between four sleepers, was analyzed for mode II FCG. All numerical simulations were performed using Abaqus finite element analysis (FEA) solver. 2.1. Crack propagation criteria Two crack propagation criteria are compared in this paper. Originally defined by Erdogan and Sih (1963), the Maximum Tangential Stress (MTS) criterion, postulates that crack propagation occurs when the Westergaard (eq. 1 2) tangential stress ( ) reaches a critical value: = √2 3 2 − √2 3 2 2 2 (1) = √2 2 2 2 + √2 2 (1 − 3 2 2 ) (2) = 0, 2 2 < 0 (3) where is the crack propagation direction according to the MTS criterion (Fig. 1 a)), is the Westergaard radial stress and and are the Stress Intensity Factors (SIF) for mode I and mode II respectively. Using the MTS criterion Xiangqiao et al. (1992) were able to define the virtual SIF ′ or crack driving force. ′ is maximum along the crack propagation direction , predicted by the MTS criterion, while is zero. ′ = 3 2 − 3 2 2 2 (4) Several authors have experimentally verified MTS criterion predictions, considering it useful for FCG under pure mode I or proportional mixed mode loading conditions, Qian and Fatemi (1996). The Maximum Shear Stress (MSS) criterion, predicts crack propagation along a direction where radial stress is maximized. When under pure mode II loading conditions, MSS criterion predicts coplanar or in-plane shear mode crack growth, Floros et al. (2019), but it can also be applied to mixed mode loading under non-proportional conditions, Yu et al. (2017). = 0, 2 2 < 0 (5) ′ = 2 2 2 + 2 (1 − 3 2 2 ) (6) Fig. 1 b) compares both MTS and MSS crack propagation direction predictions for different K II /(K I +K II ) ratios. Pure mode I and pure mode II loading conditions correspond to 0 and 1 respectively.

80

MTS MSS

40

-80 Crack angle, θ (degree) -40 0

0.0

0.2

0.4

0.6

0.8

1.0

(a)

(b)

K II /(K I +K II )

Fig. 1. (a) crack propagation direction , (b) calculated using both MTS and MSS criteria.