PSI - Issue 12

Venanzio Giannella et al. / Procedia Structural Integrity 12 (2018) 404–415 V. Giannella Structural Integrity Procedia 00 (2018) 000 – 000 For mixed-mode 3D problems, the J -integral is related to the three basic fracture modes through the components J I , J II and J III : J = J I + J II + J III (4) In Rigby et al. (1998), a decomposition method is presented, where the integrals J I , J II and J III in elastic problems are directly calculated from J . The method for deriving the three separate K values from J can be found in Rigby et al. (1998). Once the three values for K , K and K are known, an effective K value (BEASY 2016) is calculated K eff = √(K I + |K III |) 2 + 2K II 2 (5) In final, the K is inserted in Eq. 6 to compute the da/dN . / = C∆ (6) where C and n are listed in Tab. 1. 411 8 A FEM submodel (Fig. 1b), implemented by FRANC3D code, was used to simulate the crack-growth. To this aim, it was necessary to define a further domain to use as a remeshing zone where to insert and propagate the crack (Fig. 7). In particular, the code generates and insert the crack in the remeshing domain (Fig. 7) adopting tie constraints at the connecting surfaces, and eventually applying submodelling boundary conditions (in terms of displacements) on the submodel cut surfaces. Fig. 8 shows the FEM submodel when the initial crack is inserted. Subsequently, the FEM crack-growth procedure proceeds step-by-step: for each growth step, the code calculates the new crack front, inserts the new crack surface in the remeshing domain, connects such remeshed domain to the FEM submodel and solves it considering the boundary conditions coming from the FEM global model. All the models comprises purely linear tetrahedral elements. SIFs along the crack front were calculated by means of the J-integral technique whereas the crack path was assessed by means of the Maximum Tangential Stress (MTS) criterion (Erdogan et al., 1963). 4. FEM analyses

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Figure 7. FEM-FEM strategy for the crack-growth simulation.