PSI - Issue 25

R. Baptista / Procedia Structural Integrity 25 (2020) 186–194 Author name / Structural Integrity Procedia 00 (2019) 000–000

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In this paper T-Stress values were calculated for different fatigue cracks, propagating under different loading conditions. Crack propagation was simulated using a previously developed FCG automatic algorithm, based on the MTS criterion. Current goal is to understand T-Stress evolution during crack propagation. This will enable the development of a new crack propagation model, combining both mixed mode SIF and T-Stress parameters in order to calculate crack propagation direction.

2. Materials and Methods 2.1. Crack propagation criteria

When simulating FCG under mixed mode conditions, caused by biaxial loading or specimen geometry, one must determine the crack propagation direction. Several crack propagation direction criteria have been defined, including the MTS criterion by Erdogan et al . (1963). According to MTS criterion, crack propagation occurs when tangential stress ( �� ) reaches a maximum value, while radial stress ( �� ) is zero. �� �� �� � �� � � � �� �� � � � (4) As MTS criterion neglects T-Stress effect on tangential stress, it is possible to define an equivalent SIF or crack diving force ( �� ), Xiangqiao et al . (1992). �� � � � � � � �� 3 � � � � � (5) While MTS criterion postulates FCG to occurs under mode I, it is possible to define the Maximum Shear Stress (MSS) criterion, considering that FCG occurs under mode II. This criterion considers crack propagation to occur when �� reaches a critical value, allowing for crack propagation direction and crack driving force determination, �� �� �� � �� � � � �� �� � � � (6) �� � � � � � � � � �� � � �� � 3 � � � � (7) Both criteria neglect T-Stress effect on stress distribution around the crack front, and several authors have compared their usage under different conditions. Qian et al . (1996) consider MTS criterion useful under proportional loading conditions, while Yu et al . (2017) consider MSS criterion more appropriate for non-proportional biaxial loading conditions. In both cases, comparison between experimental FCG determination and simulation was made using the determined and predicted crack paths, therefore, crack propagation direction and crack driving force seem to be the two most important parameters. 2.2. Cruciform specimens Cruciform specimens were modelled using ABAQUS 6.14, considering two-dimensional elements, under plane stress conditions. Fig. 1 shows the 120 mm arm’s length specimen, with 30 mm arm’s width. A constant material thickness of 3 mm was considered. With a design similar to the specimens used by Misak et al. (2013), a 20 mm radius fillet was modelled between specimen arms, and 1 mm length and 0.25 mm wide notch (Fig. 1 detail A) was considered on the specimen centre. The notch is used to define the initial crack orientation α . In this paper two different α values were considered, 0º and 30º. A simple modification was also made to the cruciform specimen, in part of the FCG simulations. The modified specimen includes two anti-symmetric holes (Fig. 1 detail B), with 2 mm diameter, placed at 7.2 mm from the specimen centre. The angular position β of the two holes was considered to be equal to 15º, 30º and 45º.