Issue 48

R. Baptista et alii, Frattura ed Integrità Strutturale, 48 (2019) 257-268; DOI: 10.3221/IGF-ESIS.48.27 261 limited to the contour integral technique, as it can also use the XFEM method. In this paper only ABAQUS was used as the FEM solver, but the algorithm can use any solver. This is possible because of the open and modular nature of the algorithm created. The main steps of the algorithm are represented in Fig. 3. The initial conditions, the part geometry, the material properties and the loading conditions are initially set by a Matlab program. This program creates a Python script, using the necessary commands that the chosen FEM solver can recognize to create the FEM model. Python is therefore a translator that can create the FEM model in different FEM solvers. In our case the solver used was ABAQUS, that can calculate the SIF or other fracture mechanics parameters using different techniques. For two dimensional models ABAQUS can only use the contour integral technique, therefore a special mesh is required around the crack tip. Singular collapsed quadratic elements must be used, in a spider-web type mesh (Fig. 4). For three dimensional models ABAQUS can also use the XFEM technique to calculate the SIF. Our algorithm can create these three types of models, remeshing the part in each increment. For the contour integral models, a special spider-web mesh is created around the crack tip, Fig. 4, this mesh uses elements with a size of 0.1 mm, and 5 levels of elements are used of 5 SIF contours calculations. For XFEM models, the algorithm generates a square box, with a 1 mm side around the crack tip, filled with elements with a size of 0.05 mm. This is required to determine the SIF with the necessary quality, [13]. Figure 4 : Special FEM mesh design around the crack front for the contour integral and XFEM techniques, used for SIF extraction. ABAQUS returns the fracture mechanics parameters to Matlab, where the decision if the crack will propagate is made. This is the crucial step of the algorithm. If the crack can propagate, a new crack propagation direction must be calculated, and the crack driving force must be determined. Erdogan et al. [14] proposed the Maximum Tangential Stress (MTS) criterion for crack propagation in mode I. Several authors like Blažić et al. [15] or Fajdiga et al. [16], have successfully used the MTS criterion to calculate the fatigue crack growth direction in mode I and even in mixed mode conditions. According to Erdogan et al. [14] the new direction for the crack propagation, can be calculated using Eqn. (2). 2 1 1 2 8 4 I I II II K K tan K K                               (2) where φ is the new crack propagation direction, and K I and K II the SIF. While the crack driving force can be calculated by Eqn. (3). 1 3 3 3 3 4 2 2 4 2 2 eq I II K cos cos K sin sin K                        (3) Although these equations are valid in most cases, Yang et al. [17] have reported that some cracks show different behaviors in mixed modes. Some cracks opening mode will be governed by mode II and will behave according to the Maximum