Issue 48

R. Baptista et alii, Frattura ed Integrità Strutturale, 48 (2019) 257-268; DOI: 10.3221/IGF-ESIS.48.27 263 a) b) c) Figure 5 : Different CT specimens used in FEM simulations, a) normal 3D CT specimen (also simulated in 2D), b) 3D representation of the 2D simulated CT specimen containing a longitudinal weld, c) 3D CT specimen containing a longitudinal weld. Specimen Element Type Nodes Average element size [mm] Element size near the crack front [mm] Normal 2D Quadratic 8 nodes 14520 1.00 0.10 Longitudinal Weld 2D Quadratic 8 nodes 21300 0.75 0.10 Normal 3D Quadratic 20 nodes 68500 2.00 0.10 Longitudinal Weld 3D Quadratic 20 nodes 73400 1.50 0.10 Normal (XFEM) 3D Linear 8 nodes 40000 1.50 0.05 Longitudinal Weld (XFEM) 3D Linear 8 nodes 31600 1.50 0.05 Table 4 : Element types and mesh densities used on FEM simulations. Fatigue crack growth on a normal CT specimen The modeled normal CT specimens were used to validate the algorithm predictions for pure mode I fatigue crack propagation. The algorithm accurately predicts the crack propagation direction, as all the cracks propagated in the horizontal direction. The periodic boundary conditions also guaranty that the value of the K II is very close to zero, therefore there is no crack kinking tendency, as predicted by the MTS criterion in Eqn. (2). In order to compare the crack driving force, between models, one can use the results obtain with the ASTM-E647. As K II is very close to zero, the crack driving force derived by Eqn. (3) or Eqn. (4) is equal to ΔK I . Comparing the SIF obtained values with the ASTM-E647 results, one can see on Fig. 6, all the models predict a higher SIF. For cracks lengths inferior to 25 mm the difference increases as the crack length decreases. For crack lengths superior to 25 mm the differences remain constant. The 2D model maximum difference was 9% and for cracks lengths superior to 25 mm the difference is negligible. 3D models show higher differences, with the XFEM model resulting in a minimum difference of 4.5%, 1% higher than the contour integral model. This difference has also been reported by Shi et al. [13]. These differences are important when predicting fatigue life crack propagation using Eqn. (5). Higher SIF will predict a lower number of elapsed cycles for the same crack increment. As the algorithm uses a fixed value of crack increment the 3D models will underestimate the fatigue crack propagation life if one uses the same material properties. Therefore, to accurately predict crack propagation, using different models the Paris law material constants must be corrected for the appropriate model. Using the same methodology as in ASTM-E647, but the SIF values obtained for each model (Fig. 6), the Paris Law parameters were calculated for the different models. As the predicted SIF increases, the C parameter decreases, and the m parameter increases, Tab. 5. The XFEM model predicted a 4.5% higher SIF, resulting in a 32% lower C parameter and a 2% higher m parameter. While for the 2D contour integral model, where the differences between the SIF and the ASTM-E647 standard were lower, the C parameter resulted in a 16% lower value. Fig. 7 shows a good agreement between all the models, the ASTM-E647 standard and the experimental results, for the crack propagating curve. This validates the algorithm and show that this approach, very similar to the one used by Zong et al. [23], is useful to predict fatigue crack propagation.