Issue 48

R. Baptista et alii, Frattura ed Integrità Strutturale, 48 (2019) 257-268; DOI: 10.3221/IGF-ESIS.48.27 262 Shear Stress (MSS) Criterion. Yu et al. [18] have compared the crack propagation in mode I and mode II, and proposed the basis for the implementation of the MTS and MSS criteria. Both have been implemented in the algorithm. The decision of which criteria to use is still very controversial. Yang et al. [17] mention that there is always a transition phase between the material behavior, where the MTS and MSS criteria are not applicable. While Zerres et al. [19] proposed a solution to calculate the crack driving force using a combination of both the MTS and MSS criteria. This might be a possible solution, but does not offer a determination of the crack propagation direction. By default, in the algorithm the MTS criterion is used. Finally, others authors have proposed different crack driving forces, as reviewed by Wang et al. [2] one of the most used, was given by Tanaka et al. [20] and can be represented by Eqn. (4). It is limited to be used with stress ratios higher than zero, when the crack will never be closed. 4 4 4 8 eq I II K K K      (4) Once the crack propagation direction and the crack driving force are determined, the next incrementation can be calculated. There are two possible routes, using a set crack length incrementation, and calculating the number of cycles for the increment, or using a set number of cycles, and calculating the corresponding crack length increment using Eqn. (5).   m eq a N C K      (5) Nasri et al. [21] have used a similar approach, using only the XFEM technique, and a set number of cycles between increments. This is a simple approach, but as mentioned by Shi et al. [13], this will lead to an accelerated crack propagation, and the final results will have poorer quality. Therefore the present algorithm uses a set value for the crack length increment, as used by Shi et al. [13], Lesiuk et al. [22] or Majid et al. [3]. According to the previous authors the crack length increment should be around 0.5 or 1 mm. The current algorithm can use smaller values for better results, but the computation time will increase. The algorithm can also determine the appropriate increment value, in an iterative process. But one can verify that the additional computation effort is not justified. Therefore, by default the user should choose the crack increment value for the analysis. The algorithm will finally update the model with the new crack front, and the procedure will be repeated, until a stopping condition is reached. R ESULTS AND DISCUSSION n order to test and validate the developed algorithm, and to better understand the fatigue behavior of welded high strength steels, six FEM models were developed. Two 2D models, one representing a normal Compact Tension (CT) specimen and one representing a CT specimen containing a longitudinal weld. As the 2D specimens were modeled in plane strain, the welded specimen is only an approximation of the real geometry. Fig. 5 b) show a 3D representation of the developed 2D welded specimen, with different thickness on the welded area. Two 3D models, represented on Fig. 5 a) and c), of the normal and welded specimen. All four models used the contour integral technique to determine the SIF. Finally, two 3D models were also simulated using XFEM technique to extract the SIF values and to test the algorithm for crack propagation. The SIF values were used to perform a mesh convergence study. Tab. 4 show the final values of mesh densities used in the simulations. When using the contour integral technique on the normal specimens it is possible to use a lower number of nodes per model. When modeling the longitudinal welded specimens, the mesh density must be higher to achieve convergence. When using the XFEM technique the chosen mesh density was equal, but the mesh generation technique resulted in a lower number of elements overall, for the welded specimen. As one can see, ABAQUS models does not allow the use of quadratic elements, when using the XFEM technique, therefore the overall number of nodes is lower. A free mesh technique was always used, to allow for automatic mesh creation at each increment. All specimens were design in according to ASTM-E647, with a width (W) of 50 mm and a thickness (B) of 8 mm. The longitudinal weld, as a height of 2 mm and a width of 14 mm. The fixating pins were not modeled. One reference point, in the center of each specimen hole, was tied to the hole surface. Allowing for specimen rotation around the virtual pin. Periodic boundary conditions forced the vertical displacement of each pin to be symmetrical. The remaining degrees of freedom were blocked. The specimens were subjected to a vertical load with an amplitude of 9 kN and R=0.1. I