PSI - Issue 39

Daniele Amato et al. / Procedia Structural Integrity 39 (2022) 582–598 Author name / Structural Integrity Procedia 00 (2019) 000–000

586

5

3. Numerical simulation procedure The numerical analyses were performed by the synergic use of the commercial software ABAQUS and FRANC3D [27-28]. The two tools were coupled together to obtain a quasi-automatic cyclic crack propagation by using the Finite Element Method (FEM). The first tool is involved in the FE model creation and solution of the numerical problem, whereas FRANC3D is implicated in the crack insertion and propagation. The simulation procedure is schematically reported in Figure 3. Each load case is identified by a numerical code: 0_1_40_3 denoting, in order, = 0 , = − 1 , a shift phase = 40° and the mixed-mode condition of / = 0.76 ( / = 1.31 corresponds to 1 and / = 1 corresponds to 2). Once the load case is defined, the SEN-TC specimen is modelled as a discretized volume of quadratic elements (type C3D20). This is the FRANC3D input deck which includes the material parameters, the boundary and loading conditions, etc. At this stage, the simulation goes into heart of the crack propagation. The entire process consists of several propagation steps which are performed in a quasi-automatic loop in FRANC3D. Each iteration consists of three phases: the pre-processor, the numerical problem solution and the post-processor. 3.1 Pre-processor During the pre-processor phase, the model is divided into two parts: the global and the local. The latter is also known as domain, i.e., the part of the mesh where crack propagation is supposed to take place. This is a convenient choice for fracture simulations since it allows to identify a reduced remeshing volume and therefore, to speed up the analysis. The current crack geometry is inserted into the domain, which is remeshed; then, the local and the outer global mesh are merged. With the remeshing, the crack front is surrounded with several concentric tubes. The innermost tube is made up of collapsed hexahedral elements: quarter-point singular wedge elements [28-30]; these are 20-node brick elements in which the face adjacent to the crack front is collapsed to a line. This first layer is encircled by two or more rigs of brick elements. This meshing technique generates a flexible cylinder with a hexagonal cross-section around the crack front. The tube surrounds the whole crack front with exception of the terminal parts, which are meshed with tetrahedral elements. On the outer part of the tube, pyramids provide compatibility between the bricks, of the tube, and the quadratic tetrahedral element of the domain. Figure 4 provides a view of the outer mesh of the domain, after remeshing, and a detailed view of the tube.

Figure 3 Numerical simulation procedure scheme.