**2. Developed Program Framework**

The code that was developed is a simulation software to assess the 2D crack propagation process under LEFM conditions. This software predicts the growth of quasi-static crack growth in 2D components using the finite element method, taking into account the mechanical parameters of the fracture. Four essential features for the adaptive mesh finite element (FE) analysis are used for the crack direction simulation, namely, the mesh optimization algorithm, the crack criteria, the criterion of direction, and the methodology of crack propagation. The mesh refining can be controlled by the characteristic scale of each element predicted, based on the current error estimator. An incremental principle with the von Mises yield criterion is applied to this initial model. The solution errors are computed after each load stage is over. The incremental analysis is interrupted when the error exceeds a specified cumulative error at some stage and a new FE plan is generated. The program automatically configures the mesh with a new mesh refinement. After it is generated, the solution variables (displacement, stresses, strains, etc.) are transferred from the old mesh to the new mesh. The analysis is then resumed and progresses until the errors are again higher than the pre-decided amount.

In order to examine the start of the crack growth, the crack growth criterion is employed. The LEFM typically utilizes SIFs as a fracture criterion. Various techniques of estimating the path of a crack are used, such as the maximum circumferential stress theory, theory of maximum energy release, and theory of minimum energy density. At any stage of crack propagation, a FE model is defined. This model is given in the first step as an input for the modeling. The algorithm output is then generated via the models in the subsequent steps. At each stage, as the crack grows, the geometry elements are deleted and reconstructed using an adaptive technique and updated for the next propagation process. Figure 1 demonstrates the simulation procedure used to model quasi-static crack growth. The main steps of this procedure are explained in detail by [11,14].

**Figure 1.** General flow chart of the quasi-static crack growth program.
