Issue 53

A. Chatzigeorgiou et alii, Frattura ed Integrità Strutturale, 53 (2020) 306-324; DOI: 10.3221/IGF-ESIS.53.24 307 The majority of these studies are conducted with FEA programs with built-in tools (for example ANSYS [11,12] and ABAQUS [13,14]), which can calculate the stress intensity factors at the tip of a crack. In this study, it is shown that with some computational effort, a person can study cracked surfaces using a FEA program with no crack study tools. For this reason, it is chosen the FEA program FEMAP 11.3.2 [15], which is a well-known Finite Element Analysis program with special features and capabilities, but with no such built-in crack study tools. At first, in order to encounter the singularity 1/ r at the crack tip, the code is programmed to calculate the Stress Intensity Factors (K I , K II , and K III ) using the Crack Opening Displacement (COD) method [16]. Using Finite Element Method (FEM) in crack problems involves the following difficulty. If one uses regular standard elements, a very fine mesh is required at the crack tip, influencing the results. In order to deal with this singularity, the use of modified six node triangular elements (quarter-point elements) [17], has been applied (Fig. 1). Figure 1: Modified six node triangular elements [16]. Secondly, after the calculation of the SIFs, the code calculates the kinking angle, using the criteria of maximum tangential stress (MTS) for mixed-mode loading, which was suggested by Erdogan and Sih [18]. Finally, having calculated all of the above, if a cycle load is applied to the structure, the code calculates the number of cycles loads that are necessary for the crack to propagate. To verify the proposed code three applications have been made. The first one concerns the calculation of stress intensity factors in the case of a cracked plate with an edge crack. The second one is the crack propagation, using three specimens with holes, with different position and length of the crack, and the third one the verification of the fatigue lifetime estimation. T HEORY he fracture problem in the scientific community is a problem of major importance. In this section are presented the basic theory and the crack propagation criteria applied to the code. Stress Intensity Factors In the general case of mixed-mode loading condition, the relative displacement of the crack faces is evaluated in relation to each other. Using a FEA program and taking into consideration the crack opening displacement, the SIF K I , K II , and K III (mode I, mode II, and mode III respectively) can be obtained from the following equations [16] (see Fig. 1):         B B C C B C I 2 2 2 2 2 2 E' 2 π E' 2 π K 4u 4u u u 4 Δ u Δ u 8 L 8 L         (1) T