PSI - Issue 39

A.L. Pinto et al. / Procedia Structural Integrity 39 (2022) 409–418 Author name / Structural Integrity Procedia 00 (2019) 000–000

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In order to obtain crack propagation direction, one maximizes the tangential strain range in accordance to the critical plane definition adopted in this work. In this case, the reconstruction of the stress components near the crack type in terms of stress intensity factor are given by: ( , , ) = ( ) √2 � � 2 � � 1 + 2 � 2 ��� + ( ) √2 � � 2 � � 1 − 3 2 � 2 ��� , (7) ( , , ) = ( ) √2 3 � 2 � − ( ) √2 � 3 � 2 � 2 � 2 �� , (8) where and are the radial and tangential stress components according the reference system depicted in Figure 3. From plane strain assumptions, the tangential strain component over time is given by: ( , , ) = − [ + ( + )]. (9) Therefore, the expression for the tangential strain range in terms of becomes: ( , ) = 1 2 � ( , , ) − ( , , ) � . (10)

Figure 3 – Schematic representation of stresses near the crack tip. In this case, the direction of crack’s next propagation increment is obtained by maximizing Eq. 10. Notice that the distance from the crack tip in Eq. 7 to 10 does not influence the results. 3.3. Numerical model and boundary conditions Figure 4 depicts the FE model considered in the present analysis. A coarser mesh is used far from the contact region, whereas, a refined one is considered near the contacting surfaces. In the refined region, a structured mesh with linear quadrilateral elements is used with an approximate size of 28 . Outside the refinement zone, the mesh is not