PSI - Issue 41

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A.L. Ramalho et al. / Procedia Structural Integrity 41 (2022) 412–420 Author name / Structural Integrity Procedia 00 (2019) 000–000

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(3) The estimation of the fatigue life for the propagation period was carried out by integrating the Paris-Erdogan law, equation (4). � �� �� � √��� � � � � � � � � � � � � (4) For the material propagation constants were used the values, C = 1.2288x10 -8 and m= 2.6, with da/dN in mm/cycle and ΔK in MPa.m 1/2 . In present study, were maintained the three-point bending with sinusoidal loading and the material propagation constants. A local approach was used for the evaluation of the stress intensity factor, through the evaluation of the strain energy release rate (G). This model is valid in the elastic domain. The propagation of a crack occurs when the energy released equals the fracture toughness of the material. In the VCCT is assumed that, for an infinitesimal crack opening, the strain energy released equals the amount of the work required to close the crack. To simplify the evaluation of this work, is assumed that an infinitesimal crack extension, Δa, has negligible effects on the crack front, therefore the stress and displacement fields can be evaluated at the same configuration, Krueger (2004) and Elisa (2011). In the mode I of fracture, opening mode, G is evaluated by equation (5). � � ��� � � 2 1 �� � ��� � � ��� � � � � �� � � � ��� � � ��� � � � �� � �� � �� � � � ��� � � � �� � �, ��� where the superscript (a) means that displacements and stress are evaluated in the model with the crack length a. For 3-D solids, the G evaluation is done separately at each node on the crack front and the area of influence of these nodes is half of the areas of the contiguous elements. Each node at the crack front is considered as an individual crack. Equation (5) can be adapted to the mode II and III of fracture. For plane strain and 3D analysis the stress intensity factors can be found by equations (6). � � �1 � � � � � � � � , �� � �1 � � � � � � � � � , ��� � �1 � �� � � � �� � (6) Equations (5) and (6) permit the evaluation of stress intensity factors, in the presence of stress residual fields. The initial crack is generated by automatic remeshing using a faceted surface. This initial crack is propagated by fatigue. In fatigue crack propagation, a load sequence is repeated a number of times. After each sequence, cracks are grown. For high cycle fatigue, a maximum growth increment was specified, which is scaled along crack fronts. This scaling allows the determination of the shape of the crack front during growth. a maximum crack growth increment of Δa0 = 0.25 mm was considered, and a scaling of this increment to each node on the crack front (Δa) based on equation (7), Marc (2018). � ��� ��� � � � � �7� where Δ a fat is the growth increment for each crack-node in the crack front, calculated by the Paris-Erdogan law using the respective ΔK. To ensure that the crack fronts stay smooth, were used a smoothing scheme based upon running averages for the growth increments along the front.